W— —_ _"'~— 77‘ '7 ‘ ' O¢Q¢ 1-!" §cOQO- - ' -- o v u. - . ..-.-o.o-‘_.oonq-q‘..-“‘gqn ‘°"\“~"-“."'“u-s v NFC-\f'fi 09A .- sub.- ~ ‘ -. - - - 4.--. - - -_ ' - ‘ - - . . . ‘ THEORETICAL GRAVITY ANOMALIES‘DF _ ~- = . - RFACE FEATURES V . * . Thesis'f-or the Degree-Of ‘MQS. ' , . ’ ‘l I iMl‘CHIIGAN STATE UNNERSITY. * F . 7 ' ‘ DAVID JAMES KRAUSE .— - '. " 3i - 1970' ' ‘. . ‘ — . '.. ‘ o \ ‘\. 7‘11"?“ I ‘ . N i ~ '31 C 0 o . ~ V a . W ‘ . . U n. .. .. . . . . . . .. . . C |\ I ‘t .. § ! . .. I .l ‘7 3 l ‘l . I . n n n . Q . u x c o . 331“ am; ‘ v o . I o . . O a . y.-. o .n¢—- I f‘ 0- .4 . ,u. ' - ‘ -- r‘ It - .4 .,. .‘ I oJ"’O"'tA.-.. - - I . VI .. .‘.". I. .0.“‘...' "‘ "O' '- 00- 00"... 119.; ‘... . ‘ "-'v> v .. o ’ " ’ Mo- . .w—vv .¢0'.Oo-'--o')-'orI-O'tfl "r"'"QrW‘V'-vvov<.fr.h-. ..".,- ‘ "_".’ "'-‘V "4' n-"0o-oo.ca 4-... f. 01". . . . ‘a"r‘-(.u.,.;t."o; I -~ 'fp‘H“ l .- "' ‘ I '-. ‘ - 0': p. i -‘ U I -0 .0..- . I - . a -- . --.. . . . .r. -.- ’0’... O-roo'.oop4.~. -~ - -.Ao. . ..-. 0‘0... . .-....._. -{i o .. ‘ .211233tés. O . I o a o \ v a n I 0 LIBRARY Michigan State Usher ' "'V " ' v-wau -~--.‘. ‘HL-filk. ABSTRAC T THEORETICAL GRAVITY ANOMALIES OF SOME LUNAR SURFACE FEATURES BY David James Krause The gravity fields present over lunar surface features repre- sent an important potential source of information about the nature of the subsurface structures of these features. This information may in turn contribute directly to an understanding of the origin of such features and of their place in lunar history in general. Furthermore, the determination of the gravity anomalies actually present over lunar surface features by local gravity surveys may enable a choice to be made between alternative theories of their origin. In this study, models were adOpted for the subsurface structures of lunar craters, domes, lava tubes, rifles, and maria ridges, and the gravity anoma- lies that would exist over these structures were calculated by various approximate methods . Craters. If the lunar craters are meteoritic in origin, those ranging in diameter from 0. 5 to about 20 km will be characterized by negative gravity anomalies, due to an underlying breccia lens of shattered rock, whose form will be dictated by the form of the breccia David James Krause lens and whose amplitude will be directly prOportional to the diameter of the crater and to the density contrast between the breccia and country rock. On the hypothesis that the craters are of internal origin, possibly analogous features on earth exhibit both positive and negative gravity anomalies and complicated structures. These anomalies, however, are generally related to regional anomalies of greater extent. _D_9_1£e_s. If the lunar domes are laccoliths, they should be characterized by positive gravity anomalies resulting from the sub- surface intrusive rock. If due to the serpentinization of peridotitic material, however, they should exhibit negative anomalies with amplitudes possibly reaching tens of milligals. Lava tubes. If lava tubes exist near the lunar surface, their negative anomalies should be detectable and their form delineated by careful surveys . Mes. In those lunar rilles that appear to be graben struc- tures, the faulting involved may cut both the mare material and the sub-mare basement. The resulting displacements will produce gravity anomalies which will reveal the relative densities of the mare and basement materials . Maria ridges. If these ridges are due to serpentinization, they should be characterized by negative anomalies. If they are volcanic David James Krause features, they may be underlain by feeder dikes producing positive anomalies of narrow width . Ridges formed by the burial of crater walls will reveal negative anomalies of considerable width, while ridges due to subsidence and compression will exhibit positive gravity anomalies of regional extent. The reduction of lunar gravity data will parallel terrestrial procedures. The lunar free air correction will be about 0. 187 mgal/m, while the elevation correction for the moon will be less than half its terrestrial value. The lunar tidal correction may have an amplitude of several milligals, but the rate of change of the correction will be small. Axial rotation, the main source of the latitude effect on earth, will result in only slightly more than a 1 mgal difference in gravity from the lunar equator to pole. THEORETICAL GRAVITY ANOMALIES OF SOME LUNAR SURFACE FEATURES BY David James Krause A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1970 ACKNOWLEDGMENTS I wish to thank Dr. William J. Hinze of the Department of Geology, Michigan State University, for his invaluable advice, direction, and encouragement during the course of this study. ii TABLE OF CONTENTS Chapter Page I . INTRODUCTTON ................................. 1 H. CRATERS ....................................... 8 Impact Craters .............................. 11 Craters of Internal Origin .................... 46 III. DOMES ......................................... 56 Serpentinization Origin ....................... 57 Laccolithic Origin ........................... 68 Ice Origin .................................. 80 IV. LAVA TUBES ................................... 83 V. RILLES ........................................ 88 VI. MARIA RIDGES ................................. 102 Serpentinization Origin ...................... 103 Extrusive Origin ............................ 104 Buried Ridge Origin ......................... 109 Compressional Origin ....................... 115 VII. CORRECTIONS AND CONTROLS ................. 120 VIII. CONCLUSIONS ................................. 132 REFERENCES CITED .................................. 137 iii LIST OF TABLES Table Page 1 Depths of Impact Craters as Predicted by Baldwin (Equation (2)) and Pike (Equation (6)) ................. 16 2 Relationships Between Crater Parameters ............ 21 3 Contrasting Pr0perties of Simple and Modified Lunar Craters, After Pike (1968) .................... 28 4 Calculated Impact Crater Parameters ................ 32 iv LIST OF FIGURES Figure 1 Schematic impact crater section with crater parameters defined ............................... Scale cross-section of half of an impact crater of diameter Dr of 0. 5 km, showing the disks used to approximate the anomalous mass of the breccia lens and the rim ...................................... Relationship between the diameter of a crater and the percentage by which the maximum crater anomaly is diminished due to the anomalous mass of the rim. . Relationship between crater diameter and central gravity anomaly for an assumed density contrast of -1 g/cc between breccia and country rock, for craters whose surficial dimensions are those given by Baldwin or meet the allometric criterion ofPike..... ....................... . ........... .. Relationship between crater diameter, density contrast between breccia and country rock, and central gravity anomaly .................................. Relative gravity profile over an impact crater ......... Gravity anomalies associated with various terrestrial calderas .............................. Schematic section of a lunar dome resulting from serpentinization of mare material .................. Scale cross-section of half of a lunar dome of 10 km diameter and 300 m height, showing the size and shape of the underl ing serpentine body for rock which has been 100 o, 50%, and 25% serpentinized, on the assumption that the serpentine body lies 300 m below the top of the dome ........................ Page 12 36 39 41 42 44 52 62 65 LIST OF FIGURES (Continued) Figure 10 Gravity profiles over the serpentine bodies of Figure 11 12 13 14 15 16 17 18 19 9 for rock 100%, 50%, and 25% serpentinized ........ Scale drawing of half of a lunar do me and the sub- surface laccolithic intrusion, for a depth to the top of the intrusion of 2000 m beneath the original plain level ....................................... Relationships between the maximum anomaly and the diameter of the intrusive body, for various depths from the original plain level to the top of the intrusive, for bodies with a thickness/diameter ratio of 300 m/lO km or 3% ....................... Gravity profiles over a dome of 10 km diameter under- lain by a laccolithic intrusion, for various depths from the original plain to the t0p of the intrusion. . . . Anomaly-depth relationship for laccolith feeders which are assumed to be vertical cylinders 300 m in diameter and infinitely deep .................. . . Relationship between the maximum gravity anomaly and the radius of a lava tube, for various depths to the center of the tube .......................... Relative gravity profile over a lava tube .............. Schematic section of a lunar rille caused by tension. . . Half of the profile of the gravity anomalies over a lunar rille 5 km wide and 500 m deep with sides of slope 65° and a basement depth of 500 m, for both positive and negative density contrasts of 0. 5 g/cc ....................................... Half of the profile of the gravity anomalies over a lunar rille 5 km wide and 500 m deep with sides of slope 650 and a basement depthof 1000 m, for both positive and negative density contrasts of 0. 5 g/cc. . vi Page 67 74 76 78 79 86 87 95 98 99 LIST OF FIGURES (Continued) Figure 20 Half of the profile of the gravity anomalies over a 21 22 23 24 25 26 lunar rille 5 km Wide and 500 m deep with sides of slope 650 and a basement depth of 1500 m, for both positive and negative density contrasts of 0. 5 g/cc ...................................... Relationship between thickness and maximum gravity anomaly for various depths to the lower boundary of vertical dikes having a positive density contrast of 0. 5 g/ cc .................................... Gravity profiles perpendicular to the strike of verti- cal, two —dimensional dikes of thickness t and depth to lower surface Z, for various Z/t ratios. . . Generalized east -west section of the Straight Wall Plain .......................................... Gravity anomaly over the buried wall of the Straight Wall Plain ..................................... West to east cross—section of Mare Humorum with the calculated gravity anomaly assuming the Mare is filled with material of density 0. 5 g/ cc greater than the basement .............................. The lunar elevation correction ..................... vii Page 100 107 108 112 114 117 125 CHAPTER I IN TRO DUC TION For untold ages the moon has been for man an object of in- fluence and interest. Its apparent size in the sky (equal to that of the sun), its curious shadings of light and dark areas, and particularly its rapid eastward motion against the background of stars, accompanied by the continually changing phases, all contributed to making the moon the most important object in the ancient's heavens, apart from the sun itself. Today, interest in the moon continues: in fact, it is probably at an all time high. However, we no longer need the reoccurring phases to order our lives, or the moonlight to find our way at night. Rather, today the moon is the focus of so much interest simply because it is the earth's closest neighbor in space, and as man's efforts enable him to be free of earth's restraints, it was inevitable that the moon would be his first stOpping place. To the unaided eye the moon reveals few of its secrets. The basic distinction of light and dark regions is easily seen, but little else. It was with the introduction of the telescope to astronomy by Galileo in 1609 that the first real stride forward was made in understanding the nature of the moon and its various features. Since that time ever larger telesc0pes, combined with various auxiliary devices, have pro- vided man with views of the face of our satellite of ever -increasing clarity and definition. These views have shown that the surface of the moon differs greatly from that of the earth, in spite of the fact that the two bodies are closely associated in space and have apparently been so for a considerable part of their respective histories, if not from their very formation. A major reason for this difference is evidently the moon's lack of a substantial atmOSphere . On earth, the continuous Operation of the various geological agents such as wind and water, which of course require an atmosphere, tends to obliterate or alter radically the record of ancient events originally written in the materials of the earth's crust. Lacking this atmosphere and the consequent gradational agents, the moon's battered face may preserve a record of events whose traces have long since disappeared from the earth, events perhaps reaching far back in time to the origin of the earth itself. Therefore, an understanding of the moon, while interesting in itself, might greatly facilitate understanding the origin and deveIOpment through time of our earth as well. To progress toward such understanding, theories are required to account for the moon's surface as it is seen today in all of its barren glory. lbwn through the years since Galileo there has been no lack of such theories. Speaking broadly, these theories can be considered as belonging to one of two groups: the "external" or "exogenous" theories which interpret the moon as a relatively inert object which has been 3 acted upon down through the ages by certain external agents; and the "internal" or "endogenous" theories, which consider the moon's present aSpect to be primarily due to forces acting from within the body of the moon itself. In recent years investigators have generally fallen into the "meteoritic" camp, which feels that the impact of meteorites has been the dominant process in molding the moon, and the "volcanic" camp, which maintains that volcanism, in its broadest sense, has pre- dominated, although numerous other ideas are also defended strongly. With the advent of the Space age the possibility of resolving some of the questions concerning the origin of the various lunar features and obtaining data which could serve as the basis for definitive conclusions seemed near. Now (1970), over a decade into the space age, we find that the excellent data provided by the various lunar missions have given few definite answers but have raised many more questions. The nature of even the very largest of the lunar features such as the maria themselves is still contested. Someone has referred to these data as a mirror in which each man sees reflected his own particular theory. It is now becoming evident that even the early manned lunar landings themselves cannot be expected to resolve many of these questions, and that a reasonably complete understanding of the moon's surface and its origins will undoubtedly remain a long -range goal. On the earth, where geologists have had the Opportunity of years of first -hand examination, the origin of many features is still an Open question. In dealing with the moon, from which no one had until very recently ever examined 4 even one rock specimen, it is quite understandable that no definite con- clusions have as yet been reached in many areas. It is evident, then, that any approach or method which would pro- vide some information concerning the actual, or at least the probable, nature of the subsurface structure of any given lunar surface feature might also contribute to the resolution of the question of its origin and development through time. An analysis of the gravitational field over a feature is one such method. Until very recently the only method generally available for study of the moon was by direct Observation of its surface from a considerable distance. The tOpographical configura- tion of a lunar surface feature can be analyzed rather well by observa- tion alone, especially if the feature is large, but as is evident, the surficial eXpression Of any feature is only a two -dimensional view Of what must be a three-dimensional structure. The surface of the moon is an interface between outer space and the body of the moon itself. Many surface features will be underlain by characteristic structures, but these are hidden from our direct view. Drilling is an obvious way to Obtain accurate subsurface information, but with only a limited number Of drill holes the volume actually sampled is very small. Also, the equipment necessary for really deep drilling is not likely to be transported to the moon in the near future. Yet, as long as subsurface density contrasts exist, distortions in the moon's overall gravity field will be present, and will represent an important potential source of information about the subsurface structure Of the moon. These gravitational effects can be detected by gravity meters whose size and weight makes them likely candidates for inclusion on early manned lunar missions. As is well known, it is impossible to determine uniquely the structure and density distribution that exist below the sur- face solely from an analysis Of the gravity field. At best, the gravity data will reveal "a shadowy and ambiguous picture of the density distribution underneath the groun ." (Grant and West, 1965). Yet when combined with information obtained from more direct geological studies the gravity information can be very important. The gravity method, then, must rightly be considered just one of several approaches to the study of any given feature, all of which have their contribution to make to the final understanding Of the nature of the feature in question. Because of its ability to "see" beneath the ground, however, the gravity method has a somewhat unique role to play. Nevertheless, its view is hazy, and ultimately other more direct approaches must make the final decision toward which gravity has helped to point the way. These remarks could apply to most other geo- physical methods as well. That is, they compliment, rather than supplant, other methods Of geological investigation, and the best, most probable interpretation will result from a synthesis Of all of the avail- able data. In the case of the moon, however, at least for some consider- able time, the geological knowledge from direct first -hand Observation will undoubtedly also be limited and therefore the geOphysical data will probably not be capable of a unique or even highly probable interpretation. "\A o \ On the other hand, use should certainly be made Of all avenues of information, and in the absence of deep drilling on the lunar surface, geophysical methods will probably be the main source of subsurface information and therefore should be utilized fully. Although the usefulness of the gravity method and the role it can play in lunar exploration are generally acknowledged, up to the present little has been done in the way Of actual, quantitative calcula- tions designed to demonstrate the amplitude, form, and implications of the gravity anomalies that may be associated with various typical lunar surface features. This being the case, the purpose and methods of this study are as follows: 1. To determine the subsurface structures that are anticipated beneath various lunar surface features as predicted by different theories of their origins and develOpment. 2 . To model these subsurface structures as to scale and anticipated density contrasts and to determine likely ranges in these prOperties. 3. To calculate, using various approximate methods, the gravity anomalies that would exist over these subsurface structures, and to examine the implications Of these ammalies and, where applicable, their role in the interpretation of the nature and origin of the features. 4. To investigate the various corrections and controls required to con- duct a gravity survey in the lunar environment designed to detect these anomalies . This approach has been applied to a number of lunar features in the following chapters. The information derived in this study may serve as a guide in determining the amplitude and form of the gravity anomaly over a feature, which would then be important in determining such things as instrument range requirements, elevation and position controls, and the accuracy of the corrections used in the reduction of the raw data. The gravity anomalies here determined are similar to what in terrestrial work would be called the complete Bouguer anomaly. After surveys are actually conducted and the anomalies defined, a com- parison with the calculated anomalies might serve as a first step in understanding the nature of the actual subsurface structure Of the feature and in determining which of the theories under consideration are incompatible with the Observational data. CHAPTER II CRATERS Craters are the most distinctive features of the lunar surface, aside from the maria themselves. As many as 300, 000 Of these rela- tively shallow, bowl-shaped depressions range in diameter from per- haps one kilometer up to as much as two hundred and fifty kilometers. Recent spacecraft and manned eXploration have revealed countless thousands more whose diameters range down to microsc0pic size. Since the craters were first Observed by Galileo in 1609 there has been no lack of theories concerning their origin. These theories are dis- cussed in historical perspective very well by Shoemaker (1962) as well as by KOpal ( 1962), and Green (1965a). The debate over the origin of the craters is particularly important in that a person's views on this question will invariably influence his thinking on the origins of many of the other features as well. In the last twenty years or so thinking on the origin of the lunar craters has been greatly influenced by the work Of Ralph Baldwin (1949, 1963, 1965) on the meteoritic impact hypothesis. His greatly detailed work with the statistical relationships between various crater parame- ters apparently gave a firm, quantitative basis for understanding the origin of a crater as a near-instantaneous, explosive event resulting from the collision of a meteoritic body with the moon. While admitting the possible igneous nature of some of the lunar features, for the great majority of the lunar craters Baldwin (1965) has said "They can only be of meteoritic -impact origin. The 136-year argument is over. " Yet in recent years this view has been increasingly questioned by some workers. The scatter in much of Baldwin's data is consider- able. Green (1963) has argued, for example, that terrestrial features such as calderas have depth-diameter ratios that scatter around the same curves as those found by Baldwin for meteoritic craters. Shoe- maker (1962) has stated that "By their very nature the statistical arguments are inconclusive, and do not lead to the determination of the origin Of a single crater. The evidence that has been adduced for the impact origin of lunar craters is thus insufficien . " In addition, the excellent pictures returned to earth by the various Spacecraft, manned and unmanned, showing what appear to be igneous features have helped to re -Open the entire question. Even the manned lunar eXploration may not answer many of these questions immediately. As just one example of the difficulties involved, it is noted that meteoritic material, which on earth might go far toward supporting the impact origin Of a feature, will presumably be almost universally present on the moon because of the lack of an atmosphere . Therefore, any approach which can make some contribution to helping to resolve the question of origins should 10 be investigated. The gravity anomalies that may be associated with the craters caused by meteorite impact are discussed below, followed by a similar discussion for crater -like structures caused by various types of internal activity. The investigations of mo st workers concerned with the interpre- tation Of the lunar craters have of necessity been centered primarily on the surficial characteristics of the crater as seen from an external point. However, any given crater must be underlain by a subsurface structure that is directly related to the processes that created it, whether those processes be manifestations of internal or of external agents. Any endogenous origin postulated to account for the crater by some form Of volcanic action will obviously involve subsurface sources of magma, intrusions, fractures, etc . , while an impact origin will result in fracturing Of the rock beneath the crater to a considerable depth, producing what has been called an "impact breccia". In neither case would these subsurface structures necessarily be Obvious or even visible to surficial examination alone, but in both cases density con— trasts in these structures might well produce significant anomalies in the gravity field over the crater which could be detected by gravity meters. In order to predict the gravity anomaly that might be present over any given crater, whatever the origin, it is first necessary that a model for the subsurface structure be adOpted. 11 Impact Craters Figure 1 defines the various crater parameters that will be used below. There has been no general agreement among authors as to standardized symbols for these parameters. Pike (1968) summarizes the nomenclature used by various workers and introduces his own list. The symbols of Figure 1 for the surface geometry of the crater are those used by Pike (1967, 1968) with additional symbols for breccia depth, thickness, and volume. The most extensive investigations into the relationships that exist between the various tOpographic dimensions Of impact craters are those of Baldwin (1949, 1963, 1965). As a result of his statistical studies on craters of all sizes Baldwin concluded (1963) that the rim crest diameter Dr and the interior relief or crater depth Ri of terrestrial meteorite and explosion craters and of lunar craters, all ranging over diameters from about 9 m up to about 32 km, are related according to the equation log Dr=0.0256 log R12+log Ri+0.6300 (1) with all dimensions in feet. The corresponding equation for metric units (meters) is given by Baldwin as log Dr=0.0256 log Riz+1.0264 log Ri-2.3461. (2) Unfortunately these two equations, which should yield identical results except for a conversion factor, in fact do not. For example, according 12 Bd DO, overall crater diameter B d’ breccia depth Dr’ rim crest diameter Bt’ breccia thickness Dt’ true crater diameter Vb, breccia volume R1, interior relief (crater depth) R e , exterior relief (rim height) Rt’ true crater interior relief We’ exterior rim slope width Figure 1. Schematic impact crater section with crater parameters defined. 13 to equation (1) a crater whose diameter is 12, 000 ft has a depth Ri of 1545 ft or 470.9 m. Equation (2) however, gives a depth Ri of 455 m for the same crater diameter Dr Of 3, 657. 6 m or 12,000 ft, a difference of some 16 m or about 4%. In Spite of this discrepancy, and the possibil- ity that the five Significant figures given by Baldwin in these equations may not really be warranted (see the discussion of the work of Pike below), equation (2) is adOpted here as the relationship to be used between Dr and Ri’ Similarly, Baldwin's relations between the rim crest diameter Dr and the exterior relief or rim height Re’ log Re=0.004366 log Dr3—O.008506 log Dr2+0.9098 log Dr+1.5987 (3) and between the exterior rim s10pe width We and the rim crest diameter D r log We=log Dr-O.7O (4) and between the rim crest diameter Dr and the true crater diameter Dt Dt=0'83 Dr are also adOpted for use here, with all dimensions being in meters. TO complete the model of the crater, the additional assumption is made, following the work of Innes (1961), that the floor of the crater has the shape of a paraboloid of revolution. These equations and assumptions then allow the calculation Of all the pertinent dimensions of the tOpographic 14 feature that is an impact crater. In some recent investigations, Pike (1967, 1968) has re- examined the statistical relationships between these various crater parameters. In particular, from an analysis Of over 600 fresh appear- ing lunar and terrestrial craters ranging in diameter from about ten meters up to about fifteen kilometers he finds that Baldwin's rather complex, curvilinear equations relating R1 to Dr and Re to Dr can be replaced by the much simpler relationships 095 R.=0.155 D ' (6) 1 r and 0.95 Re=0.048 or x (7) with all crater dimensions being in kilometers. From the form of these equations, Pike concludes that the Shape Of fresh impact craters is in accord with a dimensional relationship known as the law of allo- metric growth, which was originally formulated by biologists and states that the rate of relative growth Of an organ, y, is a constant function of the rate of relative growth of the total organism, x, such that b y=ax where a and b are constants. For equations (6) and (7), the allometric condition would require the exponents to be 1, and this is very nearly the case. If the "growth" Of impact craters is truly allometric this 15 would imply that all fresh, unaltered impact craters, whatever their diameters, would have the same shape (be geometrically Similar). Baldwin's equations, on the other hand, predict that the smallest craters will be relatively the deepest, with the larger craters becom- ing progressively more Shallow, relative to their diameters. Table 1 compares the depths of craters Of various diameters as predicted by equation (2) (Baldwin) and equation (6) (Pike). At the smaller diameters agreement between the two is good (at Dr=0. 5 km they give identical depths), but according to Pike a crater of diamaer 10 km should be some 22% deeper than Baldwin predicts. However, as will be dis- cussed below, lunar craters much larger than 10 km in diameter, where the discrepancy between the depths as predicted by the two equations would be the greatest, have almost certainly had their shape and structure altered by processes not directly related to impact, and therefore would require a more complex model. Pike has also found that the floor of a crater can be closely approximated by a hemi-ellipse rather than a paraboloid of revolution as adOpted in the present study. However, the exact configuration of the floor of a crater will have only a very small effect on the gravity anomaly predicted over the crater. The relationships determined by both Pike and Baldwin are utilized in the calculations of the anomalies below, and the differences they pre- dict are noted. The above equations and assumptions allow the calculation of all of the necessary surficial dimensions Of a crater, but they give no 16 TABLE 1 DEPTHS OF IMPACT CRATERS AS PRE DIC TED BY BALDWIN (EQUATION (2)) AND PIKE (EQUATION (6)) Crater diameter Baldwin crater depth Pike crater depth D (km) R. (m) R. (m) r 1 1 O. 5 80 80 1 147 155 2 270 300 5 595 715 10 1074 1381 17 clue as to the subsurface structure that might exist beneath an impact crater, which might be detectable by gravity methods. However, it has become evident from many different lines of investigation that an event such as the impact Of a large meteorite on the surface of the earth or moon should result in the fracturing and Shattering of a sub- stantial volume of bedrock beneath the crater floor, thereby changing its physical prOperties and perhaps making this disrupted zone suscept— ible to geOphysical measurements. In particular, such brecciation might, in the case of an impact into solid rock, produce a large body of shattered material whose overall density is less than that of the country rock, which would then in turn result in a gravity low over the crater. The investigations of various Canadian workers such as those of Beals et_a;(1963), Innes (1961, 1964), Beals and Halliday (1965), and Dence (1964, 1965) on craters Of the Canadian Shield have been particularly important in the develOpment of present ideas concerning impact crater subsurface structures and their geOphysical expressions. In order to complete the model of an impact crater needed to predict the gravity anomaly expected over it, the form and dimensions of the breccia body beneath the crater must be Specified, and the investigations referred to above are directly applicable here . It is evident that the zone of brecciation beneath an impact crater will not be separated from the undisturbed country rock by an absolutely sharp boundary. Nevertheless, there should be a reasonably well defined surface between the completely brecciated rock and the 18 country rock which, even though it may be fractured, is still essentially in place. The brecciated rock bounded by this surface and the floor of the crater is called the breccia lens. It would be difficult if not im- possible to calculate the exact form and Size of the crater and this lens directly from first principles for a meteorite impact. However, from an analytical investigation of this problem Rottenberg (Beals et a1, 1963) found that for an impact into granite gneiss the surface separa- ting the region of brecciation from the region of Simple fracture would have a depth at the center Of the crater of about one -third Of the crater diameter. This surface will Obviously come to intersect the surface of the ground somewhere in the vicinity of the crater's rim, and undoubted- ly in a radially symmetrical crater this surface would have the Shape of some solid of revolution. In his study of a number of the Canadian craters Innes (1961) found that the assumption that this surface had the shape Of a paraboloid of revolution, which enabled the total volume of the breccia to be calculated, lead to quite consistent results with the deep drilling data and the observed gravity fields. For example, at the Brent crater in Ontario, a presumed ancient impact crater about 3.2 km in diameter, the volume of breccia as determined from the above model agreed with that determined by drilling to within about 10% and within about 5% of that obtained from an analysis of the gravity field and the density of the breccia as found by drilling. From an analysis of the drill records Obtained at the Deep Bay crater in Saskatchewan, Innes (1964) gives a cross-section Of the subsurface structure which 19 indicates that the lower surface of the breccia intersects the floor of the crater at about the level of the original plain (see Figure 1). There- fore, to complete the crater model adOpted here, the breccia depth B d is taken to be equal to one -third Of the true crater diameter Dt’ or B d=Dt/3 (8) and the lower surface of the breccia lens is assumed to be a paraboloid of revolution, intersecting the crater floor at the original level of the plain. The breccia lens therefore has the Shape of a solid bounded by two paraboloids of revolution (the other being the crater floor) and con- taining a total breccia volume Vb of 2 vb=( 1T/8) Dt [Dt/3 - at] . (9) That the depth of the breccia is about one —third of the crater diameter, however, was determined by assuming an impact into granite gneiss, and the Canadian craters, which seem to support that figure, are in rock of that general type. The possibility exists, of course, that the lunar surface layer might be of quite a different nature, and naturally leads to the question of the validity of this model for craters in other types of material. However, the fact that the relationships found by Baldwin and Pike can represent well the dimensional ratios of explosion pits and craters ranging from bomb and shell craters through terrestrial meteorite craters to the lunar craters themselves, which certainly must cover a variety of impact materials, seems to indicate, 20 as Innes (1961) has said, that "crater dimensions seem to be remark- ably insensitive to the prOperties of the material." Sioemaker (1963) gives section drawings of Meteor Crater in Arizona, which is in sedi- mentary rocks, and of the J angle U nuclear explosion crater, which was in alluvium. For both, the ratio 'Bd/Dt, as determined from direct scaling from those sections, is very nearly 1/ 3, as adOpted in the model used here. Short (1966) describes a series of experiments by Gault in which tiny, hypervelocity projectiles were fired into sand and other target materials, resulting in craters that "have morphologies and internal structures remarkably like those natural impact craters which have been studied by drilling and excavation. " In view of these lines of evidence, in this study it is assumed that the form and structure of an impact crater is independent of the nature of the target material. The equations relating the various crater parameters of the model adOpted here are summarized in Table 2, and are numbered in the order that they were introduced above. Having adOpted a model for an impact crater, there remains the question of the nature and magnitude of the density contrast that will exist between the breccia and the country rock, upon which the amplitude of the gravity anomaly will of course depend, and the question of the limits, if any, on the range of crater diameters for which this model is valid. Fr0m the Canadian craters that have been well studied it has become evident that the breccia lens is not completely uniform in structure or density contrast but rather may be quite complex. 21 TABLE 2 RELATIONSHIPS BETWEEN CRATER PARAMETERS Equat io n 2 (2) log Dr=0.0256 log Ri +1.0264 log Ri- 2.3461 3- 0.008506 log Dr2+0.9098 log Dr+1.5987 (3) log Re=0.004366 log Dr (4) log We=log Dr- 0.70 (5) Dt=0.83 Dr (8) B d=Dt/3 (9) Vb=(1Y/8) th [wt/arm] For equations (2) through (5), units are meters. 22 Melting and shock metamorphism may produce a wide variety Of litholo- gies within any one crater with distinct layering due to slumping and fallback during the process of crater formation (Dence, 1964, 1965; Short, 1966). Any gravity anomaly, however, will reflect the overall density contrast of the breccia lens as a whole, and no further attempt will be made here to delineate structures within the breccia body itself. In general the terrestrial craters investigated by the Canadian workers have negative Bouguer gravity anomalies. Of a list Of eleven craters given by Dence (1967) nine have negative anomalies while two of the smaller craters, Flynn Creek, 3. 5 km in diameter, and J eptha Knob, 2 km in diameter, both of which are in sedimentary rocks, have anomalies of zero and +1 mgal reSpectively. The negative anomalies over the remaining craters are due to both the reduced overall density Of the breccia and to the later sedinentary rock fill in the craters which is less dense than the country rock, but the two effects can be distin- guished in craters where drilling has been done. It seems that craters in sedimentary rocks have weaker anomalies than those of the same size formed in crystalline rocks. Dence (1967) has suggested that this may be due to the fact that the stronger crystalline rocks can support cavities and voids in the breccia indefinitely, producing a stronger (negative) anomaly, while the lighter, weaker sediments will collapse and fill the voids. At the Brent crater, which is in gneiss, the country rock has a density Of 2 . 67 g/cc while the average density of the breccia, although varying considerably within short distances along the drill 23 cores, averaged about 2. 50 g/cc, giving a density contrast Of -0. 17 g/cc . In sediments the density contrast would presumably not be as great. Exactly how these terrestrially determined values would apply to the lunar environment is uncertain, in the absence of definite know- ledge Of the composition and state of the lunar materials at depth. Fbr a lunar impact into material with physical prOperties similar to solid, crystalline rocks the lesser lunar gravity, which would probably allow the breccia to support void spaces more easily than on earth, and the (presumed) lack of deposition of secondary minerals in the voids by ground water or degassing might result in a density contrast between breccia and country rock considerably greater than that found in terrestrial craters of corresponding size. Shoemaker ( 1966) has sug- gested that brecciation and fragmentation of solid rock materials on the moon could result in an increase in Specific volume of 30% or more. If 2. 67 g/cc is considered to be an approximation of the initial density of such a material, an increase of 30% in the Specific volume would result in a breccia of density 2 .05 g/cc, giving a density contrast of -0.62 g/cc . On the other hand, experiments involving the exposure of molten samples of various rock types to a high vacuum as might be en- countered on the moon have resulted in frothy, porous masses of quite low bulk densities (Dibar, 1965; Dobar 9131, 1964). A mean density of 1.76 g/cc was found for such a froth of basaltic composition and 0.97 g/cc for granitic composition. If an impact were to Occur in such a material or in deep material of a fine, powder-like texture, the effects 24 of compaction and shock welding could conceivably result in a breccia of increased density, with a subsequent positive anomaly. Although such a Situation may not seem likely, the possibility does exist. Additionally, there could be further complications due to effects such as melting of rock at the time of impact. In view of these uncertain- ties it would not seem justifiable to attempt to select a certain, definite value for the density contrast and assign it to our crater model. Rather, the anomalies will be calculated independently of the density contrast. Then, if further evidence allows the selection of a particular value, (ultimately to be determined by on-Site examination Of rocks in or near a crater), the anomaly predicted for that value can immediately be found. Alternatively, if the crater model is valid, a determination of the actual anomaly over a given crater would allow the bulk density contrast of the breccia to be determined from the following data. One further question to be considered is that of the range of crater diameters for which the model is valid. As was mentioned above, the investigations of Pike and Baldwin seem to indicate that the general equations relating the various crater dimensions can be applied to craters only a few meters in diameter or even smaller. However, as diameter decreases so also does the gravity anomaly, and for very small craters the anomalies would be so small that they will be virtu- ally undetectable, particularly if measurements are being made in a geologically unfamiliar environment such as on the moon, where un- certain regional effects and subsurface structures could complicate the 25 gravity picture considerably. Therefore, rather arbitrarily, the smallest crater considered here is taken to have a rim crest diameter Dr Of 0. 5 km. Attempting to determine an upper limit on the applica- bility of the model is somewhat more involved. For terrestrial craters, particularly those investigated by the Canadian workers, there seems to be a definite distinction between craters of "simple" structure, which essentially correspond to the model adOpted here, and "complex" craters, which, while retaining the normal meteorite crater charac- teristics such as evidence of a raised rim and subsurface breccias, differ from the simple crater model primarily by the presence of a pronounced central uplift. Dence (1964, 1965) has discussed these two types Of craters and found that of ten craters studied and presumed to be due to impact, the six smallest, ranging up to 10 km in diameter, can be well represented by a simple model Similar to that used in this study. The other four, ranging from 20 to 65 km in diameter, all have definite central uplifts. In some of the craters this uplift is sur- rounded by additional annular rings of uplift and depression, reproduc- ing the essential features of structures like the Vredefort ring. Petro- graphic considerations (Shock metamorphism) and overall geometry seem to support a meteoritic origin for both the simple and complex types. In the Manicouagan-Mushalagan structure, which is nearly 65 km in diameter, the central uplift, about 15 km in diameter, stands nearly 300 m above the surrounding level deSpite being considerably eroded, and is surrounded by a ring graben which may be downthrown 26 as much as 1 km or more. That the Simple —complex distinction is a gradational one seems indicated by the East Clearwater crater (Dence, 1965) which is about 20 km in diameter. Superficially an eroded simple impact crater, its gravity anomaly is not as large as would be expected from the simple crater model. Drilling has revealed that the crater floor is shallower than predicted and there is a pronounced central uplift. Some mechanism apparently Operates in terrestrial craters above approximately 15-20 km in diameter to raise much nearer the surface rock which was originally at a considerable depth beneath the crater floor. Iso static adjustment would seem to be one possible mechanism. DeSitter (1956) has suggested that a crustal plate as small as 20 by 20 km might be Significantly affected by iso- static adjustment. Alternatively, Dence has suggested that such an uplift might possibly result at the time Of impact due to shock wave reflection from some horizontal discontinuity beneath the crater such as the Mohorovicic or Conrad discontinuities. Because the rocks previously at depth now occur nearer the surface in these craters, the geOphysical prOperties Of these rocks will be less anomalous than those of the breccias, and the gravity readings over the central uplift, for example, will approach the "normal" values found outside the crater, but may be flanked by gravity lows due to the effects of an annulus of breccia. Just such an anomaly is found at the Carswell Lake structure in Saskatchewan, where the central high is flaiked by lows of about 10 mgal. 27 Recently, studies by Pike (1967, 1968) have called attention to the fact that a similar transitional zone from simple to complex struc- ture may exist for the lunar craters, and that this transition is also made in the 10 -20 km diameter range. He has summarized the surfi- cial differences that seem to exist between the two crater types, some of which are reproduced in Table 3. Of particular interest are the rela- tionships found between Ri’ the crater depth, and Dr’ the rim crest diameter, for the larger craters. Pike's work (equation (6)) on this relationship for craters up to about 10 km in diameter has already been discussed. However, Pike found that for craters above about 15 km in diameter the SIOpe of this relationship abruptly lessens, and for these larger craters the corresponding relationship becomes 035 R.=0.880 D ' (10) 1 r so that these craters will be significantly shallower for their diameters compared to those below about 10 km diameter. That an entirely new mode of origin is unlikely for the larger craters is indicated by the fact that the DO/Dr relationship, which relates horizontal dimensions of the crater rather than vertical, is unchanged across the 10-20 km boundary. Apparently the craters have had a common mode of origin and the larger craters have had their vertical dimensions altered (lessened) by post-impact processes, which produce the differences noted in Table 3. Since many Of the craters over 10-20 km in diameter have flat floors which are widely interpreted as some form of volcanic TABLE 3 28 CONTRASTING PROPERTIES OF SIMPLE AND MODIFIED LUNAR CRATERS, AFTER PIKE (1968) Attribute Size range (Dr) RizDr (km) RezDr (km) D0 :D1. (km) Floor configuration Rim crest profile Central eminences Inner rim lepe Shape Rim crest polygonality Rim crest craterlets Simple Craters Generally under 10-20 km. R.=0.155 D 0'95 1 r R =10.042 D 0'98 e r D0=1.4 Dr Partial hemi-ellipse Even None Smooth Generally absent Rare Modified Craters Generally over 10-20 km. lower s10pe; not isometric . lower lepe; not isometric . DO=1.4 Dr Flat Uneven Present in fresh craters Terraced Generally present Often present 29 material, it seems possible that the extrusion of such materials may well be related to the forces producing the tOpographic changes that Pike has described. 1 Pike lists seven possible mechanisms sugges- ted by various workers for the emplacement of the material in the flat- floored craters, the seventh of which is his own. They are: (1) Global melting epochs brought on by continued decay of radioactive minerals within the moon; (2) Widespread melting due to upward transferral Of heat by convection currents; (3) Localized melting due to direct change of a portion of the impact energy into heat, or shock melting; (4) Both localized and regional melting and defluidization caused by accumulated heat resulting from continuing tidal flexing of the moon; (5) Volcanism induced in an impact region by lowering of the thermal conductivity of the lunar crust by brecciation below an impact crater, easy access of magma through the breccia lens, and the presence Of an impact -induced thermal anomaly near the lunar surface; (6) Subcrustal melting in reSpOnse to reduction Of overburden pressures below large craters, with subsequent intrusion into the fractured crater region; and 1See Quaide et a1, (1965) for a discussion Of the effects of gravity alone in the modification of lunar craters over 10 km in diameter. 30 (7) Magma generated beneath large lunar craters by stresses develOped during isostatic readjustment Of the impact-produced mass disequilibria . In view of the number of possible mechanisms listed above, and the lack Of quantitative data on which to base predictions of subsurface structures, it would seem to be premature to attempt to create a model Of "the" complex crater. Since from the discussion above it seems clear that several lines Of evidence suggest that a diameter of some 10-20 km is the threshold separating structurally and volcanically modified terrestrial and lunar craters from relatively simple and un- altered ones, we will be concerned below with the calculation of the gravity anomalies for impact craters only within the diameter range from 0. 5 to 20 km. The important parameters for such craters, found from the relationships given in Table 2, are shown in Table 4. It may be noted in Table 2 that all parameters involving vertical rather than just horizontal crater dimensions (see Figure 1) are not directly pr0portional to the crater diameter but reflect Baldwin's curvilinear relationships of equations (2) and (3). However, if Pike's argument that all fresh, unaltered impact craters are very nearly geometrically similar is valid, then the parameters Of a crater of any diameter can be Obtained simply by direct scaling up of the values given in Table 4 for a crater of diameter Dr of 0. 5 km, since his and Baldwin's equa- tions for the depth-diameter ratios are in agreement for this diameter, as shown in Table 1. 31 Table 4 gives all Of the information necessary to create a three dimensional model of an impact crater. A gravity anomaly will exist over the crater because of the brecciation and fragmentation caused by the impact. This anomalous mass will consist of two parts which in nature will be essentially continuous but which are separated into the breccia lens and the rim. That the rim is anomalous mass is obvious, but its structure is more uncertain. Many investigators (e.g. , Baldwin, 1963) have considered the rim to be composed simply of material excavated from the crater and dumped by the force of the explosion onto the surrounding landscape. Schr'Oter's Rule, expressing the alleged equivalence of the volume of the crater below the original plain with the volume of the rim, has often been cited as supporting this interpretation. Pike (1967 ), however, has clearly demonstrated the non-validity of Schrbter's Rule as applied to the lunar craters. Dence (1965) has called attention to the fact that the rim of the New Qiebec crater is composed largely Of bedrock which was uplifted and somewhat fractured rather than being composed of debris ejected from the crater itself. In any case, the rim will be composed Of material whose overall density will contrast somewhat with that of the country rock. There seems to be no essential reason why the density of the rim Should be equal to that of the breccia lens as a whole. One could probably argue that it would be either greater or smaller. It is here assumed that the overall density of the rim and the breccia lens are equal, and that they would both therefore contrast equally with the country rock. Since, 32 v.30 momv ommm mum; vmmfi 06 000 00.3 0.0m x308 oO 'IVNOIL ISNVHL HNOZ 00.3 0HON 05.0 v3. :0“ 0.N 000 00.0 0.0a H50 000 003 vmv mam 0.H :h 3.“. 0.0 “3000.0 50 «mm 00H 0pm #0 3.. 004 0.N 295m 003.0 0: rpm boa b: N0 0w 00.0 04 0000.0 0b 02 mm 00 H0 “N $0 0.0 3:5: 9> 0838 Soooum 05 u.m mmquofifi £82m 30 em 50% .3895 05 am 50% Oak. 05 am 50% .8020 05.0 o? 523 8E 05 em Ems: SE Asa; no 33830 map. H 33¢ a $38.36 $9.30 93328 .5020 mmmfim2558 can. 330.5 smegma oo\w 7 mo swab 3:8 38:3 383mm an no.“ 39:28 332m 3550 van .8883". 8330 5033 Eamcofiflom .v 0.395“ omaawasoumazmamuuofimmpamvmmac _ _ . F bl} _ . _ _ 7 _ . . _ . A85 .5 5555 o \ I 3. II ONI .. 8.. - v. .. 2.- m . W w I 8- A . m In 8| m. fl 1.os- I 8- 1 8- loo”- -1.0 -O.10 -0.05 DENSITY CONTRAST (g/cc) L -0.01 I ' l - ' ' l l ' 0.5 1 2 5 10 20 DIAMETER Dr (km) Figure 5. Relationship between crater diameter, density contrast be- tween breccia and country rock, and central gravity anomaly. 43 for example, an actual survey on the moon could detect anomalies only with a magnitude of, say, one milligal or more, Figure 5 would immediately reveal what combinations of density contrast —crater diameter values would give this anomaly. Also, for example, if upon actual inSpection it appears reasonable to believe that some given crater is an impact crater for which the present model is valid, then the overall density contrast of the breccia lens can be easily deter- mined. The shape of the gravity profile over the crater can be calcu- lated in a manner slightly more complicated than that used above. Off the axis of a horizontal circular disk it is difficult to evaluate the solid angle subtended by the disk. Nettleton's chart can be used only for disks that are buried some distance below the point of observation. Therefore, the chart was used to determine the effects of the lower disks of the breccia lens, and the gravitational effects of the upper portion of the lens were calculated by means of terrain correction tables (Bible, 1962). The gravity profile was determined by calcula- ting the amplitude of the anomaly at three stations off the axis of sym- metry of the crater shown in Figure 2 which, according to Pike, closely approximates the geometrical shape of any fresh impact crater. This being the case, only the relative profile is plotted in Figure 6. As previously, it was assumed that the rim effect is to be eliminated in the data reduction. For any given crater, the actual value of the peak anomaly in milligals can be found from Figure 5 or equation (12). 44 .3: 8:38 89a USS“ 0.8 madman“ 5 mosque, .3320 .353 :oflazomno «communes .333 no 38 .835, 63352.3 «$3.58 3.30 no 329 brawn .Ewfi 353.3 2: no 35.. 23 5.3an 38.8w 23 230.3 o5 3 36 E 53898 SP £398 “can: 5 ago 2489 339% 953mm .o 0."ng N x «Bum—mm x LEAVES HALLV'IHH 45 The question of the values of the density contrast that will be likely in the lunar environment has already been discussed. On-site examination would seem to be required for any firm estimates. A gravity profile over a lunar crater of undoubted impact origin would allow, by the use of equation (12) or Figure 5, an estimate of the density contrast of the breccia to be made. This figure could then be used as a first approximation in the attempt to interpret other craters in terms of the model used here. Tb summarize, an impact crater model was adOpted from which all important crater dimensions, both tOpographic and subsurficial, can be found. This model seems to be reasonably valid for fresh, un- altered lunar impact craters with rim crest diameters up to 10-20 km. The amplitude and form of the gravity anomalies over these craters due to the underlying breccia were calculated. If, as appears to be the case, all impact craters are geometrically similar at their moment of formation, the relationship between the peak gravity anomaly over the crater, the crater diameter, and the density contrast between the breccia lens and the country rock is a simple one, eyqaressed by equation (12). An accurate estimate of the density contrast likely in the lunar environment does not seem possible at the present time: on- site inSpection appears to be necessary. Impact craters up to 10-20 km in diameter should be characterized by anomalies of the form shown in Figure 6. Craters over about 20 km in diameter, even if originally 46 due to impact, appear to have had their structures modified consider- ably by post-impact processes. Craters of Internal Origin In contrast to the meteoritic impact hypothesis stand those theories which account for the origin of the lunar craters solely or primarily in terms of internal processes. It was possible to establish a reasonably consistent model of the structure of an impact crater. The establishment of a similar consistent, single model of a lunar crater on the assumption of internal origin does not seem possible, primarily because so many different modes of origin, all related to internal processes of one sort or another, have been suggested down through the years. These different theories might predict greatly dif- fering subsurface structures, even though all are internally based. Shoemaker (1962) has given an excellent summary of the historical develOpment of the main theories that have been advanced in the years since the invention of the telesc0pe to account for the origin of lunar craters. Shoemaker divides theories which attribute the origin of the craters to internal activity into three main classes, using the German terminology. The "Blasenhypothese", in its most extreme form, accounted for the lunar craters by the bursting of huge bubbles of gas escaping from the interior of the moon, although more realistically the activity that produces the terrestrial maars might be considered in this category. The "Vulkanhypothese" maintained that lunar craters 47 are analogous to terrestrial calderas. The term "caldera", however, can apparently be applied to almost any approximately circular feature on earth which appears to have been related in some way to volcanic activity. Such structures may include calderas formed by violent ex- plosions such as at Krakatoa and Crater Lake and also those formed by relatively quiescent subsidence as on the Hawaiian shields. The third class, the "Gezeitenhypothese", or tidal hypothesis, maintained that the tidal effects of the earth on the crust of a fluid moon produced fractures resulting in the craters . In its original form it is not seriously held today, although attention has been directed to the effects of earth- tides on lunar degassing in general (Green, 1965b). The boundaries between these classes were (and are) quite nebulous, each worker having his own particular version of what has actually occurred on the moon. In addition, there have been numerous theories advanced which do not fit easily into any of these classes but still involve some sort of internal activity, such as escaping water which would result in pingo- like structures and the "craters of uplift and collapse" of Currie (1965). Through the years there have also been theories involving coral reefs, asphalt, dust storms, snow, vegetation, and atomic bombs (Green, 1965a). At the present time almost all investigators concerned with the moon concede that there has been some volcanic activity on the lunar surface. The real question of course is one of degree. Shoemaker (1962) generally favors an impact origin for the majority of the lunar 48 craters. He believes that only the small lunar chain craters are likely to be volcanic in origin, presumably being analogous to terrestrial maars. Other workers, however, have argued that there are reason- able terrestrial volcanic analogs for even the large lunar craters, and that in general the lunar craters "are analogous, at least in broad out- line, to many of the large calderas and volcanic ring structures found on earth. " (Moore and Cattermole, 1967). Green (1963) maintains that the tidal effects on the moon due to the earth (because of the eccentric- ity of the moon's orbit) and the lesser lunar gravity would both contri- bute to enhanced volcanic activity, and he states that a lunar maar of 15 km diameter might be the equivalent of one of perhaps 4 km diameter here on earth. He also predicted that lunar craters of diameter less than about 15 km diameter would be of the mar type while those over 15 km would be primarily of the caldera type. 1 In contrast to Shoe- maker, Green believes that the large lunar craters have many features in common with caldera-type structures on earth (Green, 1963, Table 5). Elston (1965) argues for the analogy between features such as the 90 mi diameter Mogollon Plateau volcano -tectonic basin of New Mexico and the large lunar ring-structures. McCall (1965) concludes that the 1It is of interest to note that this distinction between maar and caldera type lunar craters falls exactly in the diameter range of 10-20 km that Pike (1968) interprets as being the threshold between simple, unaltered meteorite craters and those whose impact characteristics have been changed by post -impact processes, as discussed in the previous section. 49 large lunar craters are "surface cauldrons, genetically closely related to terrestrial calderas. " Clearly the impact-volcanic question of the origin of lunar craters is not resolved. Our concern here is with the role of gravity observations in the resolution of this question. Two approaches seem possible. One is to attempt to construct a likely model of the subsurface structure of a "lunar caldera" and calculate the gravity anomaly over it. Alternatively, since the interpretation of the lunar craters as calderas involves their comparison with terrestrial features, the gravity anomalies actually observed over these structures on earth could be analyzed and applied to the lunar environment. The first approach involves the establish- ment of a model for the subsurface structure of a caldera. Perhaps the classic paper on terrestrial caldera structure is that of Williams (1941). He establishes firmly the fact that most calderas are the result of subsidence and not to simply violent explosion, and divides calderas into a number of differing types based on the characteristics of actual examples observed here on earth. Of particular interest here are two of his types, which generally seem to include what most workers feel are reasonable analogs of lunar features. His Krakatau (Krakatoa) type owes its origin "primarily to the withdrawal of magmatic support from beneath volcanic cones by the rapid and voluminous discharge of pyro- clastic ejecta, chiefly in the form of pumice . Such calderas of Kraka- tau type are found particularly on compo site volcanoes built of andesitic and dacitic materials. . . ", and include such examples as, of course, 5O Krakatoa, Crater Lake, and Aso and Aira in Japan. A second type is the Kilauean, which is characteristic of basalt shield volcanoes, and which results when "rapid effusion of lava from fissures on the flanks of a cone or intrusion of magma as dikes and sills drains the central conduit and causes foundering at the central vent. ", the classical ex- ample of which is naturally Kilauea. This type, however, seems to resemble strongly William's Glen Coe type, and later workers appar- ently consider the two types, Kilauean and Glen Coe, to be essentially identical. 1 To attempt to model the subsurface structure of the differing types of terrestrial calderas for the purpose of calculating the gravity anomalies, or of even one type, for that matter, would seem to be a very difficult task because of the great variety of, and uncertainty about, such structure. A more direct approach might be to examine the re- sults of actual gravity surveys made over such calderas, and in the last few years such results have been increasingly forthcoming. Of particular interest here has been the work of various Japanese investi- gators on calderas in those islands, which has been summarized by Yokoyama (1961, 1963) and Malahoff (1969), especially the fact that these gravity investigations have apparently revealed the existence of two classes of calderas analOgous to the Krakatoa and Glen Coe types of 1 McCall (1963) has further argued that the Krakatoa type is simply a special case of the Glen Coe type, illustrating the perhaps obvious fact that nature rec0gnizes no man-made categories, but that all transitional forms may exist. 51 Williams. Five Japanese calderas show strong negative gravity anoma- lies, ranging from -10 to -46 mgal. 'Ihese calderas are all associated with great amounts of pumice and ignimbrite (the Krakatoa type). Two calderas, Oosima in Japan and Kilauea, show positive gravity anoma- lies of +15 and +9 mgal respectively (the Glen Coe type), with the positive anomalies apparently due to the more dense lava in the throat of the vent or in shallow magma chambers beneath the surface. This information is summarized in Figure '7. Are these caldera types, assuming they are actually distinct, analogous to the lunar craters ? And if they are, would the Operation of similar mechanisms on similar materials in a different environment, as on the moon, result in similar structures and anomalies? It seems difficult to answer, or even to attempt to answer, such questions in a meaningful, quantitative way. Even if we could consider the calderas of Figure 7 with negative anomalies to be closely analogous to lunar structures we are left with the ambiguity that we have already found in the previous section that lunar impact craters might also be eXpected to show negative anomalies. For example, Hakone caldera, with a diameter of 11 km, shows an anomaly of ~10 mgal. But, according to Figure 5, if an impact crater of 11 km diameter were underlain by a breccia lens of density contrast -0. 122 g/cc, a not unreasonable value, it too would exhibit an anomaly of ~10 mgal, and we would then have two contrasting models of very different structures, both of which were consistent with the gravity data. ANOMALY (mgal) -20 .— l w c I -50 .Z - Oosima ° Kilauea 52 AVERAGE DIAMETER (km) rlTlngjlllollTllglllelollfilzgrlrf Towada 0 'Hakone ° Toya . Ago Sikotu Kuttyaro ‘ ‘ Aira 310 Figure 7. Gravity anomalies associated with various terrestrial calderas. Data from Yokoyama (1963) and Malahoff (1969). 53 Clearly, in such a case additional ge010gical information is needed to help resolve the question of origins. One possible means of differentiating these two crater forms might, however, come from an examination of the gravity field surrounding the crater to a considerable distance beyond the rim. If a crater is of internal origin, then because of subsurface sources of magma, fracture zones, intrusives, etc. , the gravity anomaly over the structure should be directly related, although perhaps not in an immediately obvious way, to the regional gravity field of the area. Fbr example, Yokoyama (1966) has noted that four calderas, Sikotu, Hakone, Toya, and Towada, all under 20 km in diameter (the diameter range generally being considered here and in the section concerned with impact craters), have their low gravity values superimposed on regional highs, which he interprets as meaning that "there are upheavals of the basements beneath the calder- as. ", i.e. there is a direct relationship between the location of the caldera and the regional structure as revealed by gravity work. On the other hand, such a relationship would of course not be expected for an impact crater. Rather, impact craters should be distributed essen- tially at random, with no respect for regional trends. The same argu- ment should hold for magnetics. For example, Lowman (1965) has concluded that the Sierra Madera structure in Texas, thought by many to be an eroded impact crater, is actually the result of displacement and brecciation by a syenite intrusion. This conclusion is based prim- arily on the apparent relationship of the structure to a positive magnetic 54 anomaly, which would be characteristic of an intrusion, while impact breccia would normally produce a negative anomaly, as a result of the random arrangement of the breccia fragments (Innes _e_t_a__l, 1964). However, because of the lack of a detectable magnetic field, magnetic methods will undoubtedly be limited on the moon. There is always the further possibility that lunar internal activity may manifest itself in a form which would produce structures not really ana10gous to any found here on earth. A fact that to me has always seemed a rather serious stumbling block to considering terres- trial calderas to be analogs of lunar craters is that terrestrial calderas generally represent a later evolutionary stage in the development of what was originally a positive tOpographic feature, such as Krakatoa, Crater Lake, and Kiluaea, but on the scale of the larger lunar craters such positive features are not found on the moon, although craters of all degrees of freshness are seen. Advocates of the caldera nature of lunar craters seem to generally ignore this fact, but McCall (1965) has addressed himself to this point by stating that "The first, positive phase of buildup of a volcanic pile, present in the case of all terres- trial caldera centers is not represented - if there was a first stage of tumescence at all it was abortive - or largely so, little or no gas and no lava being vented at the surface. ". This being the case, it follows that the subsurface structure’might differ from that of terrestrial calderas in significant ways as well. It is quite clear that, in the inter- pretation of the origin and structure of the lunar craters the gravity 55 data can only provide clues, which must of course be examined in the light of the available direct geological evidence. Most of the previous discussion of this chapter on lunar craters, whether of impact or internal origin, has pertained to craters of about 20 km diameter or less. When one considers the larger craters, many further complications may arise. Even if originally due to impact, for example, a large lunar crater might subsequently have its form and structure altered in any number of ways, some of which have already been mentioned and any of which could affect the gravity field consider- ably. Of particular importance is the fact that the effects of a large meteoritic impact might be such as to result in immediate volcanic activity (Ronca, 19 66). The resulting crater would then exhibit the characteristics of both an impact and volcanic origin, and the interpre- tation of such a structure would be undoubtedly a complicated procedure. A similar origin has been pr0posed for a number of terrestrial features such as the Sudbury structure (Dietz, 1962). In view of the disagree- ment that still exists about the origins of such terrestrial features as Sudbury, the Rieskessel, and the Vredefort Dome, even after years of first hand examination by many geologists, there is no doubt that a real and genuine understanding of the nature and origins of the various lunar craters will remain a long range goal, taking us many years into the future . CHAPTER III mMES Lunar domes are low, generally circular blister —like swellings in the lunar surface, ranging up to about 17 km in diameter and some 700 m high (Baldwin, 1963) although some similar but more irregularly shaped features may be as much as 80 km across (Salisbury, 1961) and over 1000 m high. Their s10pes are therefore quite low, averaging perhaps 30, and frequently domes are found to possess exactly central craterlets at their summits. They usually occur in clusters, and there is general agreement that they are features of the maria (Quaide, 1965) and also of some of the large craters with mare -like interiors (Kopal, 1966), although it would be difficult to detect them even if they did exist in the upland regions. According to Baldwin (1963) and Qiaide (1965) however, they are not found near the centers of the maria but are restricted to the border regions or to areas where evidence indi- cates a shallow fill of mare material. A well developed group of domes near the crater Marius in Oceanus Procellarum was shown on a widely circulated Orbiter II photograph. The domes shown are from approximately 3. 5 to 17 km in diameter and from 300 to 500 m high. Some have central craters and seem to be formed by material super- imposed on the original surface, while others seem to be due to the 56 57 updoming of the original surface layers. A number of differing genetic theories have been advanced to account for the domes. Perhaps the mo st obvious suggestion is that they are shield volcanoes or laccoliths (Qaaide, 1965 ; Fielder, 1965). Salisbury (1961) however, interprets them as being uplifts in the lunar surface due to a mineralogical phase change with an accompanying in- crease in volume . Baldwin (1963) favors this phase change hypothesis or the laccolithic interpretation. At least one other possibility is that they are the result of subsurface ice, perhaps being analogous to terres- trial pingos. The gravity anomalies associated with domes according to these different theories are discussed in turn below. Serpentinization Origin The suggestion that the lunar domes may be due to the serpent— inization of olivine-rich rocks by waters emanating from below the lunar surface is apparently due to Salisbury (1961). The reaction between olivine and water at various temperatures and vapor pressures has been considered by Bowen and Tuttle (1949). They found that at temperatures of less than 4000C water will serpentinize forsterite to produce serpentine and brucite. If silica is also added, the serpentini- zation will occur at temperatures less than 500°C with an accompanying large increase in volume . They point out that an interpretation of most terrestrial serpentines is in best accord with the hypothesis that the serpentine resulted from the introduction of fluids into rocks containing 58 olivine which was already completely crystallized. This reaction can be approximately represented by the equation OLIVINE + WATER t=s SERPENTINE + HEAT (13) which would proceed to the right at temperatures of 5000C or less, and would involve a volume increase of about 25%. Hess (1955, 1962) has suggested that serpentinization of periodotitic material in the earth’s mantle where rising waters cross the 500°C isotherm could account for a wide variety of epeirogenic movements either upward, due to the increase in volume of the serpentine, or downward, due to a reversal of equation (13) by a rise of the 500°C isotherm or to an increase in the near-surface temperatures by volcanism with a consequent eXpul- sion of water vapor. From the relationship between seismic velocity, density, and percentage of the rock serpentinized (Hess, 1962) for example, he concludes that the oceanic "layer 3", whose seismic velocity averages around 6.7 km/ sec, is peridotite which has been 70% serpentinized. Salisbury (1961) has extended Hess' concepts to include the moon, to account for the lunar domes. That is, he suggests that, in accord with equation (13), escaping waters from inside the moon in crossing the 500°C isotherm would serpentinize the (assumed) peridoti- tic material of the moon's surface layers, and the consequent increase in volume would push up the domes. He feels that such a mechanism "would be more than adequate to produce domical structures" and even “‘l 59 argues that this process could account for the central craters on some domes as being due to a reversal of equation (13), with a correSponding decrease in volume caused by excess heat generated by the original serpentinization itself or by a release of the excess water vapor. Un- fortunately his presentation is entirely non-quantitative. No attempt is made to connect the actual dimensions of lunar domes with what is known or might reasonably be inferred about the lunar subsurface. One point seems clear: Salisbury's drawings indicate that he sees the serpentinization process as Operating on the entire layer of lunar material lying between the lunar surface and the 500°C isotherm. Walter (1965) has criticized Salisbury's theory as follows. Lowman (1963) has calculated the pressure-depth relationship for the moon. As might be anticipated, his calculations indicate that the in- crease in lithostatic pressure with depth is considerably less for the moon as compared to the earth. The lunar pressure -temperature gradient has been calculated by MacDonald (1961) on the assumptions that the moon's internal heat is radiogenic and the moon is chronditic in composition. These data taken together indicate that the 500°C isotherm would be located at a depth of about 90 km below the lunar surface, and, as Walter has pointed out, it is difficult to see just how a typical lunar dome of perhaps 10 km diameter, which is a rather localized feature, would owe its origin to a process occurring at a depth approaching 100 km. This, along with the fact that "serpentinization might often result in elongated or imbricate uplifts and thus fails to explain the generally 60 circular outlines of lunar domes", leads Walter to reject the serpentine hypothesis. It seems to me that both of these objections can be met rather directly, although to my knowledge Salisbury has not done so . There are elongated, imbricate topographic features on the moon whose heights and widths are comparable to those of domes; they are, of course, the maria ridges. Salisbury, in his original work (1961) does not discuss serpentinization as a possible mechanism for the origin of the ridges, but if this process is actually responsible for the domes it would seem that serpentinization along a subsurface fracture zone could produce a feature much like the ridges observed in many of the maria. 1 The second objection, that the 500°C isotherm is too deep to produce structures as localized as the domes is not easily met by Salisbury's original suggestion that serpentine is generated in the entire layer of the moon between the 500°C isotherm and the lunar surface. However, I would suggest that the important point here is that the serpentinization occurs at temperatures under 5000C, not just at 5000C. Assume, for example, that the maria are filled with peridotitic material to a depth of not more than a few kilometers, and that the mare basement is com- posed of some contrasting (more acidic ?) rock type. Then, even if the 500°C isotherm were some 100 km deep, the process of serpentiniza- tion could not occur until the olivine-rich materials were encountered by 1 This mode of origin for lunar ridges is considered in more detail in Chapter VI. 61 the rising waters, which might be at a much shallower depth and at a temperature considerably below 5000C. In this view, the serpentine body within a dome would be bounded on its lower surface not by the 500°C isotherm but by the mare-basement interface, which would presumably be ata much shallower depth. These suggestions are in— corporated schematically in Figure 8. In order to place this hypothesis on a more quantitative basis, an "average" lunar dome was selected to serve as a basis for further calculations. This dome is assumed to be circular in plan, having an overall diameter of 10 km and a height of 300 m, giving an average SIOpe of about 3. 50. These dimensions seem to be fairly typical. In addition, to facilitate calculation, it is also assumed that the shape of the dome is that of a spherical cap lying on the lunar surface. In order to calculate the depth to the lower surface of the serpentine body, it is noted that complete serpentinization results in a volume increase of about 25% (Hess, 1955). A free volume expansion of 25% in a unit cube would result, of course, in a volume of 1.25 and in a dimensional expansion of the cube root of 1.25 or about 1.08. If we assume that our typical dome is due to the complete serpentinization of the under- lying material, and further assume that the upper surface of the ser- pentine body lies no deeper than the level of the original plain (that is, 300 m below the t0p of the dome), then we have essentially two possibil- ities. If the serpentine is confined at the bottom but is free to expand without resistance in all other directions, the serpentine body would 62 DOME m PERIDOTITIC MARE FILL SERPENTINE MATERIAL MARE BASEMENT f NON-PERIDOTITE j H. K 2 FROM INTERIOR Figure 8. Schematic section of a lunar dome resulting from serpentinization of mare material. 63 have to extend to a depth of 4050 m below the level of the original plain.1 On the other hand, if the expansion is confined at the bottom and at the sides as well, as might seem more realistic for a subsurface mass, the only free direction will be up, i.e. the expansion will be one- dimensional, and the depth of the lower surface of the serpentine will be no deeper than 1500 m below the level of the original plain.2 If the mare material is only, say, 25% serpentinized rather than 100%, the depth of the lower surface of the serpentinized body, for our 300 m high dome, simply becomes four times as great or about 6000 m for a free expansion in the vertical direction. It seems evident therefore, that the depth to the bottom of the serpentine would not be deeper than some 10 km at most. Such a depth is too shallow to encounter the 500°C isotherm, but is quite comparable to various estimates for the depth of the mare material itself (see Chapter V). Therefore if the lunar domes are in fact due to this mineralogical phase change, it seems reasonable to believe that the mare material, but not the base- ment rock, is involved in the serpentinization process. In order to calculate the gravity anomalies over such a dome, a three-dimensional model is needed to define the shape of the subsurface serpentine body. The surficial dimensions of the dome are those al- ready described as "typical" (diameter of 10 km and height of 300 m) 1The expansion is equal to the height of the dome, 300 m, which is in turn maul to 0.08 of the length of the original rock column, which was then 30 /0.08 or 3750 m long. Upon expansion of 1.08 times, this column becomes 4050 m long. 2 Here, 300/0.25 e uals 1200 m of original rock, which when eXpanded 25% becomes 150 m long. 64 and, as before, it is assumed that the t0p of the serpentine lies no deeper than the original plain level, or 300 m beneath the summit of the dome, and that the lower surface of the serpentine is a horizontal plane presumably representing the mare -basement contact. For mare material that has been 100% serpentinized this lower surface will be at a depth of 1500 m below the original surface or 1800 m below the t0p of the dome, for an assumed expansion in the vertical direction only. In addition, on the assumption that the elevation of any point on the dome above the original ground level is a measure of the amount of expansion that has taken place beneath that point, the point will then be underlain by a column of serpentine whose lower surface lies at 1500 m below the original plain and whose thickness is equal to five times the eleva- tion of that point above the original ground level (see footnote 2, page 57 for a sample calculation). If the dome has the shape of a portion of a sphere, as assumed here, it can be shown that the upper surface of the serpentine body will be closely approximated by a paraboloid of revolution. For rock which has been only 50% or 25% serpentinized the lower surface of the body will lie at a depth of 3000 and 6000 m respectively while the upper surface is in all cases close to the shape of a paraboloid. Figure 9 illustrates the shape and position of these subsurface bodies beneath our "typical" dome. The gravity anomalies over these serpentine bodies were calcu- lated in the same way as were those over the breccia lenses of the im- pact craters of Chapter II. For the three degrees of serpentinization of 65 |-+ 5km a1 If E O s M E 50% 1° 8 CD 25% l Figure 9. Scale cress-section of half of a lunar dome of 10 km diame- ter and 300 m height, showing the size and shape of the underlying serpentine body for rock which has been 100%, ' 50%, and 25% serpentinized, on the assumption that the serpentine body lies 300 m below the top of the dome. The lower surface of the serpentine represents the mare- basement contact. 66 the country rock, 100%, 50%, and 25%, the anomalous bodies of Figure 9 were approximated by a series of horizontal circular disks, each disk having a thickness of 250 m and its median plane just tangent to the paraboloidal shape of the upper surface of the serpentine. This required, for rock 100%, 50%, and 25% serpentinized, six, twelve, and twenty-four disks respectively. The gravity anomaly due to any one disk is then pr0portional to the solid angle subtended by the median plane of the disk at the point of observation. These solid angles were determined, as they were for impact craters, by Nettleton's charts (1942). The density contrast between the serpentine and the pericbtitic material is given by Hess (1962), the contrast for 100% serpentine being -0.75 g/cc (the serpentine being less dense), for 50% being -0.38 g/cc, and for 25% being -0. 19 g/cc. The anomaly due to any one disk is given by equation (11) and the total anomaly is simply the sum of the individual disk values. The anomaly was calculated for five points on the dome over each of the three serpentine bodies, the results being shown in Figure 10. For domes of dimensions other than those of our "typical" dome but of the same general height/ diameter ratio of 300m/ 10km or 3%, it is noted that the anomalies over such domes will be different in magnitude from those values given here by the same pr0portion as the ratio of the dimensions of the domes to those of our "typical" one. It seems evident, then, that if the serpentinization hypothesis for the origin of lunar domes is correct, these domes should show 67 -10.. 452 % mgal 50% -3o_ 00% -35... LUNAR DOME (300 m high) r ' : I. 5 km 1[ Figure 10. Gravity profiles over the serpentine bodies of Figure 9 for rock 100%, 50%, and 25% serpentinized. Dots on dome are points for which the anomalies were calculated. 68 strongly negative gravity anomalies, amounting to perhaps some tens of milligals. The height and diameter of the dome and the magnitude and form of the anomaly are the basic data observable at the surface. These, in turn, will be related to the depth, shape, thickness, and density contrast Of the subsurface rock body. Of course, not all of the subsurface data can be determined from the gravity anomaly. Never- theless, other geological data could help to narrow the choice of a sub- surface model considerably. For example, seismic work might reveal the depth of the mare -basement contact, placing limits on the depth of the lower surface of the serpentine, and might even, if the seismic velocity of the anomalous body could be found, permit an estimate of the percent Of serpentinization in the body from the data given by Hess (1962), or petrological examination of the mare material may reveal the degree of serpentinization. A prominent negative gravity anomaly over a lunar dome would be an important Observation consistent with the serpentinization hypothesis, but additional data from other geOphysical and ge010gical investigations would be required to identify the nature and structure of the subsurface anomalous mass more exactly. Lacco lithic Origin A widely considered hypothesis for the origin of the lunar domes is that they are laccoliths or perhaps shield volcanoes. At first thought laccoliths and shield-type volcanoes might be considered to be mani- festations of essentially one type of volcanic activity. Yet, as is well 69 known, on the earth shield volcanoes are characteristic of quiescent, basaltic volcanism, while laccoliths are generally accepted as being the result of the intrusion of more acidic, more viscous magma into a layered rock sequence. In fact, O'Keefe and Cameron (1962) have argued that if the domes are laccoliths this is then evidence for acidic rather than basic volcanism on the moon, and this, along with other evidence, leads them to suggest that the maria are welded tuffs, rather than basalt lava flows. They have further argued that basalt would not tend to accumulate around a feeder but would spread out to form a sill, and also that if the maria were basalt flows this would not provide the "weak strata" necessary for laccolithic intrusions, whereas alternating ash flows and welded tuffs presumably would. A number of alternative arguments, however, immediately come to mind which suggest that the maria are basaltic, but that this does not necessarily imply that the domes cannot be laccoliths. Kuiper (1966), for example, holds that the maria are basalt lava flows, and this appears to have been confirmed by the analysis of the maria surfi- cial material by both Surveyor V and VI (Thrkevich eta}, 1967, 1968). The fact that some domes exhibit central craters and that some appear to be composed of material superimposed on the mare surface but yet have low lepes of just a few degrees seems to indicate that they are ana10gous to terrestrial shield (basaltic) volcanoes. Yet, as on the Orbiter photographs referred to above, these shield-like domes Occur directly associated with other domes that appear to be due to the 70 updoming of the surface layers from below, and it would seem reason- able to assume that both types are manifestations of the same type (basaltic) volcanic activity. Also, laccoliths are, at least in some cases, found on earth in sequences of basalt extrusive rocks. For example, Murata and Richter (1961) have described a laccolith in the wall of the Kilauea caldera in Hawaii as being some 900 ft long and 90 ft thick which at the time of emplacement was overlain by somewhere between 135 and 350 ft of bedded lavas. On the moon, where the upper portion of a basalt flow might consist of a very frothy, vesicular layer perhaps some ten meters thick (Kuiper, 1966) a sequence of such flows would certainly seem to provide the required layers Of weakness for the injection of magma. Also, because of the lesser weight of the over- lying rock on the moon, along with the normal fluidity of basaltic lava, such injection might Spread over a much wider area in the lunar en- vironment producing laccoliths much more sill-like than those on earth normally associated with acid volcanism, and thereby account for the small height of a typical lunar dome relative to its diameter. It is therefore concluded that even though most, but not all, terrestrial laccoliths are associated with more acidic rather than basaltic volcan- ism, the interpretation Of the lunar domes as laccoliths and some shield volcanoes associated with the basaltic material of the maria is a distinct possibility. In order to calculate the gravity anomalies that might be associ- ated with such laccolithic intrusions a three-dimensional model is, of 71 course, needed. Initially, so as to make the results obtained directly comparable to those of the previous section, the same "typical" dome of diameter 10 km and 300 m height is adOpted as the standard, although the gravity effects over domes of other diameters will also be noted. The depth to the intrusion is an important variable to be con- sidered. Since it is evident that if the domes are laccoliths they would be intruded into the layered mare material and would not be features of the mare basement, the intrusions would then of course lie no deeper than the thickness of the mare itself, which is probably a depth of not more than a few kilometers or a couple of tens of kilometers at most, since the domes tend to occur in the shallow border regions of the maria. They could presumably occur at any shallower depth, ranging up to the surface itself, in which case we would have extrusion and a feature resembling a shield volcano . The exact shape that the intrusion would assume is uncertain. Reasons have been given above for believing that if the domes are lac- coliths produced by basaltic volcanism characteristic of the maria, they might be much more sill-like than terrestrial laccoliths. For these reasons, it is here simply assumed that the shape of the intrusion is identical to the tOpographic expression of the surface of the dome above the level Of the original plain. This in turn means that stretching or thinning of the rock layers overlying the intrusion is ignored, but in view of the low SIOpes involved this would seem to be reasonable. Terrestrial laccoliths can apparently be the result Of injection 72 Of magma laterally from a central stock, as in the Henry Mountains of Utah, or from below, the feeder being more or less vertical beneath the floor of the laccolith. Fbr the lunar domes, as many of them exist as discrete, very symmetrical features, injection from below seems most probable. The exact nature of a feeder would be difficult to deter- mine. Would just one conduit be most likely, or perhaps many? Because of this uncertainty, in the initial gravity calculations below, the effects of feeders are not included but will be considered later. The final important variable is the density contrast between the intrusive and the country rock. On earth, the usual expectation would probably be for the density contrast to be positive, that is, for the in- trusive to be denser than the host rock, resulting in a positive gravity anomaly. Just this situation was observed by Greenwood and Lynch (1959) in Texas for a laccolith of one and one-half miles diameter. There a density contrast of 0.5 g/ cc (2.45 for the layered sediments, 2.95 for the intrusion) resulted in an anomaly of +2.2 mgal. On the moon, however, the intrusion would be presumably injected into ig- neous material rather like itself in chemical composition, and the density contrast might be therefore diminished. However, extrusive rocks on the moon might have their bulk densities considerably reduced by violent degassing when extruded into a vacuum while intrusives, because they remain under some confining pressure, might be expected to solidify to a more dense state. lbbar (1966) found that basalt up- welled in a vacuum under laboratory conditions had a mean density of 73 1.76 g/cc. This is not necessarily near the mean density of the maria even if they are basalt flows, as this violent outgassing might affect only a relatively shallow surface layer of a flow, the bulk of the flow solidifying to a considerably denser condition. In any case it seems likely that whatever the actual densities involved are, the intrusion, because of its non-exposure to a vacuum will be denser than the country rock, and a density contrast of perhaps 0.5 g/ cc might be a not un- reasonable value. Therefore, in the calculations made below, the density contrast between the intrusive and extrusive materials is assumed to be positive with a value of 0. 5 g/cc. If further investiga- tions should provide a reason for revising this figure either upward or downward the anomaly magnitudes found here can be easily revised accordingly because, of course, the size of the anomaly is directly prOpOrtional to the density contrast. Figure 11 is a cross-sectional diagram of half of a lunar dome showing the location and shape of the intrusion for a typical depth of 2000 m, the depth being measured from the level of the original plane to the tap of the intrusive. The gravity anomaly over the dome due to the intrusive was calculated for various depths to the body by approxi- mating it by three horizontal disks each 100 m thick and of diameters such that the median plane of each disk was just tangent to the upper surface of the body. The anomaly was then found exactly as already described in previous sections, being prOportional to the solid angle subtended by the median plane and to the disk '8 thickness, and was 74 6088080 083 58:88 05 :03? :8 0:288 05 08 08: 80895:: 0:8 .688 0.8 88585 05 08580.88 3 000: 08.08 88:35.8: 005: 0:9 2.085 :83 8:880 05 580:0: E coca 8 58:55 05 8 :3 05 8 £90: a 8m £3835 055805 003.888 05 08 0:80 8:5 8 8 H8: 8 838.8 080m .3 058E ”[7,! I .00 V‘ T a: 5 cccm 75 evaluated by equation (11) (page 37). As stated above, 0.5 g/ cc was the density contrast and the effect of a feeder was not considered at this point. Figure 12 shows the relationship obtained between the magnitude of the peak anomaly, as it would be found at an observation station loca- ted at the summit of a dome (station 1 of Figure 11) and the diameter of the intrusive body for various depths of the t0p of the body beneath the original plain level. The actual calculations were carried out only for a dome of diameter 10 km, but direct scaling allowed the results to be extended to intrusives of greater and lesser diameters, on the assump- tion that our original height/ diameter ratio of 300m/ 10km or 3% re- mained constant. The uppermost curve of Figure 12 gives the peak anomaly over the body if its lower surface coincided with the original plain, i.e. it is an extrusion. This would presumably represent the case of a shield volcano. However, this curve is probably not very realistic, as the material extruded would not have been subject to the confining pressure that we argued would create the positive density contrast. Also, additional magma chambers or intrusive bodies be- neath a shield volcano might alter the anomaly significantly. In any case, the mode of origin of a shield volcano should be relatively obvious from direct visual observation alone. The gravity profiles over the dome as observed at stations 1 through 5 of Figure 11 have also been calculated for various depths to the intruding body, the depth being measured from the original plain .050 .8 Ex 3}: com 8 28: 8808330005525 0 5:3 0080: :8 6305.35 05 8 no: 05 3 ~0>0H :88 8:880 05 Sch 05:00 052.8.» x :8 .38: 0305.55 05 8 88:88 05 08 58:88 85:58:: 05 :0050: 0980:0320: .fi 0.8.03 :5: 8:05:57: .8 0083.8 om _ 8 F 8 mm _ _ _ _ o.fl _ _ _ _ m a _ r T o I a I N I m w .. .m I m m n1 l o WA! .. mm. .00\m m .o 0: I 0 908.580 38:3 :80: 0305.35 05 8 000850 89:5 05 3 :88 8:88: 05 I 8 ~0>0~ 05 89G 00.8000:— 08 05:3 0 I IS I: _ _ p «a 77 level to the t0p of the intrusive. Figure 13 shows these profiles. As would be anticipated, with increasing depth the anomaly exhibits a decrease in amplitude and an increase in width. The exact shape and placement of the feeder (or feeders) in a laccolith is not easily established because under normal conditions it would not be emsed. In order to estimate the effect that a feeder might have on the gravity field over our "standard" dome described above it was assumed that the feeder was a vertical cylinder, centrally located, with a diameter of 300 m, which is equal to the thickness of the laccolith itself. The cylinder was assumed to have an infinitely deep lower surface to provide a maximum effect and to have a density contrast of 0. 5 g/ cc, as did the main intrusion. The anomaly due to the feeder alone, as observed from the t0p of the dome for various depths measured from the original plain level to the t0p of the laccolith to which the feeder leads is shown in Figure 14. These data were cal- culated from the standard gravity formula for the effect on the axis of a buried vertical cylinder. As is seen in Figure 14, even for intrusive bodies near the surface, the contribution of the feeder is quite small, less than half of a milligal. It seems likely that the effects of a feeder can be neglected, at least in a first approximation, without serious error unless the feeder is very large. 78 5 _ DEPTH (I 4 - o 100 ’0 3 .. '8 b0 ‘8’ 2 E 000’” 8 2 - 1 'f 000 DOME 300 m \ -< 5 km b—t Figure 13. Gravity profiles over a dome of 10 km diameter underlain by a laccolithic intrusion, for various depths from the original plain to the t0p of the intrusion. The density con- trast is a positive 0.5 g/cc. 79 Observation point ANOMALY (mgal) l t l I j 0 1 2 3 4 5 DEPTH (km) Figure 14. Anomaly-depth relationship for laccolith feeders (cross- ruled in sketch) which are assumed to be vertical cylin- ders 300 m in diameter and infinitely deep. The depth is from the original plain level to the t0p of the intrusive, which is 300 m thick. The density contrast is O. 5 g/cc. 80 Ice Origin The possibility of ice at or near the lunar surface has been dis- cussed by several workers (e.g. Gold, 1966) and has received renewed attention recently by the discovery of sinuous rilles that some attribute to the action of running water (Lingenfelter et___a_l, 1968). MacRae (1965) has suggested that the lunar domes may be a result of subsurface ice, being analogous to terrestrial pingos. These features on earth, how- ever, usually exhibit central craters which evidently become larger with time, eventually resulting in a degenerate feature resembling a crater somewhat like those due to impact. Currie (1965) has mentioned a cratered pingo in Greenland whose diameter, depth, and rim height have almost exactly the ratios predicted by Baldwin's relationships for impact craters. Some pingos may begin to grow again with renewed activity, resulting in an uplift within a crater, which MacRae believes may be analogous to the well -known spherical central uplift in the lunar crater Alpetragius. It seems evident that some terrestrial pingos, at certain stages in their develOpment, may resemble certainlunar fea- tures, but it does not seem that pingos, as a class, should be con- sidered analogous to lunar domes, as a class, as there are too many observed differences. There is always the possibility that some indi- vidual lunar features may be due to ice action, however, and gravity methods might help to reveal this. Such a feature would undoubtedly give rise to a negative anomaly because of the lesser density of the ice 81 and water involved as compared to rock materials. The form and mag- nitude of the anomaly would depend on the size and shape of the sub- surface structure. MacRae simply mentions a "lens -shaped" ice body in terrestrial pingos. In any case, as a rough first approximation the subsurface model already adOpted here for the origin of lunar domes by serpentinization would probably serve for a pingo -like structure as well, with a body of ice mixed with mare material substituting for the serpentine (Figures 9 and 10). The anomaly over such a body might run to some tens of milligals (negative) depending on the depth of the body and the percentage of ice within it. Discriminating between the two possibilities (serpentine or ice) would then of course require additional information which might be obtained from on-site geological investigations . It appears then that for lunar domes gravity surveys might be very helpful in delineating subsurface structures and pointing toward certain hypotheses as likely or eliminating others as unlikely. If the domes are due to serpentinization, they should be characterized by strong negative anomalies, while laccoliths might reasonably be expec- ted to produce positive anomalies. Shield volcanoes will have anoma- lies depending on the density contrast of the lavas with the country rock and on the nature of subsurface magma chambers and intrusions, but their origin should be obvious from direct observation. Pingo -like structures may also result in negative anomalies. In all cases, a firm 82 likely identification of the origin and structure of a dome, or any other feature, can be made only in the light of all other geological evidences as well. CHAPTER IV LAVA TUBES If the lunar maria are in fact basalt flows, as seems likely, they may exhibit some of the features found associated with such flows here on earth. Among these features are those known as lava tubes or lava tunnels , which apparently form when still-fluid lava flows from beneath a solidified crust, draining what may have been a subsurface channel for the lava. The resulting void may be a number of meters in width and perhaps many kilometers long. Such features are well known in the various flood basalt provinces around the world (e.g. Ollier and Brown, 1965). Green (1963) has called attention to the fact that if such tubes or tunnels exist on the moon they might serve as excellent installation sites for permanent or semi—permanent manned bases. They would provide shelter from various solar radiations and from smaller meteor- ites . Green also indicates that many terrestrial lava tubes, even though having ages of many tens of thousands of years, exhibit virtually no collapse effects at all, and speculates that such a feature on the moon could be easily sealed and pressurized, providing complete facilities for lunar exploration. 83 84 This being the case, locating and delineating the extent of such features in the lunar environment might be quite important. Since the tunnels are of course empty they should produce negative gravity anomalies at the surface, and therefore gravity methods might be use- ful in the search for such features . A similar type of investigation on earth might be the search for bedrock valleys in regions covered with glacial drift, and the same general techniques might apply. The size of the anomaly will depend of course on the shape, extent, and depth to the feature as well as on the density contrast. Since lava tubes are generally very long in relation to their cross-sectional dimensions, they can be considered to be two -dimensional. In cross-section they have varying shapes: triangular, nearly square, circular. In any case, however, the gravity effect of such a feature can probably be closely approximated by simply considering it to be a two -dimensional horizontal cylinder, with the result that the well known standard formu- las for the magnitude and form of the anomalies will apply. The density contrast will be simply the bulk density of the coun- try rock, since the tube is empty. For basalt, this might be a density of near 3.0 g/cc. However, the density of the basalt in the upper portion of a flow might be considerably less than this value because of extrusion into a vacuum on the moon. Therefore, a density of 2.0 g/ cc has been used as the density contrast between the empty tube and the surrounding rock. If another density contrast is finally considered more likely, the anomalies calculated here can simply be scaled up or 85 down proportionally. The anomalies anticipated over lava tubes of various diameters for differing depths to the center of the tube are shown in Figure 15, assuming that the tubes can be approximated as horizontal, two -dimen— sional circular cylinders, and that the country rock density is 2.0 g/cc. Figure 16 shows the gravity profile perpendicular to the axis of the cylinder. These data were derived from the standard formula g=o.04190’ R2 Z 1+XZ7ZZ where g is in milligals, R is the radius of the tube, Z is the depth to the tube '5 center, and X is the horizontal distance from the axis of the tube to the observation point, all dimensions being in meters . From Figure 15 it is evident that for lava tubes a few meters or tens of meters in diameter the am maly will not be very large, particu- larly if the tube lies at some depth. In early manned exploration, how- ever, the lava tubes of any use will of course be those quite near the surface (straight line of Figure 15), and these might well be detected by a gravity survey, particularly because such a survey need extend only a short distance away from the tube, as the halfwidth of the anom- aly is equal to the depth of the tube '3 center which in turn is just the radius of the tube if it is tangent to the surface . In such a survey over a small area designed to determine the extent of such a feature, eleva- tion and position control problems, as well as regional effects, would be minimal, and anomalies of the sizes indicated might well be detected and usefully analyzed. 86 Tube tangent to surface \ ANOMALY (mgal) I 1 I l l 0 10 20 30 4O 50 RADIUS OF LAVA TUBE (m) Figure 15. Relationship between the maximum gravity anomaly and the radius of a lava tube, for various depths to the center of the tube. The density contrast is 2.0 g/cc. 87 >0 [4 E 0 [I] E. 53 A [I] m i 1 1 L L 1 1‘9-4 -3 -2 -1 o 1 2 3 4 SURFACE__ , X/Z , 2 1L __ LAVA TUBE Figure 16. Relative gravity profile over a lava tube. CHAPTER V RI LLES Rilles are elongated depressions or trenches in the lunar sur- face which may be hundreds of kilometers in length but usually are only a few kilometers wide with depths generally only a fraction of the width. Many hundreds of rilles are known and they are primarily associated with the maria or with the immediately adjacent upland areas . They are by no means all identical, and virtually all workers agree that several distinct classes of rilles exist with perhaps differ- ing modes of origin. Several investigators have proposed classification schemes for the various types of rilles. Following Qiaide (1965), the rilles can be divided into four classes: the sinuous rilles, the irregu- larly branching rilles, the arcuate rilles, and the straight rilles . These are considered briefly in turn. The sinuous rilles, as the name implies, generally follow very curving, contorted paths although the general trend of the rille may be in one direction along the lunar surface. A very significant fact con- cerning these rilles is that they frequently have a crater or crater chain located at their heads, and that the rilles then follow the general s10pe of the lunar surface away from the crater. Perhaps the best known example is Schrdter's Valley, although many others are known 88 89 as well. Many more of these interesting features have been revealed by the various Lunar Orbiters, and some of these are very narrow features located on the floors of larger depressions such as the Alpine Valley. The very sinuous, meandering nature of these features and their strong similarity to terrestrial river channels has reOpened the entire question of water erosion on the moon (Lingenfelter et a1, 1968), although other mechanisms such as glowing avalanche eruptions have also been suggested (Cameron,1964). The irregularly branching rilles are characterized by frequent branching and spoke -like extensions. They are often found on the floors of what appear to be old craters such as Gassendi and are also well displayed near the crater Triesneker. The same pattern, almost resembling ordinary mudcracks, has been observed in the floors of some craters on the lunar farside by the Orbiters . Such rilles seem to be related to an updoming of the area from below with a consequent fracturing in the overlying more brittle layers, and therefore appear to be due to tension. Also apparently due to tension are the straight and arcuate rilles . The straight rilles may be hundreds of kilometers long and up to about five kilometers in width with much shallower depths . They frequently occur in sets and may exhibit an en echelon pattern as does the best example of the type, the Ariadaeus -Hyginus system. Many such rilles seem to have served to localize some form of degassing of the lunar interior, as many exhibit chains of craters along portions of 90 their length. These rilles almost always occur in the border areas of the maria where the mare material is probably relatively shallow. The arcuate rilles occupy a similar setting, generally along the edges of the maria, and are concave in plan toward the mare cen- ters . The best examples occur along the eastern margins of Mare Humorum. Here the rilles are located mostly in the upland material, but are very near the edges of the mare. From the morphology of the straight and arcuate rilles, elon- gated narrow. trenches with inward s10ping walls, they seem to be graben type structures, the result of mrmal faulting which in turn would seem to indicate an origin resulting from tension. Their loca- tion in the mare border regions seems to confirm this origin. If the maria have in fact foundered due to the infilling of the mare material (or for whatever reason), and this seems to be indicated by features such as the tilted craters along the borders of Mare Humorum and the Straight Wall, then these rilles occur in just those areas, the mare borders, where tension should have resulted as the lunar crust was stretched as the mare basin subsided. The straight and arcuate rilles, then, seem to be downdrOpped blocks of the lunar crust along normal faults resulting from tension, and the crater chains along such rilles presumably represent volcanism resulting from the release of pres- sure associated with the faulting. Undoubtedly the gravity anomalies associated with the sinuous rilles would give important clues concerning the processes that 91 originally formed them, and the anomalies over the crater chains along some rilles would provide good data pertaining to certain types of volcanism on the moon. However, the simple, unaltered rilles that appear to be just downdrOpped blocks may provide the most important information of all, that relating to the relative densities of the maria and the uplands. This is perhaps the mo st important question which gravity might easily answer, namely, is the bulk density of the mare material greater or less than that of the uplands, and by how much ? An answer to this question is critical to the interpretation of the nature, structure, and origin of the maria, and will have important implica- tions for understanding lunar history in general. The usual assumption in recent years seems to have been that the maria are filled with a material whose overall density is greater than that of the uplands, and that this fact at least partially explains why the maria tend to be (but are not always) the lower areas on the lunar surface. Baldwin (1968) for example, states that ". . . it is probable that the density of the lava after solidification is about 0.4 g/cc greater than that of the country rock", and according to O'Keefe (1968) the Surveyor working group on lunar theory and processes adopted a value of 3 .0 g/cc for the density of the highlands and 3 .2 g/cc for the maria. Reeently a remarkable step forward in the analysis of the moon's gravity field was made with the publication by Muller and Sjogren (1968) of a gravity map of much of the lunar nearside, the data 92 being obtained from an analysis of 80 lunar orbits of the Lunar Orbiter V spacecraft. The most significant result of this investigation was the recognition of large positive gravity anomalies, as observed from a normalized height of 100 kilometers, over all five of the nearside ringed maria and over Mare Orientale, ranging from about +60 mgal over Mare Humorum to +230 mgal over Mare Imbrium. Muller and Sjogren originally speculated that these "mascons" (mass concentra- tions) were asteroidal-sized bodies associated with the formation of the maria buried some 50 km beneath the lunar surface. Other inter- pretations, however, soon followed. Stipe (1968) agreed that the posi- tive anomalies were due to meteorites , but he believes they may be vuried as deeply as perhaps 300 km. Conel and Holstrom (1968) have shown that a slab-like circular body at the lunar surface could produce an anomaly of the form and magnitude actually observed over Mare Serenitatis . Fbr example, they show that mare material of density contrast 1. 1 g/cc with the less dense upland material, which presum- ably underlies the maria, could duplicate the observed anomaly if it were 14 kilometers thick at the center, or density contrast 0.5 g/cc if it were 30. 8 km deep at the middle and tapered to essentially nothing at the edges. Their geological interpretation is of a basin filled with perhaps solid basalt. O'Keefe (1968), however, has made the impor- tant point that if such an interpretation is correct the original source of the lavas would have to have been some hundreds of kilometers deep; otherwise there would be no anomaly. Kane and Shoemaker 93 (1969) likewise account for the Mare Imbrium anomaly by a plate-like slab of basaltic material perhaps 30 km thick and of density 3 .O to 3 .2 g/cc imbedded in the lunar crustal material of density 2 .5 to 2.7 g/ cc, a density contrast of 0.5 g/cc. Wise and Yates (1969), however, argue that the "basalts" have an overall density essentially the same as the rest of the crust, and that the positive anomalies are due to the solid intrusion of plug-like masses of denser material from below a Moho- like discontinuity some 30-80 km deep into the bottoms of the original mare craters soon after their formation. Gilvarry (1969a, 1969b) brings things to a full circle by arguing that the mare material is actually l_e_s§ dense than the rest of the lunar crust, being sedimentary material which was eroded from the highlands by running water and deposited in the mare craters which had previously, because of a period of internal heating in the lunar body, become completely iso- statically compensated. As Gilvarry maintains that the moon is no longer capable of yielding, these sediments are a mass excess, even though less dense than the surrounding rock, and thereby produce the observed positive anomalies . It is clear that knowing the actual density contrast between the mare fill and the upland material, which apparently forms the base- ment of the maria, would be of great interest indeed. This knowledge would immediately eliminate some of the theories mentioned above. However, the problem with determining this density contrast by gravity observations is that the interface across which this density contrast 94 occurs, the mare fill-mare basement contact, is nearly horizontal, s10ping only slightly downward toward the deeper parts of the maria, and is therefore not directly susceptible to detection by gravity ex- cept over very long distances with resulting complications due to regional effects and unknown density changes at depth. Normal fault- ing, however, and particularly high angle normal faulting as is evi- dently found in the straight and arcuate rilles, is an excellent mechan- ism for converting vertical density contrasts to horizontal ones which might then be easily found by gravity measurements made over only a limited area, eliminating or greatly reducing the effects of regionals. If the rilles, where not altered by volcanic activity, are simply blocks of the lunar surface downdropped along steep normal faults, then a gravity profile across the rille should reveal the existence of hori- zontal density contrasts and in particular the nature of the mare-base- ment contact, whose density contrast would presumably be the most pronounced. This is schematically shown in Figure 17. This is exactly the structure of the East African Rift Valley, perhaps the nearest terrestrial analog of the lunar rilles, as given by Girdler (1963), where a negative anomaly of about 50 mgal apparently results from the lighter upper block of crustal material dropping into the denser rock beneath. The straight and arcuate rilles are all very long and shallow with respect to their widths and therefore can be very well represen- ted by two -dimensional features in gravity calculations. Their maximum $8898 .3808 0 00500.8 .33 0008 0520898 0080:0095 £308“ .3 000500 0:8 8:3 0 8 :03000 03080500 .5 0:50am ..\. u H H .. an...“ H H H ../ 2052352 9/5039?.....;s; .HH\\ / A 8m .N 000850 .832 3 5:00 0:0 0 0005050 8 000:0 880888 -25 4003.85 8 005.50 05 3 8808:0500: 00:88 30800 . «a 0:50am 00 r t. 8 LIHIY S 2:. TH .IN. I”. Tm. IQ. to.“ MIAVHD HALLV'IEIH 109 meters wide and/or exhibits a marked density contrast with the coun- try rock the anomaly will not be large, amounting to perhaps a few tens of milligals at the very mo st. The amplitude of the anomaly is not particularly sensitive to differences in the depth of the lower surface of the dike, and no firm conclusions about this depth seem possible based only on the gravity data. Figure 22 shows that even if a dike extends to a considerable depth relative to its width the anomaly dr0ps off rather rapidly away from the dike's center. There- fore, if the lunar ridges are in fact extrusive features underlain by dikes of a positive density contrast with the country rock, positive gravity anomalies of rather low amplitudes and narrow widths rela- tive to the widths of the ridges themselves would be anticipated over these features. Buried Ridge Origin According to this hypothesis, the maria ridges are the surfici- al expressions of sub-mare ridges or crater walls that have been buried by the mare fill, the present surficial expression of the fea- tures being due to the shallow depth of burial of the original ridge or wall and to possible differential compaction of the mare fill. Such an origin is most obvious for the various "ghost" craters of the maria, which are clearly craters which have been overwhelmed to a greater or lesser extent by the material forming the maria. It is not likely that all maria ridges originated in this manner. Nevertheless, 110 Baldwin for example (1965) has pointed out that the ring of which Sinus Iridum is a part is completed by a series of ridges in Mare Imbrium, which he interprets as resulting from the buried portion of the original crater wall. Perhaps the best example of ridges that may have originated in this manner are those found in the region of the Straight Wall. According to Alter (1964), who gives several excellent plates of this region, the Straight Wall is some 130 km long and 300 m high, having a Slope of about 410 . 'I'nis normal fault lies on a north-south diame- ter of a large, ancient ring-structure, the Straight Wall Plain, which is some 210 km across. The half of this ruined ring on the upland side of the Straight Wall is clearly visible, but on the downthrown seaward side of the Wall the other half of the ring is absent, appar- ently buried beneath the mare. However, under low sun angle condi- tions a series of ridges are visible on the mare surface which rather obviously complete the ring and which therefore appear to be due to the buried ancient crater wall which foundered along the Straight Wall fault. If this is correct, then the presence of this buried crater wall might well be detectable by gravity methods. In order to estimate the amplitude and form of the gravity anomaly that would exist over such a buried wall the various dimen- sions of the subsurface structure must be known. It appears on photographs as if the mare fill feathers out completely at the base of the upland eastern wall of the ring and just covers the buried seaward 111 wall in the west. No direct method of estimating the depth of the mare material away from the ridges is apparent. However, directly south of but immediately adjacent to the 210 km diameter Straight Wall Plain is Deslandres, another very similar ancient ring-struc- ture virtually identical in size, but which is not flooded with mare material. It would seem reasonable to assume that the various di— mensions of Deslandres approximate the pre -flooding dimensions of the Straight Wall Plain. These dimensions of Deslandres were deter- mined from the Lunar Chart LAC 95 (Purbach) of 1961. Although the walls and floor of Deslandres are irregular, the crest of the wall appears to average about 1500 m above the relatively flat floor and about 600 m above the surrounding plain. The horizontal distance from the wall crest to the base of the wall on the interior of the ring and to the level of the plain on the outside appears to be about 20 km. Figure 23 gives an east -west section of the Straight Wall Plain on the assumptions that its pre -flooding dimensions were similar to those exhibited at the present by Deslandres and that as a result of flooding and foundering the mare material just touches the base of the inner upland wall and just covers the downdrOpped wall. The post-flooding crater Birt, which lies just seaward of the Straight Wall, is also shown in section, its dimensions being obtained from the same map. If this subsurface model of the Straight Wall Plain is valid it can be seen that the interior walls of Birt would cut the entire mare section and penetrate the pre-mare basement as well, 112 r 14 .0063 :00 00 02000000000 “003.000? 602000.00 00 Ha 0.008 05. .505 303 300.0000 05 no 003000 0003:0000 0002000000 .3 0.3.0?” Tiles. 3'4 00080 0.50 /\|| 22sz .503 05.2 0.002.090 09,2qu 9mm? Bmflm 113 whereas the Straight Wall itself would exhibit only mare material in its face. It is interesting to note that the map referred to above shows a break in SIOpe in the inner wall of Birt some 600-800 m above the bottom of the crater. Whether this is the result of a change in lithology across a boundary such as the mare—basement contact pre- dicted here is of course uncertain, but in any case such localities would be very important geological sites, at which a great deal could undoubtedly be learned about the history and origin of the maria. It seems evident that the upward projection of the buried sea- ward wall of the Straight Wall Plain could produce a gravity anomaly over the surface ridges. A section of this portion of the area is given in Figure 24. The gradual rise landward to the east in the mare-base- ment contact has been ignored in this section as it is less than 10 and would simply contribute to a regional effect over the entire plain. The gravity anomaly over the buried ridge was calculated by assuming that the ridge could be considered to be two -dimensional and by breaking this buried ridge up into horizontal slabs 100 m thick. The gravity effect of such a slab in milligals is (Nettleton, 1942, with a conversion factor) g= 13.35 Gdt (14) where 6 is the angle subtended by the median plane of the horizontal slab at the point of observation, 0' is the density contrast in g/cc, and t is the slab thickness in km. As the surficial ridges are rather ANOMALY (mgal) 30— 114 20... 10— STRAIGHT WALL PLAIN MARE NUBIUM \\\ ‘zow\\\\ Figure 24. i Gravity anomaly over the buried wall of the Straight Wall Plain. Mare fill is cross-ruled. The density contrast between the mare fill and basement is 0. 5 g cc. 115 irregular and are only schematically shown in Figure 24, the anomaly was calculated as if observed at the level of the plain itself. The problem of the density contrast between the mare material and the mare basement has already been discussed. In the calcula- tions here it was assumed that the mare fill is denser than the base- ment, the contrast being 0.5 g/cc. The form and amplitude of the resulting negative gravity anomaly over the buried wall of the Straight Wall Plain is also shown in Figure 24. It would appear, then, that on the buried ridge hypothesis the maria ridges should be characterized by negative gravity anomalies with amplitudes of perhaps some tens of milligals and widths considerably greater than the width of any one surficial ridge, reflecting the greater width of the buried structure beneath the mare surface. Co mpressional Origin According to this hypothesis the maria ridges are compression- al folds in the mare fill material formed by the subsidence and foundering of the mare basement by tilting and/or faulting. There- fore, the ridges would be located over those areas where the mare material is thickest, in contrast to , for example, the buried ridge hypothesis which requires exactly the opposite condition. Ronca (1965) gives a detailed consideration of subsidence, tilting, and com- pression as applied to Mare Humorum. He interprets Mare Humorum, a near-circular mare some 400 km in diameter, as a basin which 116 subsided by tilting and normal faulting and was filled with volcanic material which was compressed by the subsidence to form the well known system of ridges which arcs along the eastern side of the mare. These ridges should therefore mark the area of greatest subsidence of the mare basement and greatest thickness of mare fill. That the subsidence of the basement was at least partially due to tilting seems clear from the fact that craters such as Gassendi on the north and D0ppelmeyer on the south are strongly tipped toward the center of the mare. However, numerous rilles are located on the eastern and western sides of the mare, indicating that faulting may also have played a part in the subsidence. Ronca gives a maximum thickness of about 2 km for the mare fill under the ridges in Mare Humorum, with a thinning of this material to essentially nothing at the mare edges. In order to calculate the gravity anomaly that would exist over the maria ridges due to this thicker underlying material the hypothe- tical east-west section of Figure 25 was adOpted. This is a cross- section of Mare Humorum from the crater Mersenius D in the west to the crater Hippalus in the east. The surficial elevations and dimen- sions were obtained directly from Lunar Chart LAC 93 (Mare Humor- um) of 1962, with the curvature of the moon neglected. Following Ronca, the maximum thickness of the mare material is assumed to be about 2 km. In order to illustrate the effects of both tilting and fault- ing the mare basement is assumed to slepe uniformly to the maximum 117 03080000 000 030:0 000000 005. 30060000 05 005 0030000 00\w m .0 500000 00 00000308 0303 30:3 00 0002 003 00303000 308000 .3300» 000030300 003 .303 80000033 0002 «0 00300000000 0000 00 3003 .00 0009.00 tazz///////// mDA