A GRAVITATIONAE. lNVESTlGATIQN OF NIAGARAN‘ REEFS {N SOUTHEASTERN MECHIGAN Thesis. {Or the Segre» a? Ms. D. MECHIGAN STATE UNNERSWY Gary Gardm Santos M965 sat-5‘3 ~ w . LIBRARY Michigan State WI “WI W “I MI W WI mm “H “mm university This is to certify that the thesis entitled A Gravitational Investigation of Niagaran Reefs in Southeastern Michigan presented by Gary Gordon Servos has been accepted towards fulfillment of the requirements for Ph.D. Geology degree in 1 , -, (:Q'xfwré \\ \x// - Majoj professor/ Date February 4, 1965 0-169 ABSTRACT A GRAVITATIONAL INVESTIGATION OF NIAGARAN REEFS IN SOUTHEASTERN MICHIGAN by Gary Gordon Servos Precision detailed gravity surveys can detect Niagaran reefs buried at depths up to at least 3500 feet in the Michigan Basin. Three southeastern Michigan reefs, Marine City, Belle River Mills, and Berlin, are studied by the gravity method using graphical statistical and analytical techniques of interpretation. The characteristics and sources of the anomalies are studied and Optimum methods of reef anomaly enhancement are suggested. The gravity anomalies associated with reefs in the Michigan Basin are positive with a magnitude of about 0.2 milligals. The ratio of the width of the anomalies to the width of the reef varies from 2:1 to l.3:l depending on the technique used. There are negative anomalies parallel and adjacent to the reef anomalies. In areas where bedrock tOpography is known, these negative anomalies coincide with bedrock channels. Theoretical calculations using the configuration of the bedrock channels show that the channels can produce a gravity effect with the magnitude of the observed negative anomalies. Gary Gordon Servos The sources of the reef anomalies are lateral varia- tions in the density of the dolomite formations overlying and surrounding the reef. The reef mass alone cannot cause the anomaly. The graphical and statistical techniques isolate the anomalies, but many of the undesirable effects of shallow source anomalies are retained by these techniques. The analytical technique of downward continuation of an upward continued surface has a high resolution and eliminates the shallow source anomalies. The maximum resolution occurs when the upward continued surface is calculated at a height equal to the depth of the reef and then downward continued to a depth not greater than the reef. The second deri- vative of an upward continued surface has the highest resolution using Henderson's 1960 formula. The optimum enhancement occurs when the mesh interval used in these techniques is equal to one—half the reef depth. A GRAVITATIONAL INVESTIGATION OF NIAGARAN REEFS IN SOUTHEASTERN MICHIGAN By Gary Gordon Servos A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geology 1965 COPYRIGHT B1 GARY GCRDLN 1965 SERVCS ACKNOWLEDGMENTS The author wishes to express his sincere thanks to the following individuals and organizations. To Dr. W. J. Hinze for his sincere interest, patience, guidance, and helpful criticism during the study and pre- paration of this manuscript. To Dr. C. E. Prouty, Dr. H. B. Stonehouse, and Dr. J. W. Trow for reviewing the manuscript and for their helpful suggestions. To the McClure Oil Company, Alma, Michigan, parti- cularly Mr. Harold McClure, for financial assistance in the gathering of the field data. To Mr. D. W. Merritt for his assistance in preparing the data for the computer and for the use of several of his programs in interpretating the data. To Messers R. Kellogg, W. Keith, J. Bradley, R. Ehlinger, R. Shaw, D. Hill, J. Norris, R. Cranson, and D. Walker whose hard work made the collection of the data possible. To Michigan State University for free use of the C.D.C. 3600 computer. 11 TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF TABLES. LIST OF FIGURES Chapter I. INTRODUCTION . . , . General Statement Location and Physiography of Areas II. GRAVITY STUDY. Field Methods. ; Reduction of Data III. GEOLOGY. Regional Structure and Stratigraphy of Michigan Basin IV. INTERPRETATIONAL METHODS General Statement V. GRAVITY ANOMALIES FROM REEFS. . . VI. INTERPRETATION METHOD Regional Gravity of Study Area . . Marine City Reef Study . . . . Belle River Mills Reef Study. Berlin Reef Study . . . VII. SUMMARY. Detection of Reef Anomalies Characteristics of Reef Anomalies iii Page ii vi '._.l com ON DUI-4 l“ 14 22 22 A7 “7 79 111 . 111 Ill Sources of Reef Anomalies Recommendations for Further Study BIBLIOGRAPHY APPENDIX. iv Page 112 1.114 116 120 LIST OF TABLES Table Page I. Accuracy of Gravity Data . . . . . t . 13 VII. Reef Gravity, Average Conditions and Results in Three Regions . . . . . . . . A3 LIST OF FIGURES Figure Page 1. Location of Areas“ . . . . . . . . . 5 2. General Stratigraphy of the Michigan Basin . 15 3. Location of Reefs in the Michigan Basin . . 17 A. General Stratigraphy of Niagaran and Salina Groups . . . p . . . . . . . . 18 5. Structure of a Typical Reef . . . . . . l8 6. Bedrock Topography of Marine City and Belle River Mills Areas . . . . . . . 2O 7. Bedrock Lithology of Marine Cit y and Belle River Mills Areas . . . . . . . . 21 7a. Flow Chart of Interpretation Procedures . . 25 8. Regional Gravity from Bouguer Anomaly Profile 24 9. Template for Analytical Techniques . . . . 30 10° Geometrical Elements for Talwani's Two-Dimen- sional Calculations. . . . . . . . 35 ll. Geometrical Elements for Talwani's Three- Dimensional Calculations . . . . . . 38 12. Portion of Regional Gravity Map of Michigan . A6 13. Marine City Bouguer Gravity Anomaly Map . . “9 IA. Typical Bedrock Channel and Gravity Anomaly . 51 15. Cross—Section of Units Used in Three-Dimen- sional Gravity Calculation and Resulting Gravity Anomaly . . . . . . . . . 53 16. Mg/Ca Density Ratios and Theoreti.cal Gravity Anomaly. . . . . . . . . . . . 55 vi Figure Page 17. Marine City Cross-Profile Residual Map. . . 65 18. Marine City Least Squares Residual 0-3rd Degree, 500 foot Station Interval . . . 66 19. Marine City Least Squares Residual 0-5th Degree, 500 foot Station Interval . . . 67 20. Marine City Least Squares Residual 0-3rd Degree, 1000 foot Station Interval. . . 68 21. Marine City Least Squares Residual 0—5th Degree, 1000 foot Station Interval. . . 69 22. Marine City Interpolated Bouguer Gravity Map. 70 23. Marine City Bouguer Gravity Anomaly Upward Continued 2500' . . . . . . . . . 71 2A. Boundaries of Analytical Techniques. . ' . 72 25. Marine City Bouguer Gravity Anomaly Upward Continued 2500' and Downward Continued 5000' . . . . . . . . . . . . 73 26. Marine City Bouguer Gravity Anomaly Upward Continued 3000' and Downward Continued 5000' . . . . . . . . . . . . 7A 27. Marine City Bouguer Gravity Anomaly Upward Continued 5000' and Downward Continued 5000' s o e : .. o a a s o o o 75‘ 28. Marine City Second Derivative of 2500' of Upward Continued Surface . . . . . . 76 29. Marine City Second Derivative of 3000' of Upward Continued Surface . . . . . . 77 30. Marine City Second Derivative of 5000' of Upward Continued Murfare . . . . . . 78 31. Belle River Mills Bouguer Gravity Anomaly. . 85 32. Belle River Mills Cross—Profile Residual . . 86 33. Belle River Mills Least Squares Residual 0-3rd Degree, 500 foot Station Interval . 87 vii Figure Page 34. Belle River Mills Least Square Residual 0—5th Degree, 500 foot Station Interval . 88 35. Belle River Mills Least Square Residual O—3rd Degree, 1000 foot Station Interval. 89 36. Belle River Mills Least Square Residual O-5th Degree, 1000 foot Station Interval. 90 37. Belle River Mills Interpolated Bouguer Gravity Anomaly . . . . . . . . . 91 38. Belle River Mills Bouguer Gra ity Anomaly Upward Continued 2500' . . . 92 39. Belle River Mil s Bo ugier Gravity Anomaly Upward Continued 5000' and Downward Continued 5000' . . . . . . . . . 93 “0. Belle River Mills Second Derivative of 2500' Upward Continued Surface . . . . . . 94 Al. Belle River Mills Second Derivative of 3000' Upward Continued Surface . . . . . . 95 H2. Belle River Mills Second Derivative of 5000' Upward Continued Surface . . . . . . 96 43. Berlin Bouguer Gravity Anomaly . . . . . 101 HA. Berlin Least Square Residual 0-3rd Degree, 500 foot Station Interval. . . . . . 102 U5. Berlin Least Squares Residual 0— 5th Degree 500 foot Station Interval. . . . . 103 “6. Berlin Least Squares Residual 0- 3rd Degree, 1000 foot Station Interval . . . 10A 47. Berlin Least Squares Residual 0- 5th Degree, 1000 foot Station Interval . . . . 105 48. Berlin Interpolated Bouguer Gravity Anomaly . 106 U9. Berlin Bouguer Gravity Anomaly Upward Con- tinued 2500' . . . . . . . . . . 107 50. Berlin Second Derivative of 2500' Upward Con- tinued Surface . . . . . . . 108 viii Figure 51. 52. Berlin Second Derivative of Continued Surface Berlin Second Derivative of Continued Surface ix 3000' Upward 5000' Upward Page 109 CHAPTER I INTRODUCTION General Statement Exploration for oil and gas bearing Niagaran reefs has been emphasized in the Michigan Basin since 1960. This has resulted in the discovery of several reefs in southeastern Michigan in St. Clair and Macomb Counties. In additiion, isolated reefs have been found at several locations around the basin and, thus, the prospect of locating additional reefs is excellent. Exploration for the reefs has included both geolog— ical and geophysical techniques. Seismic investigations have had limited application, but the gravity method has been widely employed and is credited with making several major discoveries. Despite the wide use of gravity no detailed reports of case histories have been presented for reefs in the Michigan Basin. The purpose of this investigation is to study the gravity anomalies of known reefs in the Michigan Basin and to establish the optimum methods of interpretation and isolation of the anomalies. Although the results of gravity prospecting in the Michigan Basin have not been reported, several investigators l have discussed gravity prospecting for reefs. Yungul (1961) has produced the most comprehensive report on reef anomalies in several areas including the case histories of a reef in Ontario (Pohly, 1954). Geyer (1962), using theoretical approximations, concluded that reefs in the Michigan Basin could be found by gravity. Three well defined reefs of different relief, areal extent, and depth of burial were selected for study. A precision detailed gravity survey was conducted over the three reefs during the summers of 1962 and 1963. A high station density was used to obtain all the details of the gravity anomalies. The three reefs chosen are Belle River Mills, Marine City, and Berlin. The Belle River Mills reef is one of the larger reefs discovered. It is approximately 3000 feet wide and two miles in length. It is buried at a depth of 2300 feet below the surface and has a relief of 300 feet. The Marine City reef is three miles south of the Belle River Mills reef and is buried at the same depth. It consists of two circular cone shaped pinnacles on a broad base. The pinnacles are one mile apart and have a relief of 250 and 300 feet. The Marine City reef contains less reef mass than the Belle River Mills reef. The Berlin reef is located thirty miles west of the Marine City and Belle River Mills reefs and is buried at a depth of 3500 feet. It has a width of 2500 feet and a length of one mile. The relief is about 200 feet. Séveral graphical, statistical, and analytical techniques were used in the interpretation and isolation of the reefs. The techniques used include cross—profiles, least squares polynomial analysis, upward continuation, downward continuation and second derivatives. Two—dimen— sional and three-dimensional gravity formulas were used to calculate the theoretical gravity of the reefs. All com- putations were performed on a digital computer. Location and Physiography of Areas The areas of study, shown in Figure l, are located in St. Clair and Macomb Counties, Michigan. The Marine City and Belle River Mills areas are in the extreme eastern part of St. Clair County along the St. Clair River. This area lies between latitude 42°40'00” N and 42°48'30" N and longitudes 82°30'00" w and 82°35‘00" w. The Berlin area is located along the northern Macomb and southern St. Clair County line. This area lies between latitudes 42°52'00" N and ”2°56'30" N and longitudes 82"53'u5" w and 82°58'45" W. Both the Marine City and Belle River Mills areas I are situated in the Erie—Huron Lowland, a tOpographic sub— province in the Southern Peninsula of Michigan, (Newcombe, 1933). This sub-province is characterized by surficial glacial lake clays and lake bed sands. This area was covered by several glacial lake substages of the Wisconsin glacial stage (Leverett, 1939). This area is generally flat with a maximum relief of fifty-five feet and the elevation gradients of five to ten feet per mile. The only exceptions are the several stream channels in the area which have a maximum relief of thirty feet. The Berlin area is situated in the Thumb Upland, a tOpographic sub—province characterized by several moraines (Newcomb, 1933). The immediate area of the Berlin survey is flat with a maximum elevation difference of about forty— five feet. The elevation gradients also are five to ten feet per mile. Both areas are divided by a network of sectionjdmmzand intermediate roads. Generally the area consists of privately owned farms. Primary drainage in the Marine City-Belle River Mills area is to the south and east. The major tributary is the Belle River. The Berlin area exhibits little or no drainage pattern and there are no major streams in the area. r0 SANILAC \ LAPEER ST. CLAIR RINARE \ V 0,,EELLE RlyER OAKLAND MAC MB V I AR A 20 MILES LOCATION OF AREAS FIGURE l CHAPTER II GRAVITY STUDY Field Methods The areal extent of the gravity surveys was selected to cover the reefs adequately and include the regional gravity of each area. The existing road network allowed good coverage, but in addition to the road traverses, cross- country traverses were placed in the immediate vicinity of the reefs at one—half mile intervals. These cross- country traverses were made in the areas whenever possible and in all cases at least one cross—country traverse was placed in the sections associated with the reefs. A station spacing of five hundred feet was selected for the survey. The station elevations were established with a Zeiss self-leveling level and elevation control was obtained from three U. S. Geological Survey and several Michigan State Highway Department bench marks. All traverseS' were closed and cross—country lines were tied into established elevations. Horizontal distances were determined by stadia intervals and control was carried from road intersection to road intersection to eliminate cummulative error. Two exploration type gravity meters were used in the survey. These were World Wide meter number 45 and Worden number 99. These meters had calibration constants of 0.10093 and 0.0995(1) mg. per scale division respectively. These constants were checked prior to the beginning of the survey each summer and midway through the summer. Both meters measure the relative acceleration of gravity to an accuracy of 0.01 mg. The meters are subject to time variations or drift even though they are temperature compensated and barometrically controlled. These time variations are a result of tempera- ture changes, tidal variations, spring fatigue, and handling of the meter. To determine these variations a check reading was made at a number of pre-established base stations at least once every hour during the course of the survey. A primary base was established near the center of each area and sub—bases were established at strategic points by the base-lOOping method. The Belle River Mills and the Marine City areas are adjacent and the primary bases of each area were tied to allow correlation. The Berlin area was not tied to the other two surveys because it is thirty miles away. Gravity readings were made every five hundred feet at the pro-established elevation. These readings were tied to the base station by the hourly drift check. In addition, a number of stations were reread at various times during the course of the survey to establish the accuracy of the readings. At each gravity station the meter was read until two values were obtained which did not differ by more than 0.2 scale divisions or 0.02 mg. Reduction of Data Introduction Observed gravity, to be useful in geological studies must be corrected for station elevation, latitude, and terrain. These corrections are applied to each station. The resulting values are called the Bouguer gravity anomaly. The complete Bouguer gravity anomaly was calculated on a digital computer according to the following formula: Gcbs g go -g£ +ge&m +gt (l) where Gcbg = complete Bouguer gravity anomaly go = observed gravity g, = latitude correction ge&m = combined elevation and mass correction gt = terrain correction. Observed Gravity The observed gravity values are obtained by correcting the meter readings in scale divisions for drift, and then multiplying the values by the calibration constant of the meter. The drift is determined from graphs of hourly base—readings. When the drift exceeded one scale division per hour, the drift check readings were decreased to three— quarters of an hour. Latitude Correction The Earth's gravity increases from the equator to the poles. The latitude correction takes into account this change in gravity. Latitude corrections are made from a base latitude by multiplying the latitude distance of each station by a constant, K. Nettleton (1940) determined K to be 1.307 Sin2G mg. per mile, where G is the mean latitude of the survey area. In the survey areas of this study a base latitude of 42°40'00" N was used for the Marine City- Belle River Mills area, and a base latitude of 42°52'00" N for the Berlin area. The value of K is 0.0002A7A mg. per foot for these areas. The stations of the three surveys were placed on the Michigan Coordinate System, east zone, a plane-coordinate system established by the U. S. Coast and Geodetic Survey. This allows each station to have x (ordinate) and y (abcissa) coordinates which are on a rectangular grid system. In the process of reducing the data by the digital computer, the Michigan Coordinate System was rotated to correspond with latitude and the latitude correction was made in the normal manner . 10 Elevation and Mass Correction The elevation or free-air correction and the mass or Bouguer correction are often combined and called the elevation and mass correction. The combined correction takes into account the vertical decrease of gravity with an increase in elevation and the increase in gravity due to the attraction of the material between the datum and individual stations. This correction is calculated from the combined formula: ge&m = (0.09406 — 0.0l276p)h (2) where h = elevation difference between the datum and the gravity station in feet 0 = density of surface material in g/cc. The datum to which the gravity was reduced was chosen near the lowest elevation of the surveys. Density_Determination The determination of the correct density for the near surface material in the survey areas is extremely important. A density value for glacial drift is often given in the literature as 1.8 g/cc. This value does not appear to be correct for near surface glacial drift in eastern Michigan. A density value of 2.1 g/cc was determined by the Nettleton density profile method at several locations in the vicinity of the survey areas. Klasner (196A) ll determined a density of 2.15 g/cc for the near surface drift in western Michigan. An incorrect density of 0.3 g/cc and relief of thirty feet will cause the gravity values to be in error by about 0.12 mg. In the search for reefs this value alone is close to three times the desired accuracy. In areas with no t0pography, a larger error in density can be tolerated. However, in areas with relief it is very important to deter- mine the desnity with the highest precision possible. Terrain Correction The relief in the survey areas was low enough that no terrain corrections were needed. Where the local variations of the several stream valleys in the areas were encountered, stations were placed far enough away from the feature that the effect was negligible or the stations were not used. The placing of stations in these areas was determined from correction curves calculated by Hubbert (1948). Summary of Accuracy In making gravity reductions, there are several factors which cause errors in the Bouguer gravity anomaly. These are: 1. Errors in observed gravity 2. Errors in elevation 3. Errors in latitude 4. Errors in assumed density of the glacial drift. 12 To check the accuracy of the gravity readings for the Belle River Mills survey, 16 stations were reread during the survey. The standard deviation for the repeated stations is i 0.01 mg. The errors in elevation affect the elevation and mass correction. Thirty—six closures were made during the survey. The standard deviation of the closures is $0.09 feet. The maximum possible error in the elevation and mass correction caused by 0.09 foot error, using a density of 2.1 g/cc, is 0.006 mg. The latitude measurements were made to an accuracy of fifty feet. They were measured on a base map with a scale of 1:12000. The maximum error from the latitude correction is 0.012 mg. An incorrect density value of 0.1 g/cc with a maximum change in elevation between any two stations of 10 feet will cause an error of 0.01 mg. The formula for calculating this error is: Error = 0.001280”h where 0.00128 = magnitude of error in milligals per foot for each 0.1 g/cc error in density 0‘ = error in density in units of 0.1 g/cc h = maximum relief in feet. The maximum error possible considering these sources is :0.038 mg. 13 Table 1 shows a comparison of the maximum errors for the Belle River Mills, Marine City, and Berlin Surveys. The errors for the Marine City and Berlin surveys were cal- culated in the same manner as those of the Belle River Mills survey. TABLE 1 ACCURACY OF GRAVITY DATA .wE CH manfimmom moppm Esefixmz .mcoapMpm ozp cmmzpmn .pm OH mo mono uanMfiQ mCOHpm>mHm cam popnm muamcma uoxw H.o mom monnm Esefixmz .pmmm om on mama Izoo¢ mCOHpMpm .we CH popnm mpzpfipmq Ezefixmz .oo\w H.m mo mufimcma gem nonsmoao no soap ImH>mQ UnmUCMpm wean: m: poppm Ewe Ezefixmz pmmm CH mmmzmoao go cofipmfi>ma unaccepm mmhzmoao coapm>mam mo Monasz .m& CH mCOHpmum pmmnmm mo soapmfi>oa chmccmpm ummnom mCOHpmpm >ua>mnw mo honezz L 10.038 01 0.006 0.012 0. .09 0 36 16 27 30 10.041 01 0.004 0.012 0. 06 30 0. l3 14 10.043 01 0.007 0.012 0. 0.11 CHAPTER III GEOLOGY Regional Structure and Stratigraphy of Michigan Basin The Michigan Basin is an oval intracratonic sedimen- tary basin enclosed by the Findlay, Algonquin, Kankakee and Wisconsin Arches, and the Canadian Shield. The development of the basin probably began in middle Silurian time (Ehlers and Kesling, 1962). During the middle Silurian (Niagaran Series) a system of reefs was formed on shelf areas surround- ing the Michigan Basin. Slight rises in the areas bordering the Michigan Basin, accompanied by a barrier of Niagaran reefs, caused a restriction of the basin late in Silurian time. The Michigan Basin continued to receive sediments throughout the Paleozoic period. The general stratigraphy of the basin is shown in Figure 2 (after the Michigan Geological Survey). The Niagaran and lower Cayugan Series of the Silurian, which are of major interest in this study, consists of the Niagaran Group (or Guelph) and the Salina Group respectively. Lowenstam (1950) suggested that Niagaran reefs possibly surround the entire Michigan Basin. Isolated reefs which have been found around the *margins of the basin l4 15 STRATIGRAPHIC SUCCESSION IN MICHIGAN PLEISTOCENE NOM NCLAIURE W oauumn 01 cousnunou nu D-m mm W "“570le “I II. 5.9—- locx ““va GROUP FORMATION MEMIER nut-Ina»! POTYSVILH Al IXMDIIM GKINNAYMN l6 substantiate this (Figure 3). Reefs also are present in the Silurian outcrOps on Drummond Island, Michigan (Manley, 1964). Generally the reefs developed around the basin are of the pinnacle type. Niagaran Structure and Stratigraphy of Stg'Clair County The regional dip of the geological formations in this area is in the order of 30—40 feet per mile. This becomes an important factor in searching for reefs in the Michigan Basin as the gravity method is useless if the reef is below a limiting depth. The general stratigraphy of the Niagaran and Salina groups in the St. Clair area is shown in Figure 4 (Alguire, 1962). There is a possibility that the carbonate sequences of the Niagaran and Salina Groups are regionally limestone and only locally dolomitized about the reefs (Jodry, 1965). Typical reefs in the St. Clair County area have relief up to 300 feet with an areal extent usually less than one half mile in width and one mile in length. Basinward the reefs are more pinnacle in nature and have a smaller areal extent. The structure of a typical reef is shown by a cross- section through the Marine City reef (Figure 5, Alguire, 1962). This cross-section includes the stratigraphic units from the Clinton shale (Niagaran) through the B-Salt member of the Salina group. The entire geologic column from the reef facies upward show some degree of doming over the reef 17 LOCATION OF REEFS IN MICHIGAN FIGURE 3 18. NIAGARAN AND SALINA STRATIGRAPHY Formation Unit Description G DOLOMITE: brown, finely crystalline; shaly dolomite; some anhydrite. F SALT: in thick beds separated by beds of shale, shaly dolomite, gray and buff, I and brown, crystalline dolomite; anhydrite nearly always present. I E SHALE: with argillaceous, gray and buff dolomite. I g D SALT: nearly pure; thin partings of buff dolomite. I a C SHALE: gray, dolomitic. I m B SALT: thick salt beds with thin dolomite layers. I DOLOMITE: brown, brown gray, gray and dark gray, finely crystalline; some I A-2 dark bituminous shale. SALT: where salt is absent the base of A-2 is marked by anhydrite. DOLOMITE: buff, brown, brown gray and dark gray, dense to medium crystalline; A-l some dark bituminous shale. ANHYDRITE: at base. 2 m Guelph- DOLOMITE: tan, gray brown and brown, very finely to coarsely crystalline and a 8 Lockport vugular; often finely laminated near top. I O m 01‘ . . . . I S 0 Niagaran DOLOMITE. light and dark gray mottled, finely crystalline. I: DOLOMITE: light to blue gray, finely to coarsely crystalline. STRUCTURE AND STRATIGRAPHY OF MIDDLE SILURIAN NIAGARAN FIGURE 4 A PART OF THE MARINE CITY REEF FIELD, ST. CLAIR COUNTY, MICHIGAN. Mme/or «K’ESALINA I 3 C < o S 2 I lief—f —-—- ‘ SILURIAN __. W ‘A I L L. L L. L. L P—- I/Q “LE ‘———0 I . 2 .- 3 J J J J J J J J J J Jé; J J J J Jiz" J J .I J J J J J J J J J J); J J J J J{ J J J' J J J J J J J J J J g) J J .J J Jj' .J J ‘ J ' J . l I J J ,I B EVAPORITE J J J J J :41, JJJJJJJJJ J J 41'; I“. J J J J .I J J J J J I {'7'” I J J J J J J J J J J " 2" 1...] 74' ; x“ 1"." .J \JJJJJ J A- 2 EVAPORITEJ -J .I I A- I CARBONATE J J .J g; AFTER ALGUIRE AND UPPER SILURIAN SALINA STRATA ACROSS VERTICAL SCALE 6.6x HORIZONTAL SCALE .5 L L W'f‘f‘ L I WNW” KANT“ I J I I I— p— ;, "GS 1962 FIGURE 5 ANHYORI YE —I300 HAIIYE —I4OO “Tr- GAS -Isoo 0“- -I600 -I700 -IOOO AFTER ALGUIRE l9 (Ells, 1964). In most cases this doming of the sediments can be accounted for by compaction. Details of the structural and stratigraphic develop— ment of reefs have been reported by many authors (Cummings and Shrock, 1928), (Lowenstam, 1950, 1957), (Textoris and Carozzi, 1964). Bedrock Geology The glacial drift deposits covering the St. Clair County area consist primarily of lake bed clays and sands. Is0pach maps of the glacial drift (Brown, 1963) show varia— tions in the drift thickness in the order of 200 feet. Structure contours of the bedrock surface beneath the drift show numerous bedrock channels (Figure 6, Brown, 1963). Klasner (1964) showed that gravity can be used successfully to determine the location of these bedrock channels. Bedrock channels with depths of 200 feet can cause negative gravity anomalies which will tend to mask the anomalies of the reefs. According to Brown (1963) the bedrock lithology varies from older to younger beds to the west as illustrated in Figure 7. These changes in bedrock lithology are important in the theoretical gravity to determine the bedrock t0po- graphic effects, as variations in lithology change the density contrasts between the bedrock and glacial drift. \J \‘\;T ,l, ”I I \ CerI' BROWN [963 BEDROCK TOPOGRAPHY OF MARINE CITY AND BELLE RIVER MILLS AREAS c.I.=2o' FIGURE 6 21. O o O #1 . @ O . T A» V s . ' .. fl after BROWN.I9$3I BEDROCK LITHOLOGY OF MARINE CITY AND BELLE RIVER MILLS AREAS FIGURE 7 CHAPTER IV INTERPRETATIONAL METHODS General Statement Gravity measurementshave been used for a number of years as an eXploration tool, but the confidence placed in the method has been limited. However, in the last decade confidence in the gravity method has increased markedly for several reasons. First, a better knowledge of geology by geOphySicists and a better understanding of the applica- tion of geophysics by the geologist has contributed much to the change in attitude. Second, previous studies have defined the usefulness and validity of the gravity method for various geologic Situations. Third, a better knowledge of the assumptions and variables used in gravity interpre— tation has been gained and applied in evaluating gravity data. New and useful techniques such as density logging are and will be a great help in future gravity interpre— tations. The determination of the correct density contrast between geological formations is often difficult, but is extremely important in gravity interpretation. The gravity method depends on horizontal changes in density and, fortunately, geological conditions produce these density con- trasts. 22 23 An inherent problem in gravity interpretation is the ambiguity of results. Skeels (1950) has shown that any gravity anormaly produced by a mass (x) can be reproduced by another mass (y) at a different depth. Studies in the last decade have helped to overcome the ambiguity by defining the types of anomalies produced by various geological features in different geological situations. Regional gravity surveys are widely used, but detailed surveys have not been fully utilized in the search for small geologic features. Noise levels are constantly being lowered as detailed gravity survey are used more frequently. When the data is collected in the most accurate form and pr0per assumptions made in the interpretation, the detailed survey can be used with confidence. Digital computers now allow many new and older inter— pretational techniques to be used which have been impractical due to involved and time consuming arithmetic. There has been much discussion and disagreement on graphical versus analytical and statistical techniques in interpretation. The graphical techniques are simple, but are subject to per— sonal bias of the interpreter while the analytical techniques have a higher resolving power and are readily performed on the digital computer. The statistical methods also are easily adapted to the computer and are subject to less bias than the graphical methods. Each method has its use in gravity interpretation given the pr0per set of geological and ge0physical conditions. Theory of Techniques is d for Imi errretation Graphical, statistical, and analytical techniques were used in the inte pretat L‘On of the reef anomalies as one of the purp ses of this study is to determine optimum methods of inte pretation for a particular geologic situation. A 7'“ 1“ flow diagram, shown in igure 7a, illustrates the step by step procedure followed in the interpretation and the re— sults of each particular method. The theory of these techniques is presented in the following sections. Cross—Profiles GraphicalLTechQi que ' The cross—profile method was used to determine the relationship of the residual anomaly obtained using a gra aph nical technique to those obtained using analytical and statistical techniques. This method consists of drawing a smooth curve of the estimated regional gravity gradient along a profile as shown in Figure 8. CROSS PROFILE METHOD BOUGUER GRAVITY PROFILE _ ESTIMATED REGIONAL ‘ FIGURE 8 on mmsoi mmmzomoomd zo_._.<.rmmn_mw._.z_ L0 .5310 30.7. 25 1d a. IITIR I a we“! I w I Folii LI H «.6 1. 313.» 58:10 In... T. I _.I. 1 JII_II4 .2...» 2...: II 32!.6 1...: _ Ta . {to E...» T. ,c 26 This is done for all profiles of gravity values which inter— sect another profile. If the regional gradient selected is a good approximation, the point of intersection on two pro— files will agree in value. If the values do not agree, then the approximated regional greadient is adjusted until the values at the intersection points agree and are geologi— cally reasonable. When all values of intersection agree, it is assumed the regional gradient has been correctly determined. The approximated regional gravity is then removed from the“ Bouguer gravity values leaving the residual gravity. This method has the advantage of being a Simple method to obtain the residual and permits the knowledge of an area to be used. The results from this method are, however, subject to the personal bias of the interpreter which can be both an advantage and a disadvantage. The method is limited if the residual anomalies are low in magnitude or the regional gradients are complex. Least Squares Polynomial Statistical Analysis This method consists of fitting a polynomial equation to a three—dimensional surface. In this case the surface consists of x, y coordinate points and a gravity value at each point giving the third dimension in the z direction. The polynomial equation is fitted to the surface to a degree where the regional gravity is adequately defined. 27 The portion Of the surface which is not fitted exactly by the equation is considered the residual. The success of this approach depends on the validity Of the assumption that the regional can be described accurately by a polynomial equa— tion. The least squares principle states that the coeffi— cients of the polynomial equation must be such to make 21(51)2 a minimum, where e is the residual or the portion of the surface not fitted exactly by the polynomial equation. The basic polynomial equation used is AgRegional = 0(00 + 410x + 410y + .O..+(¥qupyq (4) where the 6(‘S are the coefficients of the equation and (p, q) is the degree of the equation. The equation can be solved easily by matrices on a digital computer and the resulting gravity value expression is subtracted from the Bouguer gravity to give the residual. Analytical Techniques Upward and Downward Continuation Often in the interpretation of gravity data it is desired to study the gravitational field on a plane above or below the original plane of observation. The upward continuation method results in moving the plane of Obser- vation further away from the source of anomalies. The effect of this method is to eliminate small sharp gradient anomalies from sources close to the plane of observation 28 further away from the source of anomalies. The effect Of this method is to eliminate small sharp gradient anomalies from sources close to the plane of observation and to retain the broad lower gradient anomalies caused by masses at a greater depth. The downward continuation method allows the plane of Observation to be moved to levels near the masses producing the anomalies. This results in an enhancement and increased resolution of the anomaly. Both upward and downward continuation have proven highly useful in gravity interpretation. The following mathematical evaluation based on Henderson's (1960) development resultsixia practical approxi— mation for both the upward continuation and downward contin— uation equations. Basicaly, the problem is to compute the gravity value A0(x, y, 2,) above and below the plane of observation. The origin of the rightvhanded coordinate system is taken at the point where the field is to be computed, with the z—axis positive downward. The integral solving the Dirichlet problem for a plane (the upward continuation integral) in polar coordinates is ”m maAggLr) r dr (5) A¢ (—ma) = o (r2+m2q2)3/2 m = l, 2, 3, ...., n 29 where a is the mesh interval Of the gravity values, m is the number of mesh units above the original plane, and En AdIr)= 2n A¢(r,e)de. (6) O The physical meaning of A; on (r) is the average value Of Ad circles of radius 1' about a point. Experimentally it has been found that radii Of r = 0, a, czf2: a 5, aV8: aVIgl a V25, a‘YED, a YI36, a V271 and a I625 adequately sample the field. The number of mesh points falling on the circles having these radii are respectively 1, 4, 4, 8, 4, 8, l2, l2, 8, 8, and 12 as shown in Figure 9. Next a Lagrange interpolation polynomial is fitted to A¢ (0) and the n values A¢ (—ma) computed from equa- tion 5 to Obtain the approximation formula, n n no. A¢(a) 2 2 (-l) a (z+a)(a+2a) (z+na) A¢(—ma). (7) m=o an(s+ma) (n-m)lm! From eXperimental work it has been found that the approxima- tions are good for n<5. The accuracy of equation 7 depends on the accuracy of A¢(-ma) as computed from the upward continuation integral, equation 5. A numerical integration employing a mean value theorem over each integral r érér is carried out. The i 1+1 integral in equation 5 is replaced by the sum :1 -l ri‘I’l . 2 2 ‘1/2 AIM-ma) = 2 ”HF r1) A¢(r)dr] ma [r1 +_(ma)] 2 2 ‘5 —l_I [ri+l + (ma)] + 0 rn/ (8) 30 TEMPLATE FOR ANALYTICAL METHODS FIGURE 9 31 By setting a equal to unity and successively evaluating equation 8 for m = 1, 2, 3, 4, 5, the five sets of coefi— cients adopted for upward continuation are Obtained. The working equation is given as 10 A¢(~ma) : 12 A; (r1) K (ri,m) (9) =0 where K (r1, m) is the set of coefficients which Operate on the center value and the ten ring~averages values, A$(ri), to give A¢ at ma mesh units above the original plane. For downward continuation, z is set equal to a, 2a, 3a,, 4a,’ 5a,, in equation 7. This results in the calculation of the gravity on these levels below 2 = 0, using the same ten ring averages, A? (r1). The working equation is given as 10 MW) = Z A¢(P1)D(ri k) (10) i=0 ’ where D (r1,k) is the set of coefficients for computing A¢ K mesh units below the original plane. Second Derivative The second derivative method has proved useful for gravity interpretation. Its importance arises from the fact that the second derivative analysis tends to emphasize the smaller, shallower geologic features at the expense of larger, regional features. The subject of second derivatives 32 is treated by many authors, including Peters, (1949); Elkins (1951); Henderson and Zietz (1949); Rosenbach (1953), and Henderson (1960). Henderson's method was used in this study. The comprehensive character of equation 5 for upward continuation is demonstrated in that it can be differentiated to give the first and second derivatives of the gravity field. The second derivative equation uses the same ten ring averages, AT (ri). Equation 7 can be written in the following equivalent determinantal form: 2 n O l -z/a (z/a) ... (~z/a) A¢(0) 1 0 0 o A¢(—a) l 1 l l A¢(Z) : - IV'l—l A¢(_?a) l 2 2 2n (11) 2 n AIM-1’18.) l n n .... n where (V) is the Vandermode determinant Obtained by deleting the first two rows and columns of equation 11. If n equals 5 in equation 11 and differentiating with respect to z the first derivative equation is Obtained. I n q 2 3 I. I I. I) -l -2(z/a) -3(z/a) -4(z/a) —‘)(z/a) flow) 1 2 0 3 9 9 Ache) 1 1 1 1 1 1 - i£§%l_ i-La;v!)'1 LOI-2a) 1 : 22 23 2“ 25 (12) col-3a) 1 3 32 33 3“ 35 I I ¢.(—La) 1 u u? A3 a“ u5 ' ;.(-5a> 1 5 52 53 5“ 5S 33 If 2:0 in equation 12, first vertical derivatives can be calculated on the plane of Observation by the equation (~11m5! r) 13¢)(v‘lna) (13/ 1 mc(m—l)!(5-m)! ' Q ) L‘) O- I SDI}—J l 5 1+ + + + A¢(O)+ E Z In- Q) :11 5:0 To Obtain the sets of coefficients for computing [MAM/azjz:k using the ten ring averages, 03 (ri), setting a equal to unity, and putting the working upward continuation equation into equation 12, the first derivative working equation is obtained, 10 z=k igoa$ D'(ri,k), (in) (I MM») 3 s where D' (r k) are the first vertical derivative coeffi— i) cients for the apprOpriate K mesh units below the plane of Observation. Similiarly the second vertical derivative formula can be obtained by differentiating equation 12 with respect to Z. 1 J A 3 «0(z/a) 19(2/312 —20(:/a)3 “(0) 1 O J O 0 0 MI-a) 1 1 1 1 1 1 gig-fl : _ (a2IvII'1 ao(-.‘a) 1 2 .13 g3 3“ 25 (151 A¢(-33) 1 3 32 33 3“ 35 A.(_ua) 1 A u? A3 u“ as AoI-Sa) 1 z 3* 53 5“ 55 ‘ 34 The resulting working equation for the second vertical derivative is 2 10 _ .a (19) = 2 11¢ (ri)D'" (ri,k) (16) 35 B=k i=0 where D" (r k) are the coefficients of the second derivative. 1, Theoretical Gravity Formulas Talwani's Gravity Computations for Two-Dimensional Bodies In geological and geOphysical studies, many of the structures of interest are horizontally linear and can be approximated by two—dimensional forms of analysis. The outer boundarycfi‘any two dimensional body can be approximated by a polygon. This approximation can be made as accurate as one wishes by making the number of sides of the polygon sufficiently large. The vertical component of gravity due to the polygon can be obtained at any given point and there are no limits on the Size or position of the body. The digital computer allows the complex expression for the vertical component of gravity to be solved easily and rapidly. Given an n sided polygon ABCDE, Figure 10. FIGURE IO Geometrical elements for Talwani's 2-0 calculations. - Let P be the point at which the gravitational attrac— tion will be calculated. The point P lies in the xz plane as does the polygon. Let a be definede%3positive downwards and a is measured from the positive x-axis downward. The vertical component of gravity at the origin (P) from the two-dimensional polygon is 2Go§zd0 (17) where G is the universal gravitational constant and P the volume density differential, with the line integral being. taken around the outer boundry of the polygon (Hubbert, 1948). The above integral is then evaluated for the given polygon. The contribution of a Side of the polygon, say, Side BC_can 36 be computed. The side CB is extended to meet the xeaxis at q at an angle a1. Let P0 = a1, then B = x tane (18) for any point R on Side BC and z = (xvai) tanai. (19) From equations 18 and 19 a = aivtanetanq)i (20) tanOi-tane C a tanetan¢ now zde = tin —tane 1 d6 = Bi. (21) BC B I1 The vertical component Of gravity V can now be given as m v = 20p 2 5 i=1 i (22) with the summations being made over the n Sides of the polygon. The integral for Zi must now be solved. For the general case it can by shown that cosei(tanei—tan(¢i) i = aisin¢icos¢i ei—ei+l+tan¢i loge (23) cosei+l(tanei+l-tan¢i where 61 = tan"1 ii X1 I1 = tan-1 z1+1'zi x1+1 ‘ x1 and a = x + 5 1+1 ‘ xi 1 1+1 1+1 _ 37 It Should be noted that 6i, 0 ¢. i+l’ i’ be explicitly expressed in terms of the xi's and z. s. This is advantageous as ‘the easiest way to define the outer edges of a body is to Specify the coordinates of adjacent points or the vertices of the body. Talwani's Gravity Computations for Three Dimensional Bodies of Arbitrary Shape A three—dimensional body can be represented by contours on the body. By making the number of sides of a polygon sufficiently large, any irregular outline can be CIOSely approximated. If each contour of the three«dimenslonal body is replaced by polygonal lamina, the gravitational attraction caused by the lamina can be calculated at any pcint external of the body. Thus, by interpolating between Contour lines and numerical integration, the gravitational attraction of a three dimensional body can be computed. 38 'Z-QVIS y-qns \ 0., \I J HGURE II C- (‘§?I’Y£ol)e) Geometrical Elements for Talwani's 3-D Calculation 39 Figure 11 shows geometrically the elements involved in the gravity computations for a three—dimensional body. Point P represents the point at which the gravitational attraction of the three-dimensional mass will be calculated. Point P also is the origin of a left handed cartesian coordinate system with the z—axis positive downward. A contour on the surface of the body is represented by the polygonal lamina ABCDEF‘-°' of infinitesimal thickness dz. Let Ag“ be the gravitational attraction at P from ABCDEF Then Ag = de (24) where V is the attraction caused by ABCDEF --- per unit thickness. V can be expressed by a surface integral, and this can be reduced to two line integrals along the boundary of ABCDEF°°°. Now V = Gp[§dW—§B/(r2+ zz)%dw], (25) where G is the universal gravitational constant, p is the volume density differential of the lamina and z, W and r are the cylindrical coordinates used to define the boundary of ABCDEF°". If P' is the projection of P on the plane ABCDEF--'. then PP' equals 2, The line r is the radius vector in the plane ABCDEF---, and V is the angle which it makes with an arbitrary x—axis in this plane, where V is positive in a clockwise sense from the positive x-axis. 40 If we evaluate the contribution of the two line inte— grals from side BC, the first integral gives §dw = wi+l - wi (26) —-—> ...—...) for P'C and P'B. The second integral can be evaluated by drawing P'J perpendicular from P' to BC. Let P‘J equal P and e and ci be respectively the angles which EP' and CP' i i make with BC. It can be seen from Figure 11 that Pi = sin (ci—Ii+l+w) (27) Making this substitution, and noting that Pi’ 6i, and wi+l are all constants, so that w is the only variable left, the integral can then be solved to give the value, arc sin Z cos 6i - arc sin a COS(Ii - 2 2 A. “—777“. (28’ (P1 +z ) (Pi +5 ) Thus (29) V = Gp {Ii+l - Ii — arc sin 8 COS¢i +arc sin 5 cosei c c L . c c.» ' (P12+B2)2 (Pid+8é)2 The above eXpression is the attraction caused by the triangular lamina P'BC per unit thickness at point P. The total attrac- tion is then Obtained by summing V over the n Sides of the polygon to Obtain n a V = Gp Z w — w. - arc sin Z COS¢i + arc sin a COSGi I _i=l “1 l .(__.____P 2,82 )2 *0: 2+;Eja’. i i jj (30) Al The terms P 0056 and cos¢>i can be EXpressed 1’ W1: Vi+l, i in terms of x the coordinates of B, and x. the 1’ yi’ 1+1’ y1+1’ coordinates of C. Thus V can be expressed in terms of coordinates of the vertices of the polygon ABCDEF--°. The attraction caused by equation 30 is only for one lamina. The total attraction Ag from the mass can be evaluated by integrating equation 24 between z—tOp and z—bottom. Thus /r% tOp 2 v a s. (31) Ag total = B // bottom CHAPTER V GRAVITY ANOMALIES FROM REEFS Yungul (1961) reviewed the problem of gravity eXplor— ation for reefs and answered some of the classical questions concerning reefs and gravity. Those questions which Yungul sought answers to are: ”DO reefs create recognizable gravity anomalies?” and "If they do, what causes these anomalies?" At the time of his review, Yungul found liter— ature concerning reefs and gravity for three geologic provinces. His summary of the case histories prior to 1961 is shown in Table II which is shown on the following page. A summary of the literature prior to 1961 as assembled by Yungul is as follows: 1. "Reefs frequently Show recognizable gravity_ anomalies which may be (a) a simple high, (b) a high with a negative rim around it, (c) a low with a positive tendency in the center, or (d) a simple low. Most frequently it is a high with a negative rim around it, like a 'sombrero." 2. When the anomaly is of the sombrero type or a simple high, its intensity is of the order of +0.5 mg. This is greater than an allowable density contrast between the reef mass and the enclosing sediments could produce. What is more, a gravity high may be present even when the reef density is less than that of the enclosing sediments. Clayton (1951) reports that at North Snyder the cores Show the reef is less dense than the surrounding Shales. Yet the anomaly is +0.6 mg. 42 .43 mamnm m.H mm.o+ xcmam m mm» nsomhmoamo mbHEoHOQ o.H oom Loop moamnae mmx ”mema Loop pawn Lo>o mcfimpmz cofimmm psocufiz Lo meaccficp wmxmq o: ”Amman memo pawn new nacho m.a 2.0+ w a pawn spam hump OHBHEoAOQ a n.H mom comm OLE OHHE\wEm swag m mo swan Acflmmm x was aszofimmp m m . ncmfipfiiv new: Lm>o pm“: wow mfimdm spcmm oomo m.u com coon mmxoe m.m o.o+ .xcmfia Amoos ummz AmOHHEV we we chaposhbm mcfismhn cofipmsbom xoom Ammflflsv Apmmmv Aummav coca: I. Hmmmm cacaw>cm Loom Loom Lo Loom LO EOpuom oneN AV\, HmeoAmmm can“: sesame some ob cofimmm peace Hannammm mbfl>mho smofiomo acambmooo _ Aaomfi .stcsw Access monumm mmmme map 7H mun.mmm cza moneHozoo muqmmsa iwuHsamo ammm 3. 10. ll. 12. 44 "The existence of a negative rim has so far not been satisfactorily eXplained. The gravity highs are too narrow to be generated by masses at specified reef depths. When the anomaly is of the sombrero type, the width of the positive is of the order of the width of the reef, irrespective of the reef depth. The local (residual) anomalies are frequently located near the apexes of regional gravity highs. As far as west Texas is concerned, the reef bottoms are local positive reliefs. We have no such data for the other regions. Thinning and draping in the shales over and around the reefs are more than that indicated by conventional calculations of differential compaction. Either because of certain underlying causes, or merely because of world—wide abundance of shales, the surrounding regional formations are shales in most cases. The equivalent porosities in the reefs are estimated to be of the order of 12 per cent. The main constituent of most reefs is calcium carbonate. Consequently, the density is about 2.5. The reef heights are from about one hundred to about eight hundred feet, widths 1/2 to 3 miles, and the known depths 2,000 to 7,000 ft. The slopes on the flanks may be up to 40 degrees. In view of the wide ranges Of the Observed reef geometries and anomaly types, it seems, at present, that there is no direct, evident relation between the reef mass specifications (depth, height, extent, density) and the gravity anomaly specifications (type, intensity, extent). Consequently, certain factors other than the reef mass play the major roleJ' 45 Yunguls conclusions, after his study of sedimentation and compaction around the reefs, were: 1. Isolated reefs Show gravity anomalies on the order Of +0.5 mg, with a true negative ring around it. 2. NO direct relation between reef Specifications and gravity anomaly Specification ban be eXpected. 3. The importance Of the reef is not the reef itself but the conditions it created following its develOpment. 4. The gravity anomaly depends on what happened after the reef was covered and to some extent pre—reef formations. 5. The major cause of the anomaly is probably the lateral variations of sand content in the shales around and above the reef. He also mentions that while regional surveys could be used to locate reef belts, the potential of the gravity survey at present, is to locate the isolated reefs in a known reef belt. As stated earlier, one purpose of this study is to define the anomalies from reefs in the Michigan Basin Province. The geological conditions for the Michigan Basin are understandably different from the reef areas discussed by Yungul, thus reef anomalies in the basin also can be expected to show differences from the anomalies of other areas . 42.45 . \ ' / . y g1 4r Q:I\/I ‘ " , - \ ‘1 +42’30' after HINZE,|963 PORTION- OF REGIONAL GRAVITY MAP OF MICHIGAN C.|.=I mg FIGHRF i—‘l‘ CHAPTER VI INTERPRETATION METHOD Regional Gravity of Study Area The Belle River Mills and Marine City survey areas are situated on the rim Of a closed regional gravity minimum. This minimum, shown in Figure 12 (Hinze, 1963), is centered along the northern Macomb and Oakland County border. The Berlin area is situated closer to the center of the minimum than the other areas. The regional gravity of each of the survey areas agrees with the regional gravity pattern shown in Figure 12. Marine City Reef Study General Statement The first reef selected for study is the Marine City reef. This reef is buried at a depth of about 2300 feet and has a base which is about one mile long and 3000 feet wide. Two pinnacles about one half mile apart are located on the broad base. These pinnacles have relief of 250 and 300 feet. The step by step procedures used in this study are shown by the flow chart (Figure 7a). 47 L48 ObserVed Bouguer Gravity Anomaly Map As Shown on the regional gravity map, Figure 12, the Marine City survey is located in an area where the regional gravity gradient changes from a north—northwest trend to a western trend. The Bouguer gravity map (Figure 13) shows the regional gradient increasing 3.2 mg from north to south. There are several anomalous areas which are readily Observed. The closed low in the north—central portion of the area is quite noticeable. At first this was believed to be a result of a deep bedrock channel. However, the Size and low gravity gradients indicate a much deeper source. The other recognizable anomaly is a north—northeast trending gravity high associated with the Marine City reef bordered on bOth sides by linear gravity lows. The magnitude of this high determined by the cross profile method is about 0.3 mg. It has a width of about 1.2 miles. The gravity lows have a magnitude Of -0-3 mg. The linear nature Of the two lows immediately brings to mind the possible presence of bedrock channels. A check of the bedrock tOpography map (Figure 6), confirms the presence of the channels. The sharpness and narrowness of the lows is a good indication that they are caused by features buried at a shallow depth. The outline of the reef mass is shown by dashed lines on all maps. 49 I I a 82° 35‘00" g; g _>‘ ‘50000 “MAL ,_ 42. 451 00" 42. 45.00.._ “50000 _ 42° 4213 0,. ‘uoono TM” ST CLAIR COUNTY. MICHIGAN Fl G UR E I3 BOUGUER GRAVITY ANOMALY C.|.'O.IM DENSITY ale/cc MILES J “mflifiififimm; g 0 I009 2W0 3000 .000 5000 I955 g FEET " 82°35'00" I seam g | ... i 50 Theoretical Stugy Effects of Bedrock Geology The bedrock tOpography in this study area is quite irregular as seen on Figure 6. There is no doubt that the linear gravity lows flanking the Marine City reef anomaly are coincident with the bedrock channels Shown by Brown (1963). Profiles were constructed perpendicular to the strike Of the channels at several locations. The gravity effects from the channels were calculated using Talwani's gravity computation method for two—dimensional bodies. The results indicate that the gravity effect Of the channels in the area can produce the -O.3 mg anomaly Observed on the Bouguer gravity map. Figure 14 shows the profile of a typical bedrock channel in the area and the resulting gravity effect. A density contrast of -0.2 g/cc was assumed for the calculation. The width of the anomaly is about two miles. From this portion Of the study it was concluded that bedrock topographic effects cause significant anomalies which can mask the reef anomaly. When the bedrock tOpography is known these gravity effects can be calculated using the two- dimensional method and removed from the Bouguer gravity. Another method of eliminating the bedrock effects will be discussed later. TYPICAL BEDROCKEICHANN EL GRAVITY ANOMALY AND r—-0.0 1- -O.I I. -0.3 I— -O.4 460 [— I 440 - 420 . 400 I 380 I 360 . 34o " 320 I-300 FEET JL 0 I 5000 1 J MILLIGALS BEDROCK CHANNEL FEET ABOVE SEA LEVEL . 52 Expected Gravity Effects from Reefs The structure of the Marine City reef is well defined from a large number of wells drilled both on and Off reef. Structural contour maps of units which exhibit definite lithologic changes were obtained from the Michigan State Geological Survey (Ells, 1964) for the Marine City reef. Using the known geological conditions around the reef, the gravity effects of the reef were calculated using Talwani's three—dimensional technique. The density contrasts used in the approximation were obtained from two density logs in St. Clair County and from an unpublished density study of the department of Geology, Michigan State University, using well cuttings from the St.‘Clair County area. The formational units which exhibited a density contrast were divided into sections which could be approxi- mated by a three-dimensional body. The density contrasts of the bodies used for the approximation were both positive .and negative. The resulting gravity effect, calculated on the plane of observation, is on the order of +0.006 mg or essentially zero. A geologic cross—section of the reef with the associated gravity anomaly profile is illustrated in Figure 15. The gravity effects produced only by the thinning Of salt over the reef also were calculated. A small positive anomaly of 0.08 mg was obtained. This indicates that the 5 3. MGALS. I will IOOO 1 l I, ‘ -IIOO I. -I l200 DENSITY: 2.5 g/cc _ J4 -’_, 4I300 LL— \ Ll. LL / /[ 7Z—‘JJ 4J\ -I4OO / //L%741-// / ~DENSITY= 2W / I I _I_I _J JJH HJJJJJJJJ L / /_I7J .I_I_J_I_IJ_I..|5OQ .JJJJ/ J_I_IJ_IJJ .17 I// I] \qID Il100... 5:0 092002 SatunEmzuo a 838.9»:ng E 8... .muLEmzuo ... 5% I uzoLhwz: IIJ \ outmotlze. % ooxohmutazwo eexumauEmzmo 5m... Loo L L meLmImtsoLJoo L uALioJoo J coo. ILHII _ _ IITLILI ILII L L L ILIHLIIII - ILI IAIII I I I I I l \ \ \ -oot \ \ \LI L L L L L 11111111n11117111 1111111111010111111 00111111117111 «IqlqlnILI L. ..1 LIL. 7.1 L \ \ \ IIINILIILIJ L L XIUI \ x x \ \ \NIYIAILI I; \ \ \ 47:]1.112.143.04113441111 LILILILILILILILILILILILILILILI .I 11n01fl111111110001nfi01fifl InnLILILIaLIAI1111a11LM111 LILILI LILLMLILILILL... n11 _.O 'SWVOW m .0 ;\ com. 108. IANILIVILIILIHL _ L I 00! 1.114 loom. LIL] OONL 13A31V3$ M0138 133:] >J.L._>to szSz mm>o mzo_F<_m<> >tmzmo 56 l. The principal cause of the anomaly is not from the reef itself or the post—reef structure alone, but from lateral variations in densities around the reef associated with the post—reef structure. 2. The thinning of the salt over the reefs alone can- not produce the observed gravity anomaly. 3. Theoretically, the reefs can produce a gravity anomaly which can be detected by detailed surveys. 4. A reef with the same set of geologic conditions as the Marine City reef, but buried at twice the depth still can be detected by a detailed gravity survey. Cross-Profile Method The cross-profile residual is shown in Figure 17. Each of the anomalous areas discussed on the observed Bouguer map (Figure 13) are readily isolated by this technique. The highest magnitude attained is +0.22 mg. The lows flanking the high have magnitudes of —0.3 mg and -0.2 mg and the low in the upper—central part of the area has a residual magnitude Of —0.3 mg. In addition, a +0.2 mg high is observed in the left center portion of the area. In rechecking the Observed Bouguer map, an indication of this anomaly is apparent. This anomaly is associated with the small China East reef. It was not known by the survey party that the area included the China East reef and the 57 fact was not checked until the residual anomaly was isolated by the cross-profile method. The width of the zero contour of the Marine City reef is 6500 feet. This is less than the value obtained from the theoretical calculations. There is no question that the cross—profile tech— nique isolates the reef, but the undesirable effects of the bedrock tOpography are still present. Least Square Polynomial Analysis A least squares approximation of the original data. was made using a 3rd, 5th, 7th, 9th, and 11th degree polynomial equations. The 3rd and 5th degree approximations isolate the reef anomaly with approximately the same amplitude as the theoretical anomaly. The 7th through 11th degree equations approximate the original data too closely and no recognizable residual is left. The 3rd and 5th degree residuals are shown in Figures 18 and 19. The extreme edges of the maps were not contoured as anomalous effects are created in areas where station density is limited. The anomalous areas previously discussed are apparent on both the 3rd and 5th degree residual. The 3rd degree residual does not Show a completely closed zero contour around the reef anomaly. This is an indication that the 3rd degree polynomial may not have adequately approximated the regional surface. The 5th degree residual map indicates 58 a north—northeast trend to the positive anomaly which con— forms with the trend Of the reef. The magnitude attains a value of 0.19 mg, but the contours only Show 0.10 mg due to the 0.10 mg contour interval. The width of the positive anomaly is 6000 feet. This agrees closely with the cross- profile residual, but is less than the theoretical anomaly. The anomaly from the China East reef also is isolated by this technique. The anomalies over the Marine City and China East reefs are the only areas on the map which attain a magnitude of about +0.20 mg. The data used in the previous discussion were the original data at a 500 foot station spacing. The data were then divided into two groups based on alternate stations, resulting in two maps with a 1000 foot station Spacing. The 3rd and 5th degree polynomial approximations were cal- culated for both groups Of 100 foot stations. The results Show no appreciable difference from the results of the 500 foot stations. The 3rd and 5th degree residuals for the even number stations are Shown in Figures 20 and 21. It was concluded from the least squares polynomial analysis that: l. The least squares analysis using random spaced data, will isolate the reef anomalies, but like the cross-profile method leaves the undesirable effects. 59 2. A 1000 foot station spacing is sufficient for detailed gravity surveys searching for reefs, however, there must be coverage in the immediate vicinity of the reef other than along the road network. Interpolation of Bouguer Gravity In order to apply the upward continuation, downward continuation, and second derivative techniques, gravity values must be interpolated from the original random Spaced data onto a rectangular grid or square mesh system. This can be done manually by overlaying a grid system on the Bouguer map and interpolating gravity values at the desired points or the process can be accomplished with the aid Of a computer in a relatively short time. Figure 22 shows the results of interpolating the gravity values on a 500 foot grid system for the Marine City area. There is a slight lateral shift in some gravity values on this map due to the interpolation process, but it is small enough to be unim— portant. Downward Continuation and Second Derivative on Original Surface AS described in the section on upward and downward continuation theory, the term A; (ri) is the average of the values computed on ten rings surrounding a center point. If all ten rings were used with a mesh interval of 500 60 feet, the diameter of the largest ring would be greater than the distance across the survey area. Therefore, a test was made using only seven rings. The results were compatible with the known reef anomaly and it was assumed that seven rings give the approximation desired. Using seven rings the radius of the largest ring 13'7507 times the mesh inter- val. By calculating the gravity values on a plane below the original Observation plane the perceptibility of gravity values is increased. The Bouguer gravity values were cal- culated on planes m mesh intervals below the original plane where mFl, 2, 3, 4, 5 and the mesh interval equals 500 feet. The Size of the interpolated grid system is an impor- tant factor in the results as the mesh interval chosen depends on the lateral extent of the anomalies and the sharpness of the gradients. If the mesh interval is too small, oscillation will develop and if it is too large only regional anomalies will remain (Henderson, 1960). A mesh interval of about one—fourth the depth to the tOp of the mass causing the anomaly is usually satisfactory (Henderson, 1960; Vacquier, 1951; and Nettleton, 1940). There was no correlation between any Of the anomalies on the downward continued planes and the anomalies on the original plane. The anomalies on the downward continued planes showed an oscillation character indicating the mesh interval was too small. 61 Upward Continuation Gravity effects caused by features buried at a Shallow depth are minimized by calcUlating the Bouguer gravity values on a plane above the original plane of Observation. The gravity values were calculated on surfaces m mesh intervals above the original plane where m = l, 2, 3, 4, 5 and the mesh interval equals 500 feet. The Bouguer gravity values on the plane five mesh intervals or 2500 feet above the original plane are Shown in Figure 23. This method eliminates most of the small Sharp anomalies and leaves the broad anomalies as desired. The anomaly over the Marine City reef is present but the anomaly from the China East reef is almost eliminated. The large low in the northern portion of the area is still present indicating a source other than a bedrock channel. Downward Continuation of Upward Continued Surfaces The size Of the rings used in calculating A$(r1) cause an area to be lost around the periphery Of the original area. When using a 500 feet mesh interval, the center point of the rings must be moved toward the center Of the map a factor of seven mesh intervals before a complete set of values will be Obtained as Shown in Figure 24. This means a distance of seven mesh intervals is lost around the edge of the map when the upward continuation surface is calculated and an equal distance is lost from the upward continued surface when the downward continuation and second derivative values are calculated. 621 If the downward continuation and second derivatives techniques are performed on the upward continued surface, which is void Of undesirable effects, the reef anomaly may be isolated. The upward continuation surface 2500 feet above the original surface was downward continued one through five mesh intervals maintaining the 500 foot mesh interval. The reef anomaly was not isolated by the downward continua— tion method, however, it was apparent that isolation of the reef was increasing for each successively lower plane. The reef anomaly is successfully isolated on the plane 5000 feet below the 2500 foot upward continued surface as Shown in Figure 25, however, the anomaly is narrower than obtained by previous methods. The maximum width is approximately 5000 feet. This is not unrealistic as the plane on which the Bouguer gravity is calculated is about equal to the depth of the reef. The magnitude of the Bouguer gravity values are relative to one another and are in milligals. NO other anomalies attain a magnitude equal to the reef anomaly. Nettleton (1954) compared the results of several derivative techniques using a mesh interval of one-fourth, one-half, and equal to the kepth of the source. The results indicate that while a mesh interval of one-fourth the depth of the source in most cases is Optimum, a mesh interval of one—half the depth also is satisfactory. Because the 500 foot mesh interval appears to be too small for this study area, the mesh interval was changed to 1000 feet. When the 63 mesh interval equals 1000 feet, only five rings of the template are used. This was tested and the results indicated the approximation using five rings was adequate for this type of Survey. By changing the mesh interval on the upward continued surface from 500 feet to 1000 feet the downward continued planes can be calculated at intervals of 1000 feet. This effectively places the highest upward continued plane at 5000 feet above the original plane. By placing the planes of observation higher, the Bouguer gravity values show little change, except for a smoothing effect. The downward continuation technique, using the 1000 foot mesh interval, applied to the 3000 and 5000 foot up- ward continuation surfaces successfully isolates the reef anomaly On the plane 5000 feet below each upward continued surface as shown in Figures 26 and 27. The anomaly on the plane 5000 feet below the 3000 foot upward continued plane is narrow with a maximum width of 4000 feet. This is consistent with the previous downward continuation results. The magnitude of the closed anomaly is +0.8 mg. The anomaly on the plane 5000 feet below the 5000 foot upward continued surface is unique in that it isolates not one but two anomalies which almost coincide with the two pinnacles of the Marine City reef. The plane on which the two anomalies are isolated is essentially the same as 64 the original plane. The magnitude of the closed anomalies is +0.3 mg which is near the value of the original Observed anomaly. The widths of the anomalies are approximately 5000 feet. The Marine City reef anomaly is thus isolated on planes 5000 feet below the upward continuated surfaces Of 2500, 3000, and 5000 feet. It is concluded that by using a mesh interval of one-half the depth of the reef, the downward continuation method will isolate the reef anomalies from a surface upward continued a distance equal to the depth of the reef. Second Derivatives The second derivative technique of Henderson (1960) was applied to each upward continuation surface calculated. When the second derivative is calculated using seven rings and a 500 foot mesh interval, an oscillatiOn effect results and no isolation of the reef anomaly occurs. When the deri- vatives are calculated using five rings and a 1000 foot mesh interval, the reef anomaly is isolated from the 2500, 3000, and 5000 foot upward continued surfaces (Figures 28, 29, and 30). The magnitudes of the reef anomaly produced by the second derivative techniques are not duplicated elsewhere on the map, however, the magnitude of the second derivative values were not evaluated quantitatively. The width of the anomalies is generally greater than those produced by the 65 I I g 82‘ 35'00" I g 82" 30'00" cccccc L 42. 45-00.. 42. 45.00"— aaaaaa + _ 42.4213 0., 42°42‘30“ — +. . _I. ~., MARINE CITY AREA °°°° ST. CLAIR COUNTY. MICHIGAN FIGURE '7 , CROSS PROFILE RESIDUAL CL-oJmo — mamas; g 3 V , I955 I 82'3ls‘oo" 82 3) 90 .. 66 I g 82' 35‘ 00" l 82'30‘00" ‘ 0000 ‘ 00‘ _. 42. 45: 0°" 42. 4500"— N can uaoaa‘ + —. 42.42I30u 42'42‘30“ — " nnnnnn . «0953‘ +. . V .1. \“m, MARINE CITY AREA S12 CLAIR COUNTY. MICHIGAN Fl G UR E I8 LEAST SQUARES RESIDUAL 0— 3rd. DEGREE V _ c.|.-0.llno 500' s‘rmous In Mil/‘55 5!! | WARN! EMT 0F my 0 77—, W MIWIBM STATE UNIVERSIYV g ' rzsr I“ n ‘ '5‘5 i sz- 3|5'oo" I 8230‘ oo" .. 67 I 82‘ so'oo“ _-— I g 52' 35'00" I a \‘mcoo + + + + I / /.// G60000~ ‘— 42' 45‘ 00“ fi\ // u / ) M/ / , / /' "\ ‘ / / /_4 \ / / / °° ,o\/// - \> /I 7 /‘/ 42-4500"- Kammo “new“ + ._ 42942-3 O” 42'42'30" — \‘floooo . . «008‘ +- - V .7 + \W. MARINE CITY AREA ST. CLAIR COUNTY. MICHIGAN FIGURE '9 LEAST SQUARES RESIDUAL 0-5Ih. DEGREE _ QL-OIlmg aoo‘ s'nmous MILES I]. ”2 y. 1 DEPARTMENT OF KEOLDGY g g IAIWIGM STAYS UNIVERSIYV § § GEN 2 ms?» w a we, I 82' 315'00" I 52°30 00" ... k ¥ 4 J 68 I I g 82‘35'00” I 82°30'00" +I + + l/ oooooo fi “ 4 2 0 45‘ 00a- 42. 45.00.._ R one + _. 42. 42-3 0., l \ ooooo . + . . + ‘Wm’ ST. CLAIR COUNTY. MICHIGAN FI G UR E 20 LEAST SQUARES RESIDUAL O-3rd. DEGREE _ CL‘OJ no law STATIONS MILES I12 I DEPARTMENT or GEOLOGY a lumen! snv: UNIVERSTY 2°. 00 2000 FEE? .965 A 82' sls'oo“ I 82° 330" ... 69 I I I 82' 35'00“ E,I, g 82. 30.00.. a o o _ 42. 45a 00.. 42' 4500"— T‘Haooo + _ 42. 42-3 0.. 42'42'30" — +' ~ V + ‘m MARINE CITY AREA ST. CLAIR COUNTY. MICHIGAN FIGURE 2| LEAST SQUARES RESIDUAL O-5II'L DEGREE __ CL-mmq Iooo‘ STATIONS e In MIIIEES an i DEPARTMENT or my E s 0 woo zone on MICHIGAN any: UNIVERsuv 5 § FEET '555 82' 3'5‘00“ . I 82' 30' oo ... 7O aaaaaa _‘ 42° 4500" - 42° 42.3 on I I I I, 82° 35' oo" MARINE CITY AREA QI.‘ 0.lll|0 MIL Es I,‘ u, m , nEPARTMENY or GEOIDGV MIGRIGAN STATE UNIVERSITY :ooo seen u .95, FEET Iooo | 82. 30x00" 42" 45'00"- 42°42'30" __ ST. CLAIR COUNTYg MICHIGAN FIGURE 2 INTERPOLATED IBOUGUER GRAVITY ANOMALY ‘ DENSITY ale/cc 71 I I 82‘35'00” 82' 30‘00" I a 3 o o 0 ° 9 a I . Isoooo ‘ uouoo asnmoa~ _ 42. 45:00.. 42- 4500.. _ \‘loocu Aaooao‘ .— 42.42l3 0" 42-4230" — \unouo «0063“ MARINE CITY AREA ‘mm ST. CLAIR COUNTY.,MICHIGAN I FIGURE 23 BOUGUER GRAVITY' ANOMALY UPWARD CONTINUED 2500' fl GL-Oqu MILES WNENY OF GEOLOGY ll‘ Ill SI. W me»: we uuwsnsrv D IOOO IWO I a F EEY I 82°30'00" ... manna 19mm 32° 3'5'00" 72 BOUNDARIES OF ANALYTICAL METHODS / ,/RA_DI s or LARGEST TEMPLATE RING I BOUNDARY OF 20d DERIVATIVE AND DOWNWARD CONTINUED DATA BO NDARY OF UPWARD CONTINUED DATA BOUNDARY OF INTERPOLATED DATA FIGURE 24 73 ._42. 45:00.. + ...42n42I3o" - \ o . +, . + I 3 82°35'00" I I g 82“ ao'oo" 42a 4500"“ 42‘42'30" — MARINE CITY AREA ST. CLAIR COUNTY. MICHIGAN FIGURE 25 BOUGUER GRAVITY ANOMALY UPWARD CONTINUED 2500' AND DOWNWARD CONTINUED sooo' (LL-(Ifiln MILES "I . GEDLDGV ,, DEPARTMENT or MICNIGAN STATE UNIVER sun use: coo sea FEEY 74 I I 3 82° 35.00.. I a 82° 30'00" g 0000 + ‘GDDOO§ _ 42. 45. 00.. 42. 45.00.._ + "nsoooo + qsaaoa‘ _. 42042-3 0.. 42°42'30“ — . \‘40000 + ' _I_ I1 + + ‘mm ST. CLAIR couNTY.MICI-IIGAN FIGURE 26 BOUGUER GRAVITY ANOMALY UPWARD CONTINUED 3000' AND DOWNWARD CONTINUED sooo' C.I.'°.5m7 MILES 0 V4 II: BIA | m MENYOEGEOLOGV g g ”ICHIGM STATE UNIVERSITY CI a 0 I000 2000 3009 “7 9 .965 3 g FEET I 82°35'00" I 62°39 00" ... I 75 “ «Dana _. 42. 45400" “uation ._ 42- 4213 on ‘O‘uooo §uooon l 82° 35' oo“ noooo "COCO 82'315‘00" zooooo o a n o S I 82° 30'00" anooo‘I 4Iaoon_ 42. 45-00.._ 42°42‘30" — uaoéF\ MARINE CITY AREA ST. CLAIR COUNTY, MICHIGAN FIGURE 27 BOUGUER GRAVITY ANOMALY UPWARD CONTINUED~5ooo AND DOWNWARD CONTINUED sooo' (LL-0.3m! MILES ‘J‘ I DEFNRTMENT OF GEHLDGV V. II! MICHIGAN STATE UNIVERSITY n IOO FEET I 82' 30' 00\m‘ 76 I . . I. 3 82°35'00" GI § 32 3O 00 ‘ “0000 ML —. 42. 45l 0°“ 42' 4500"— —‘ GSOODO AWOOOK + + +- ~ — 42‘42'30“ 42'42'30" — ‘uoaoo uooé‘a‘\ MARINE CITY AREA ~uaoao . sT. CLAIR couNTY,MICHIGAN FIGURE 8 SECOND DERIVATIVE OF 2500-“UP A CONTINUED SURFACE c.l.- 0.0T unIh MILES u . I KPARTMENT OF MY a o MICHIGAN STATE UNIVERSITY a g o Ioao 2m “ 1965 S 8 FEET E ' 3 32°35'00" I I Q " R J m , E 77 I . I. D 82‘ 35'00" l E 82' 30 00 K IRDOUO + + + + // /T '7 7 fl // I - “0000‘ . 0* // _42. 45.00.. , ,, 7 ,7 7’ u / ' I :1 /\ u [I I ’ ‘03 . . l u__ I , ‘\ 42 45 oo \\ . ~ \ . ,/ ,0“ 7/ , ‘I— ‘ , ’ ' 77\‘\_ + // 7 ‘93s / I. / / u / s. / .. g“Dom; , . I . : I ad . , I I I . . , + . . .Ti , ",/ , ‘ \ I . I . . . . . 'I' ‘suaou‘ 42-42-30" _ \«n o . ’ \'° /// / / 0° / \ / . ,4/ // K '\\~:/l.//I/,°”°/ / I .\ / / / “was?“ MARINE CITY AREA \‘30900 . ST. CLAIR COUNTY. MICHIGAN FIGURE 29 SECOND DERIVATIVE OF 3000' UPWARD _ CONTINUED SURFACE M L: C.|.I 0.0l unlnI ‘ ' .OEPARTMERT or 650mm 0 § -._—_.-— MICHIGAN am: UNIVERSHV g g - ISBD I 62. 3|5|oou 82 30' 00 w an 5% 78 If I I a 82‘35'00” c g 82'30'00" + A + — 42a 45: 0qu 42° 45'oo"— _I. Nuance + uaooa_ + + - - _. 42° 4213 on 42°42'30" — +. . + + -I- MARINE CITY AREA ~ucm ST. CLAIR COUNTY.MIcI-IIGAN FIGURE 30 SECOND DERIVATIVE OF 5000 UPWARD — CONTINUED SURFACE was an Coos-min I12 3“ I EPAHTMENY of GEOLOGY a S MICNIGNI STATE UNIVERSITY :33 9g, 9 mac Econ FEEYO 400 I965 I 62" 3'5'00“ I 3:310 00 ... I 79 downward continuation technique below the surface, but less than the original observed and theoretical anomaly. They are on the order of 5000 feet wide. The anomaly isolated by the second derivative method from the 5000 foot upward continued surface (Figure 30) is actually two anomalies coinciding with the two pinnacles of the Marine City reef. This is consistant with the results of the downward contin- uation techniques. It is concluded that the second derivative technique has a high resolving power and will successfully isolate the reef anomaly using a mesh interval of one—half the depth of the reef on upward continued surfaces calculated on planes approximately equal to the depth of the reef. Belle River Mills Reef Study General Statement The second reef studied is the Belle River Mills reef. This reef is about three miles north of the Marine City reef and possesses several characteristics which are different from the Marine City reef. The two reefs are buried at approximately the same depth, but the Belle River Mills reef has a greater areal extent and is not a pinnacle type reef. The reef maintains a relief of 300 feet along its length of two miles. Its overall width is about 3000 feet. Compared to the Marine City reef, the Belle River Mills reef is greater in both areal extent and reef mass. 80 Observed Bouguer Gravity Anomaly Map The Belle River Mills area is situated in an area where the regional gravity gradient flattens out and changes from a northwest direction to a western direction as shown in Figure 12. The resulting pattern for the area is a saucer shaped depression with a maximum change in magnitude of only 0.9 mg (Figure 31). Three anomalous areas are readily apparent on the Bouguer gravity map. A gravity high with a magnitude of 0.3 mg trends northeast across the center of the area. Two closed gravity lows with magnitudes of —O.15 mg and -O.35 mg flank the gravity high. The northernmost part of the high is associated With the Belle River Mills reef. The southern portion of the high will be discussed later. Comparing the Bouguer gravity map with the bedrock topography map (Figure 6), it can be seen that several bedrock features coincide with the gravity anomalies in the area. The linear low on the southeast side of the high does not correlate with any bedrock channels, but well control in this area is sparce and there is a good possibility that a bedrock channel exists. The trend of the low can be followed into the Marine City area to the south. A major bedrock channel does exist in the area bordering the southern edge of the Belle River Mills area and the northern edge of the Marine City area. The channel predicted for the Belle River Mills area could possible be a tributary of this bedrock 81 channel. For comparison purposes, the gravity stations on the southern border of the Belle River Mills area are coincident with those on the northern border of the Marine City area. Theoretical Study Effects of Bedrock TOpography The gravity low to the northwest of the reef anomaly coincides with a broad bedrock depression. The gravity effect from this depression was calculated using Talwani's two—dimensional method. The resulting theoretical anomaly of —O.15 mg indicates the depression can cause the observed anomaly. Expected Gravity Effects from Reef The theoretical gravity effect of the Belle River Mills reef was calculated using Talwani's three-dimensional method. The average density contrasts were used because information on lateral density variations around the reef are not available. The calculated gravity anomaly is on the order of 0.006 mg. This is consistant with the anomaly calculated from the Marine City reef. Results of Isolation Techniques General Statement The isolation techniques used in the Belle River Mills study were essentially the same as employed in the Marine 82 City study. These are the cross—profile, upward continuation, downward continuation, and second derivative methods. Cross—Profile Method The cross-profile residual is shown in Figure 32. An anomaly is associated with the reef, but it does not isolate the reef satisfactorily. The width of the zero contour is nearly two miles and the magnitude is +0.2 mg. Least Squares Polynomial Analysis The same degree polynomial approximations calculated for the Marine City area were used for this area. Again the 3rd and 5th degree polynomial equations for both the 500 and 1000 foot station spacing isolate the reef anomaly. The residual maps are shown in Figures 33, 3A, 35, and 36. For this area, however, the 3rd degree fit was better than the 5th degree fit. This may be explained by the fact that the regional gradient is very small. The 5th degree poly— nomials for both the 500 foot and 1000 foot station spacing tend to approximate the original surface too closely. The magnitude of the reef anomaly from the least square polynomial analysis is +0.18 mg. This is almost identical with the value obtained for the Marine City reef. It had been expected that the Belle River Mills reef would cause an anomaly larger than the Marine City reef. The similarity of the magnitudes substantiate the previous con— clusion that the anomalies are not caused by the reef, but 83 by post reef conditions. The southern high is also indicated with a magnitude of about +0.13 mg. It is concluded from the comparison of the Belle River Mills and Marine City least squarea analysis that the degree of approximation depends on the nature of the regional gravity pattern and not the nature of the anomalies. Interpolation of Bouguer Gravity Several spurious effects are created in the inter— polation of the Bouguer gravity for the Belle River Mills area (Figure 37). This is an inherent problem in interpo— lating the Bouguer gravity by the method adOpted for the com— puter. These Spurious effects are generally created in an east-west direction. The spurious effects on the Belle River Mills interpolated gravity map are near the edge of the reef anomaly but are not directly associated with the anomaly. Downward Continuation and Second Derivative on Original Surface The results were identical with the Marine City study and confirmed the previous conclusions that a mesh interval of one—fourth the depth to the anomaly causing mass is too small. Upward Continuation The upward continued surface 2500 feet above the original plane of observation is shown in Figure 39. The reef anomaly remains with two minimum areas on either side. The anomaly on the northwest side is the anomaly discussed 8A previously which coincides with a bedrock depression. It was not removed in the upward continuation method indicating the anomaly is too broad. Downward Continuation of Upward Continued Surfaces The same techniques applied to the Marine City study were used for the Belle River Mills area. The only com— bination which successfully isolates the reef anomaly is the downward continuation technique which calculated the values on a plane 5000 feet below the 5000 foot upward continued surface (Figure 39). A gravity high with the same magnitude of the reef anomaly also is isolated to the south of the reef anomaly. The values calculated 5000 feet below the 2500 and 3000 foot upward continued surfaces failed to isolate the reef, but showed a general gravity high over the area. The only major difference between the Marine City study area and the Belle River Mills study area is the regional gravity gradient. It is possible that the regional gradient of an area can cause the downward continuation techniques to vary in their isolation capabilities. Second Derivatives The second derivative values were calculated for the upward continued surfaces of 2500, 3000,and 5000 feet. Each of the second derivative calculations successfully isolate \ 400000 42'48'00" N 470000 42'46‘30“ 480000 I 82'33' 00" o o o o o n -+ RISE T4N FIGURE 3I ' O ‘ 8é°30' 30 BELLE RIVER MILLS AREA STCLAIR COUNTY, MIcI-IIGAN BOUGUER GRAVITY ANOMALY DENSITY 2mm _ 3 D we 1m DEPARTMENT OF GEOLOGY ° %E o MICHIGAN STATE UNIVERsITv 5 I000 3000 4000 965 I 450000 \ 42°48‘00“— 470000 N 42 °4e' 30"— Gas 98 500000 [I I g I ll 82°33' 00" 82 so 30 I aloooo ‘- \430000 480000 ‘ 42’48'00" + 42°48'00"— 98 4.. 42°46'30" 42°46'30‘L + 'T BE-LLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN 1 RISE T4N FIGURE 32 CROSS PROFILE RESIDUAL C.I.=O.I mg MILES v4 l/Z m DEPARTMENT OF GEOLOGY MICHIGAN STATE UNIVERSITY mm 2000 3000 4000 FEET 5 +I 82°3'3I 09!: 82°3'3'od' I 000000 400000 \ 42°48’00"— L8 Jr 42 '46' 30"— BE-LLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN R I6 E T4 N ’ FIGURE 33 LEAST SQUARES RESIDUAL O-3rd. DEGREE 500' STATIONS CL- 0.05 m 0 MI LB 0 v4 ,,2 3,. DEPARTMEMI‘ OF GEOLOGY % MMMMMM N STATE IIIIIIIIII 0 .000 2000 3000 4000 .955 , FEET \anocO 42.4300" Known: 42'46'30' 460000 I 82°33' 00" I 0 8 o c . 32°30'3o 828030" _I._ _I_ 42%:00'L +. 42‘46'30‘L ~+ BELLE RIVER MILLS AREA STCLAIR COUNTY MICHIGAN RISE T4N FIGURE 34 LEAST SQUARES RESIDUAL 0- -5th. DEG GREE c.l.- 0.05m 500 STATIONS NI ILEs II 2 31¢ DEPARTMENT OF GEOLODV flfim MICN NIGAN STATE UNI IVERSIYV 2000 I965 25+ “I 88 \asoooo 42°48‘00" \ «700 00 42°46'30" 460000 II . I . .. 82°30'30" 82 33 00 I + 480000 \ 42°48'00"— 4.. 470000 \ 42°46'30"— II» BELLE RIVER MILLS AREA SICLAIR COUNTY, MICHIGAN RISE T4N FIGURE 35 LEAST SQUARES RESIDUAL 0- -3rd. DEGR REE IOOO STATIONS § 8 3m DEPARTMENT or 550mm :5: S—Ik c 747000 MIcmGAN STATE UNIVERSITY I m ' 82°3I3'o I!I 82II°3IO 30 865 68 E§__ I"30 I 82° 82°33' 00" o o o o o m moooo~— + \450000 480000 \I 42'48'00“ -.I- «9 42°48'00“— 0. +. ‘470000 470000 ‘ 42°46'30" 42 °46' 3o"— BE-LLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN RISE T4N FIGURE 36 LEAST SQUAREEG$ EREESIDUAL O-5’Ih.D OJ! 005mg IOOO' STAWONS % MMTEZZZL"§?ZIEZST5’§§§L 2000 460000 O6 \ 400000 42'48'00" \ 410000 42°46'30“ 460000 800000 a 0000 -— + 480000 a + 42°48'00'L + . 070000 \ 42°46'30“— ~ + BELLE RIVER MILLS AREA STCLAIR COUNTY. MICHIGAN RISE T4N FIGURE 37 INTERPOLATED BOUGUER GRAVITY ANOMALY c.I.-o.osm DENSITY Z.|g/I:c Ia DEPARTMENT 0F GEOLOGY ‘ MICNIGAN STATE UNIVERSITY II I ,, 82°30' 30" 82°33‘ 00 T I6 \430000 42°48'00" \470000 42"46‘30" \460000 I I . .3 .. 82°33'00" 82 3? 0 a 8 0 0 ° 9 g a . 050000 N -I- 42°48 00L + . 4 7 0000 x. 42 °4e‘ 30"— - + BELLE RIVER MILLS AREA ST.CLAIR COUNTY. MICHIGAN RISE T4N FIGURE 38 BOUGUER GRAVITY ANOMALY UPWARD CONTINUED 2500' +---I CJ.l 0.05 mg 0 0 3].: DEPARTMENT OF GEOLOGY g MICNIG‘N sTATE UNIVERSITY 3000 4000 I I955 on 82°313'0 a6 \uoooo 42.4900" \ 410000 42'46'30'I § «0000 I 82°33'00" 000000 3% 00000 —— 8.: 3. “0000 ‘I BELLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN RISE T4N FIGURE 39 BOUGUER GRAVITY ANOMALY UPWARD CONTINUED 5000' AND DOWNWARD CONTINUED 5000' + 42‘4doo“— )2 + . 470000 \ I3 42 '46'30‘L - + C.l.- 0.2 mg “ILES o In I12 314 DEPARTMENT or ozowav E MICNICAN STATE UNIVERSITY 0 mm 2000 3000 4000 I965 r T 50 '9' E6 R400000 42°48'00" \ 410000 42'46‘30" “460000 I o I I 82°33'00" 82 3,0 3° aooooo 490000 BELLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN RISE T4N FIGURE 40 SECOND DERIVATIVE OF 2500l UPWARD CONTINUED SURFACE C l. = 0.005 unl's MILES 3,4 DEPARTMENT OF G 0L0 E E MICMIGAN STATE “UNIVERSITY 2:00 4000 42°48’00"— 470000 A 42 °46' 30“— I76 ‘080000 42’48‘00" R 470000 42°46'30" 5 460000 I 82°33' 00" 0 o 0 o o a II 82° 30' 30'I {“0000— 480000 \ 422800"— 470000 R 42 “4630“— BE-LLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN RISE T4N FIGURE 4| SECOND DERIVATIVE OF 3000' UPWARD CONTINUED SURFACE C.I.- 0.005 unit In 3,4 DEPARTMENT 0F GEOLOCT NIICMIGAN STATE UNIV“ ITv I000 2000 3000 4000 s ~480000 42°48'00" ‘410000 42°46‘30“ 5480000 II I g a n 82°33' 00.. 82 30 30 o o o o o o BIOOOO ~— 080000 \ 42°4e‘oo'2 070000 % 42 “4630"— BE'LLE RIVER MILLS AREA STCLAIR COUNTY, MICHIGAN RISE T4N FIGURE 42 SECOND DERIVATIVE OF 5000I UPWARD CONTINUED SURFACE C.L= 0.005 units ES I/Z MIL 3m DEPARTMENT or GEOLOGY MIcmGAN STATE UNIVERSITY I000 2000 3000 6000 FEET 96 97 the Belle River Mills reef anomaly (Figures #0, 41 and “2). This is consistant with the Marine City results. The second derivative techniques also isolate the gravity high to the south of the reef anomaly. The magnitudes of the two anomalies are again about the same. There is a good possibility that another reef may exist to the south of the Belle River Mills reef. The results of the second derivative method on the Belle River Mills area indicate that the isolation power of the derivative technique is greater than the downward continuation techniques. Berlin Reef Study General Statement The Berlin reef is situated more basinward than the Marine City and Belle River Mills reefs and is buried at a depth of about 3500 feet. The reef has a width of about 2500 feet and a length of one mile. The major portion of the reef mass is salt filled, but there are several producing wells in the reef. This study was made assuming that nothing was known about the conditions surrounding the reef. A theoretical study was not made and the cross profile method was not employed. 98 Observed Bouguer Gravity Anomaly Map The Berlin area, as shown on the regional gravity map (Figure 12) is located near the center of a closed regional gravity minimum. The Bouguer gravity map is shown in Figure “3. The nature of the regional gradient is readily observed on the Bouguer map by the semi-circle pattern of the contours. There are several anomalous areas on the Bouguer map, but the anomaly associated with the reef is not as obvious as in previous areas. Two linear lows flank a small positive trend which enters the area from the north— east. Well control in this area is limited and no bedrock channels are indicated on the bedrock tOpography map (Brown, 1963). However, it is reasonable to assume that the linear gravity lows are reflections of bedrock channels. Results of Isolation Techniques Least Squares Polynomial Analysis The results of the least squares polynomial analysis for the Berlin Survey are no different than the Marine City and Belle River Mills areas. The 3rd and 5th degree polyno- mial approximation for the 500 and 1000 foot station spacing isolate a positive anomaly over the reef. Negative areas are present on the west and east sides of the reef anomaly. The magnitude of the anomaly is again about +0.20 mg. This reaffirms the conclusion that the anomaly is not due to the 99 reef itself. The least square residual maps are shown in Figures an, MS, 46 and 47. Interpolation of Bouguer Gravity Again a spurious effect was created by the interpola— tion technique, but it is not in the reef area and, there— fore, was disregarded. The interpolated Bouguer gravity map is shown in Figure 48. Upward Continuation Technique The results of the gravity values calculated on the plane 2500 feet above the original surface is shown in Figure 49. The 2500 foot plane does not show the effects of the linear gravity lows, indicating further that a possibility of bedrock channels exists. A high is still present in the vicinity of the Berlin reef. Downward Continuation The downward continuation techniques failed to isolate the reef anomaly. The gravity values downward continued 5000 feet below the 2500, 3000 and 5000 foot upward continued surface showed a tendency to isolate the reef anomaly, but only indicate a positive area in the reef vicinity. Second Derivative The second derivatives were calculated for the 2500, 3000 and 5000 foot upward continued surfaces. Each of the techniques successfully isolate the anomaly over the reef lOO (FigurES 50, 51 and 52). For the values calculated from the 2500 and 3000 foot upward continued surfaces the closed contour with the highest value is essentially coincident with the reef pinnacle. The overall anomaly is about 5000 feet wide. The values calculated on the 5000 foot surface Show the broad anomaly from the reef, but do not show the closure coincident with the reef pinnacle. This may indicate that the distance between the depth of the reef and the upward continued surface was too great and a portion of the anomaly was lost. The conclusions reached from the Berlin study are: l. The second derivative techniques have a higher resolving power than the downward continuation techniques. 2. The upward continued surface should not be calcul— ated higher than about 7500 feet above the expected reef depth. 3. The salt filling of the reef mass has no bearing on the magnitude of the observed anomaly. lOl % 520000 _ 42° 55.00.. —— 5I0000 ._42-53I30n \ 500000 + 82’57'30 I) o o o m a 90000 ez-é'r'so" 2°55'00" 7 00000 _m_ 520000 42°55'00"— swoon 425330"— 100000 82°55' 00" I ST CLAIR-MACOMB COUNTY, MICHIGAN R 3 N 0 V. m . n MIWIGAN SVAYE UNIV€RSIYV can» %—o SOME Iooo 5°” me A BERLIN AREA E T5N,T6 FIGURE 43 BOUGUER GRAVITY ANOMALY c.|.-0.Img DENSITY alum: I Din mam or azowav FEET 102 E 520000 _ 42. 55-00" + . -_ sIoaoo + . -42-53n30u \500000 82°57'30 '0 o o o m w u T 00000 -m_ 2° 55'00'I 520000 42°55'00"— 5I0000 —_ 42°53'30"— E 44 LEAST SQUARES RESIDUAL 0008;3' D BEFSTATIONS § § 0 l 4000 In: E 2 L 32°;5l7'3o" I 82'5'5‘00" .. ST. CLAIR-MACOMB COUNTY, MICHIGAN Rl3 6N BERLIN AREA E T5N,T 103 520000 .. 420 55-00" KSIOOOO r-4Z'53'30II “500000 + , 82°5I7'II50" {132°95'00" + + + // IL I ' //..7« 7 4i. + \ + r ’ ' I+\\\ szoooo \\ . \ \I ,_ 23 I 29 N 42°55‘00"— \ / , I I I I A ,I I’ , I ‘ \I I I’LL, / 5 I I IITII/ I - I - I I IIIAI , A . . I , \J,/. .+ . . . . . //\I- //> Ry d: )\ I} or: \ w/é/ I / /< .\ \ /°° /‘ I, / , / , _ . I\_/,,33, _ . \ _ _ yI \\ so p/i / HIT/\of / . I I I j/ ,4‘” -—\\ I T { I I I , . . I L,/ / _ ( J, / >§ , / \ . . / // ‘ '/ / \.°.( smooc— H/ , T. M; ,, -. a - y / 0 ~ , fi\/° . 42°53'30"— // //-OI—-/"— \\\ . w/ _ I _ L A / / ‘ // 0.0 + /+ j + + < / . / B E R L I N A R E A ' s1: CLAIR-MACOMB COUNTY. MICHIGAN . mas T5N,T6N ‘ LEAST SQUAUR'EES45RESIDUAL + + + 0-5Ih. DEGREE 500 STATIONS § § .... g 2 32°57'30" az-sls'oo" .. 1011I I .I .. 82'57 so a 0 o o o- to ~ 520000 __ 4 20 55-00“ § 5:0000 _ 42.53I30u N500000 .. s a 1’ , az'fi'r'm" -——- 100000 2°55'OO" 700000 —m_‘ 520000 42'55'oo"— 5I0000 42°53'30"— B E R L I N A R E A ST. CLAIR-MACOMB COUNTY. MICHIGAN | E TSNéTGN LEAST SQUARE?)£1 RESIDUAL O-Srd. DEGRE (IL-alum I00 STATIONS NIL DEPARTMENT or «sown memo-N "ATE umvsnmv Ins 82'5'5‘ 00'I 105 82'57' O" 590000-01— “ 520000 r ' ' / , I V??? / . Tm \/f/ ‘ I : C: +' ' ' / ' ' 51”!“ ' ' 1,4.w\4:"‘/>«4.3,; _ 42.53 30" I /. y/V , ‘ . . _ ‘\._/ .oI . ' / «/ ~ /7 5500000 90000 . 82’?7'30" _.420 55|°°n \ 29- ‘ ‘ _ /,r . I I , / a . I '//.:\'\\ / / ' . I I" \‘ ‘ “ I I K - / 700000 B ,\ L 5I0000 "5500" N 700000 ~m_ 520000 42°55'00"— 42'5 3' 30"— + BERLIN AREA ST. CLAIR-MACOMB COUNTYI MICHIGAN R E T5N,T6N 7 LEAST SQUARESI-RESIDUAL - 1h. DEGRE- C.|-0.I(n?q 5 IOOOESTATIONS MILES 0 v4 ya I DEPARTMENT or seoumr NIcNmN sum: UNIVERSITY Ins 82° 55' 00" I 106 ~ 520000 _ 42. 55'00" _ 5I0000 _42~5313°n _— 500000 0 7| | 3 . o o o o ... In I 82‘5 “5500" N 700000 —m— 520000 42-5500"— smooc— 42‘53'30"~ BERLIN AREA ST. CLAIR—MACOMB COUNTY. MICHIGAN RISE 6N FIG u RE 43 INTERPOLATED “BOUGUER + GRAVITY ANOMALY C.|.IOJEl2I ~ ’DENSITY 2.|o/cc v. ”'5. y. . ,_ nan-mm mm." NICNIII‘N STATE UNIVERSITY a o 0 0000 :~ ‘9“ a g FEEY § § 92°67'30" I 82°55‘00” II I m 107 R 320000 .. 42. 55.00.. —— 0I0000 ._42053I3°u E 500000 + . I I I. . 92-57'50 92°55 00' E; g 520000 42°55'00"— 5I0000 42‘53'30"— BERLIN AREA ST. CLAIR-MACOMB COUNTY, MICHIGAN RI3E T5N,T6 FIGURE 49 BOUGUER GRAVITY ANOMALY UPWARD CONTINUED 2500' LE5 C.I.- 0.Im9 0 v4 V: m l mmmznv a: 020mm 6 ‘ a .000 MICHIGAN STATE UNIVERSITY a g FEE? '9” 8 o . g 9 I I II 0 l ‘l 82'57 3O 32 55 00 II I m ~fi 520000 _ 42¢ 55'00" ~5I0000 _42053I30n §5ooooo + . 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