A—v—f A GRAVITATIONAL INVESTIGATION OF THE SCIPIO OIL HELD IN HILLSDALE COUNTY, MICHIGAN, WITH A RELATED‘STUDY FOR OBTAINING A VARIABLE ELEVATION FACTOR Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY DONALD WARREN MERRITT 1.958 118318 III/IIIIIflflII/I/MM/fl/W WLIBRA R Y 0524 Michigan State This is to certify that the thesis entitled A GRAVITATIONAL INVESTIGATION OF THE SCIPIO OIL FIELD IN HILLSDALE COUNTY, MICHIGAN, WITH A RELATED STUDY FOR OBTAINING A VARIABLE ELEVATION FACTOR presented by Donald Warren Merritt has been accepted towards fulfillment of the requirements for Ph.D. Geology degree in 7 H K,, /:;u (fiflV/figegi-(jp Date//"/”///f//¢ cf 0-169 ABSTRACT A GRAVITATIONAL INVESTIGATION OF THE SCIPIO OIL FIELD IN HILLSDALE COUNTY, MICHIGAN, WITH A RELATED STUDY FOR OBTAINING A VARIABLE ELEVATION FACTOR by Donald Warren Merritt A detailed gravity survey was conducted in the north central portion of Hillsdale County, Michigan for the purpose of delineating gravity anomalies associated with the Scipio Oil Field. The error in the Bouguer gravity reduction caused by near surface density vari- ations in the glacial drift was minimized by a method deve10ped for obtaining an individual station elevation factor from the elevation and observed gravity values of surrounding stations. Fourier analysis involving band pass filters is successful in isolating elongate positive anomalies which are associated with the geographical location of the Scipio Field. These anomalies have a magnitude in excess of 0.2 mgal and are similar to those theoretically calculated from a geologic model of the producing zone based on porosity values obtained from core analysis. Donald Warren Merritt The complexity of the Bouguer surface in the study area precludes the objective use of polynomial and double Fourier series analysis for delineating anomalies associ- ated with the production. A regional gravity profile striking northeast into the Michigan Basin reveals a displacement in the uniform gravity gradient. This displacement, which occurs along the Albion-Scipio Oil Field is interpreted to originate from basement topographic relief in the form of a fault- line scarp. Renewed activity along the fault associated with the scarp may have established the conditions neces- sary for the development of the linear Albion—Scipio Oil Field. A GRAVITATIONAL INVESTIGATION OF THE SCIPIO OIL FIELD IN HILLSDALE COUNTY, MICHIGAN, WITH A RELATED STUDY FOR OBTAINING A VARIABLE ELEVATION FACTOR By Donald Warren Merritt A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geology 1968 ssCopyright by DONALD WARREN MERRITT 71969 ACKNOWLEDGMENTS The author wishes to express his sincere thanks to the following individuals and organizations. To Dr. W. J. Hinze for his deep interest and gui- dance throughout the project. To Dr. H. B. Stonehouse, Dr. J. W. Trow, and the late Dr. J. Zinn for their active participation on the guidance committee. To the McClure Oil Company, Alma, Michigan, for financial assistance in the gathering of the data, and to Messers F. P. Hurry and W. K. Roth for providing geological insight into the problem. To Messers G. D. Ells and F. Layton of the Michigan Geological Survey, Department of Conservation, for fruit- ful discussions concerning the regional aspect of the study. To Messers J. Roth, R. G. Geyer, R. Ehlinger, and S. Wilke whose hard-work made the gathering of the data possible. To Michigan State University for the free use of the C. D. C. 3600 computer. iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . iii LIST OF TABLES . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . vii INTRODUCTION . . . . . . . . . . . 1 Objective 0 0 O O O O O O O O O O 1 Approach . . . . . . . 3 Location of the Study Area . . . . . . A Physiography of the Study Area . . . . . A GEOLOGICAL SETTING . . . . . . . . . . 7 FIELD METHODS. . . . . . . . . . . . . 11 DATA REDUCTION . . . . . . . . . . . . 12 Observed Gravity. . . . . . . . . . 12 Latitude Correction. . . . . . . 12 Elevation and Mass Correction . . . . . 13 General Statement . . . . . . . . 13 Previous Work. . . . . 1A Approach for Obtaining a Variable Elevation Factor. . . . . . . . 18 Theory . . . . . . 19 Elevation of the Proposed Method . . . 20 Gravity Model of the Glacial Drift. . 21 Gravity Model of the Glacial Drift and Bedrock Channel. . . . 2A Gravity Model of the Glacial Drift and Reef Structure . . . . . . 36 Gravity Model of All the Sources . . AA Increasing the Density Contrast Within the Drift. . . . . . . 53 iv Page Decreasing the Station Spacing . . . ‘ 53 Altering the Elevation Datum. . ._ . 57 Summary of the Model Studies. . . . . 59 Elevation and Mass Correction for the Field Data. . . . . . . . . . . 61 METHODS OF DATA ANALYSIS . . . . . . . . . 68 Polynomial Approximations to the Bouguer Surface. . . . . . . . . . . . 69 Double Fourier Series Analysis . . . . . 70 Linear Filtering Methods . . . . . . . 7A Theory . . . . . ., . . . . 77 Band Pass Filtering. . . . . . 80 Low Pass Filters That Include the Regional . . . . 82 High Pass Filters That Exclude the Regional . . . . . . 92 Combining High and Low Pass Filters . . 92 INTERPRETATION . . . . . . . . . . . . 101 Model Study of the Scipio Oil Field . . . 101 Geological Factors Which Will Distort the Anomaly . . . . . . . 102 Residual Map Interpretation . . . . . . 107 Least Squares Residuals . . . . . . 107 Double Fourier Series Residuals. . . . 107 Band Pass Filtering. . . . . . . . 108 High Pass Filtering. . . . . . . . 108 Regional Interpretation . . . . . . . 109 Summary of Interpretation. . . . . . . 113 Residual . . . . . . . . . . ., 113 Regional . . . . . . . . .A . . 114 CONCLUSIONS . . . . . . . . . . . . . 115 REFERENCES. . . . . . . . . . . . . . 118 LIST OF TABLES Table Page 1. Porosity Values Obtained from Core Analysis . . . . . . . . . . . 10“ vi Figure 8'30 8—b. 10. 11. 12-8.. l2—b. LIST OF FIGURES GENERAL Trenton—Black River Annual Oil Production Location of the Survey . . . . . . Geologic Column of Michigan. . . . . Trenton Structure Map. . . . . . . Elevation Factor Chart . . . . . . MODEL STUDIES Plan View Map of the Sources of Anomalies Model Study Elevations . . . . . . MODEL INVOLVING THE GLACIAL DRIFT Graph of the Error in the Calculated Den- sity Values-5th Degree . . . . . Graph of the Error in the Calculated Gravity Values-5th Degree . . . . Map of the Individual Station Density Error- 5th Degree . . . . . . Map of the Individual Station Gravity Error-5th Degree . . . . . . GRAVITY MODEL INVOLVING THE GLACIAL DRIFT AND RIVER CHANNEL Calculated Gravity Effect of the Buried River Channel . . . . . . . Graph of the Error in the Calculated Density Values-3rd Degree . . . . Graph of the Error in the Calculated Gravity Values-3rd Degree . . . vii Page \OCDU'I 15 22 23 25 25 26 27 28 3O 3O Figure Page l3-a. Graph of the Error in the Calculated Density Values—5th Degree . . . . . 31 13-h. Graph of the Error in the Calculated Gravity Values—5th Degree . . . . . 31 1A. Map of the Individual Station Density Error-3rd Degree 0 o o o o o o o 32 15. Map of the Individual Station Density Error-5th Degree . . . . . . . . 33 16. Map of the Individual Station Gravity Error-3rd Degree . . . . . . . . 3A 17. Map of the Individual Station Gravity Error-5th Degree . . . . . . . . 35 GRAVITY MODEL INVOLVING THE GLACIAL DRIFT AND REEF STRUCTURE 18. Calculated Gravity Effect of the Reef Structure . . . . . . . . . . 37 19-a. Graph of the Error in the Calculated Den- sity Values-3rd Degree . . . . . . 38 l9-b. Graph of the Error in the Calculated Gravity Values-3rd Degree . . . . . 38 20—a. Graph of the Error in the Calculated Density Values-5th Degree . . . . . 39 20-b. Graph of the Error in the Calculated Gravity Values-5th Degree . . . . . 39 21. Map of the Individual Station Density Error-3rd Degree 0 o c o c o o o I-IO 22. Map of the Individual Station Gravity Error-3rd Degree . . . . . . . . Al 23. Map of the Individual Station Density Error-5th Degree . . . . . . . . A2 2A. Map of the Individual Station Gravity Error-5th Degree . . . . . . . . A3 viii Figure 25. 26-a. 26-b. 27-h. 28. 29. 30. 31. 32-a. 32-b. 33-3. 0 33-b. 3A. Page GRAVITY MODEL INVOLVING ALL THE SOURCES Gravity Effect of the Combined Sources . . A5 Graph of the Error in the Calculated Density Values—3rd Degree . . . . . A6 Graph of the Error in the Calculated Gravity Values-3rd Degree . . . . . A6 Graph of the Error in the Calculated Density Values-5th Degree . . . . . A7 Graph of the Error in the Calculated Gravity Values-5th Degree . . . . . A7 Map of the Individual Station Density Error-3rd Degree . . . . . . . . A8 Map of the Individual Station Gravity Error-3rd Degree 0 o o o o o o o ’49 Map of the Individual Station Density Error-5th Degree . . . . . . . . 50 Map of the Individual Station Gravity Error—5th Degree . . . . . . . . 51 COMPARISON OF ALL THE MODELS Graph of the Error in the Calculated Den- sity Values-5th Degree . . . . . . 52 Graph of the Error in the Calculated Gravity Values—5th Degree . . . . . 52 INCREASED DENSITY CONTRAST IN THE GLACIAL DRIFT Graph of the Error in the Calculated Den- sity Values—5th Degree . . . . . . 5A Graph of the Error in the Calculated Gravity Values-5th Degree . . . . . 5A Map of the Individual Station Density Error—5th Degree . . . . . . . . 55 ix Figure Page 35. Map of the Individual Station Gravity Error-5th Degree . . . . . . . . 56 DECREASED STATION.SPACING 36. Map of the Individual Station Density valueS‘lst Degree. 0 o o o o o o 58 ELEVATION DATUM ALTERED 37. Map of the Elevations After Raising the Elevation Datum . . . . . . . . 60 FIELD STUDIES 38. Contour Map of the Survey Elevations . . 62 39. Map of the Residual Elevations from a Third Degree Polynomial Approximation to the Elevation Surface . . . . . 63 A0. Variable Density Map. . . . . . . . 6A A1. Profile of the Residual Elevations- Density Values—Bouguer Gravity . . . 66 A2. Map of the Bouguer Gravity. . . . . . 67 POLYNOMIAL APPROXIMATIONS A3. Profile of the Bouguer Gravity and the Residual Values from the 7th Degree Polynomial Approximation . . . . . 71 AA. Map of the Residual Values from the 7th Degree Polynomial Approximation to the Bouguer Surface . . . . . . 72 DOUBLE FOURIER SERIES APPROXIMATIONS A5. Profile of the Bouguer Gravity and the Residual Values . . . . . . . . 75 A6. Map of the Residual Values from the Double Fourier Series Approximation to the Bouguer Surface . . . . . . 76 Figure Page BAND PASS FILTERING A7. Frequency Response of Band Pass and Low Pass Filters . . . . . . . . . 81 A8. Profile of the Bouguer Gravity and Residual Values from the Band Pass Filters. . . . . . . . . . . 83 A9. Residual Map of Half Wavelengths from 10,000 to 30,000 Feet . . . . . . 8A 50. Residual Map of Half Wavelengths from 5,000 to 15,000 Feet . . . . . . 85 51. Residual Map of Half Wavelengths from 2,500 to 7,500 Feet. . . . . . . 86 LOW PASS FILTERING 52. Profile of the Bouguer Gravity and Residual Values from the Low Pass Filters. . . . . . . . . . . 87 53. Residual Map of Half Wavelengths from Infinity to 20,000 Feet . . . . . 88 5A. Residual Map of Half Wavelengths from Infinity to 10,000 Feet . . . . . 89 55. Residual Map of Half Wavelengths from Infinity to 5,000 Feet . . . . . 90 56. Residual Map of Half Wavelengths from Infinity to 2,500 Feet . . . . . 91 HIGH PASS FILTERING 57. Profile of the Bouguer Gravity and Residual Values from the High Pass Filters. 0 O O O O O O O O 0 93 58. Residual Map of Half Wavelengths Less Than 20,000 Feet. . . . . . . . 9A 59. Residual Map of Half Wavelengths Less Than 10,000 Feet. . . . . . . . 95 60. Residual Map of Half Wavelengths Less Than 5,000 Feet . . . . . . . . 96 xi Figure 61. 62. 63. 6A. 65. 66. 67. COMBINED HIGH AND LOW PASS FILTERING Profile of the Bouguer Gravity and Residual Values from the Combined High and Low Pass Filters . . . . . . . Residual Map of Half Wavelengths from 10,000 to 20,000 Feet. . . . . . . Residual Map of Half Wavelengths from 5,000 to 20,000 Feet 0 o o o o o 0 Residual Map of Half Wavelengths from 2,500 to 20,000 Feet . . . . . . . MODEL STUDY OF THE SCIPIO OIL FIELD Calculated Gravity Anomaly of the Scipio Oil Field for a Density Contrast of 0.05 gm/cc Between the Dolomite and Dolomitic Limestone . . . . . Calculated Gravity Anomaly of the Scipio Oil Field for a Density Contrast of 0.125 gm/cc Between the Dolomitic Lime— stone and Dolomite. . . . . . . . REGIONAL GRAVITY STUDY Regional Gravity Profile Through Berry, Hillsdale, and Jackson Counties, Michigan . . . . . . . . . . . xii Page 97 98 99 100 103 106 110 INTRODUCTION Objective The 1957 discovery of oil in an anomalous dolomite zone in the Middle Ordovician rocks of Hillsdale County, Michigan, led to the eventual development of the Albion- Scipio Oil Field. Preceding the discovery, the annual production from the Trenton and Black River Formations in Michigan was slightly in excess of 10,000 barrels. By 1961, the annual production approached the 12 million mark as shown in Figure l. The Albion-Scipio Field is located in Hillsdale, Jackson, and Calhoun Counties and, although the length exceeds 35 miles, the average width is less than one mile. Geological exploration methods used for extending the production proved unsatisfactory, resulting in a large increase in geophysical activity involving both seismic and gravity methods. The confidential nature of these company conducted investigations has resulted in a paucity of published information on the applicability of the geOphysical approach to delineating the geographical location of the production. The lack of published information, other than the results of an isolated gravity profile across the area by . umber. vw N w 00 mm mm V0 No On we. @v I» N¢ 0? mm _ _ _ >mw>oom_o 04!... O.a_omlzo.m4< 159.855 3:3 25:12.2 2. zoioaooma go fiszzq 52m 6915-29sz O_ N. 4 .0 no mqwmmdm “.0 mzo_.j_2 Ferris (1962), provided the incentive for conducting a gravity investigation in the north central portion of Hillsdale County. The threefold purpose of the investi— gation was to develop a method of minimizing the error in the Bouguer gravity reduction due to near surface density variations, study the applicability of repre— sentative gravity anomaly enhancement methods for iso— lating the anomaly directly or indirectly associated with the Scipio Oil Field, and ascertain the geological source of the gravity anomaly associated with the Scipio Oil Field. Approach A generalized three dimensional geological model of the producing structure was constructed from subsurface geological data. ApprOpriate density contrasts between the productive dolomite and the non—productive dolomitic limestone host rock were assigned to the model, and the gravity effect of the structure calculated at the surface elevations. This study provided limits on the magnitude and configuration of the associated gravity anomaly. The error in the assumed density value used on the Bouguer gravity reduction may mask the small magnitude geologically significant gravity anomalies. This pro- blem is common to gravity surveying throughout Michigan, but is particularly pronounced in the area of the Scipio Field. The marked surface topography, and the abrupt horizontal changes in the composition of the glacial drift precluded the use of a single density value. As a result, a method was developed and evaluated through the use of model studies by which a near surface repre— sentative density value is obtained from the gravity data for each station in the survey. The field data was corrected with individual station elevation factors, and the Bouguer gravity was analyzed with polynomial, double Fourier series and linear filtering methods. Location of the Study Area The geographical location of the area of investi- gation includes portions of Allen, Litchfield, Scipio, Fayette, Moscow, and Adams Townships in Hillsdale County, and small portions of Pulaski and Hanover Town— ships in Jackson County, Michigan. Figure 2 is a location map of the area of investigation. Physiography of the Study Area The physiographic character of the county is appropriately described by Veatch (192A) in the statement that, . . . the relief is largely constructional, due mainly to the uneven disposition of a thick layer of glacial material. The county has the rolling or billowy surface, smooth rounded slopes, sandy and gravelly knobs and ridges, numerous lakes and swampy depressions, sandy and gravelly plains, and nearly level clay plains characteristic of land of glacial origin. 1 I I , PULASKI 1| HANOVER I I a I I .J u | :l SCIPIO : - l moscow E" I .l I— _ __ _ __ _ _' | F““ 5' FAYETTE I ADAMS a" | 4 I 1 I j > W rf I l . e I LOCATION OF THE SURVEY FIGURE 2 MILE. The elevations in the survey area range from 1,000 to 1,300 feet. GEOLOGICAL SETTING In 1957, random drilling resulted in commercial production from the Middle Ordovician carbonates in Hillsdale County, with subsequent drilling resulting in the develOpment of the Albion—Scipio Field. The pro- duction comes from the Trenton-Black River Formations (Figure 3) and is confined to an anomalous dolomite zone formed in the regionally dolomitic limestone province. The vertical extent of the dolomite zone is not defined due to the lack of drilling below the oil—water contact, but is at least 610 feet thick. A structure contour map on tOp of the Trenton Formation is shown in Figure A, illustrating the northwest regional dip that controls the -2750 foot gas-oil contact datum and the -2920 foot oil—water contact datum in the Scipio Field (Bishop, 1967). Bishop concludes from his Albion-Scipio Field study that it, . . . exhibits a northwest—southeast trending syncline deveIOped on the Middle Ordovician Trenton limestone. This northwest plunging syncline has approximately 30 feet of relief, and is directly associated with fracturing, solution activity, dolomitization, and the deveIOpment of a porosity oil trap in the Trenton—Black River limestones. The Albion- Scipio Field was formed in Devonian time by a movement along lines of pre—existing weakness 7 STRATIGRAPHIC SUCCESSION IN MICHIGAN PAUOZUCTPIOUG'I In" mm 5 I22 FIGURE m comm fl WAY“ nua- HII‘I—I-UI n—aadq-u nun—nun... m‘—v—-fi-l~d~d~: :uau—d-w-u- (nu—d0“. a... nun—upw— wI-hn—Ifil—n Minn—nun—II-mu— ”aqua—I “Inland—uni pad- “I‘d-land dflp—Cmdh—n-y—l ht- mm mm as hid—l inn—I- bu.- hb—u—‘d __':_ na— -. I— -u - ht. WI- his. nun—n {In-l I. 5-..“: Mil i—r ”4|.- uns. huh-14“:- ic-Ilals h I—J _ Vru-IlG-h I——— .__.-n- w...‘_ —.u-_ u.“- ”on. an. u-I- an. Dal-MM“!- n-‘Ju—l-PI Ha.__auu- _...- h. an.- m—r- -- u...- .— ano- Iu-‘qi- n.- mdu— _ (5.“. tuna—4 u Due—IN Cat-nil- I"... .. w ul- Mc‘n— un—a an. lIa—p-Id h...- |~ I ‘_.uu. |::. deh_. I—‘h‘ Inn-c.- out nun—r..— uh-Gu. “p... _m|a— l —_ a...“ 3.--Geologic Column of Michigan cum— 10 Feet CI = DATUM = Sea Level '9‘, m I I FIGURE A.--Structure map Formation. on tOp of the Trenton 10 in the basement complex. The movement was re— flected in the tilted Trenton—Black River lime- stones not as a single continuous fracture, but as a system of fractures trending northwest- southeast. These fractures served as a channel way for solutions that dissolved the calcium carbonate and provided sufficient additional magnesium ions to make possible the precipitation of dolomite. This solution activity created an approximate 8-9% loss of volume of the Trenton- Black River Formations. Devonian sedimentation filled the subsiding depression and it was no longer present after Devonian time. FIELD METHODS Gravity readings were taken along all available roads at approximate 500 foot intervals. Additional traverses were run cross-country where the road system failed to provide uniform coverage in the area, and where it was desirable to have additional coverage across the production. Regional coverage was extended through the use of gravity readings from a previous quarter mile station spacing survey. Accuracy of the meter readings was maintained by taking repeat obser- vations at each station until duplication was obtained within 0.2 scale divisions (sd.). World Wide Meter number A5 (calibration constant of 0.10093 mgal/sd) was used throughout the survey. Station elevations were established by leveling. Elevation control was maintained by tying to U. S. Geo- logical Survey bench marks and closing all traverse lines. The largest closure error throughout the survey was less than 0.25 feet. 11 DATA REDUCTION Observed Gravity Base ties were made on an hourly interval and the mid-hour station reoccupied immediately after the base tie. Drift curves were used to eliminate meter drift and tidal effects. The drift rate between base ties was checked by the mid-hour repeat reading. If the drift rate exceeded a scale division per hour, or the mid-hour repeat reading did not check within 0.2 sd., the stations observed within that hour were reoccupied. After cor- recting the station readings for meter drift, they were multiplied by the meter constant to obtain the station observed gravity. Latitude Correction Station distances were calculated from the stadia intervals and plotted on 7-1/2 minute U. S. Geological Survey topographic sheets. The station coordinates were taken from the tOpographic sheets in reference to the Michigan Coordinate System, East Zone, established by the U. S. Coast and Geodetic Survey. Latitude corrections were made by rotating out of this system into the latitude and longitude system and applying a correction factor of 0.0002A7A mgal/ft. l2 13 Elevation and Mass Correction General Statement The elevation correction compensates for the normal vertical gradient of gravity by applying a correction factor to the difference in elevation between the station and a reference datum. The mass correction compensates for the mass of a horizontal sheet of infinite extent and thickness equal to this same elevation difference. Because both corrections are linear functions of the elevation, they can be combined and expressed as g(em) = (0.09A06 — 0.01276 0) h (1) where h is the elevation difference in feet between the station and the datum, and o is the density in cgs units assumed for the material within this interval. Through- out the remainder of this report, the combined correction -will be referred to as the elevation factor. The small magnitude (generally less than 0.3 mgals) of the geologically significant anomalies in the survey area combined with the pronounced surface topography and abrupt horizontal changes in the glacial drift compo— sition precludes the use of a single density value for the entire area. The use of a single density value and the ensuing errors for other geological conditions are presented in an excellent review of the subject by VaJk (1956). 1A The relative error in gravity between two stations for a relative error in density is shown in Figure 5 as a function of the elevation differences. This graph, modified from Ivanhoe (1957), provides an easy method for checking the feasibility of a suspected correlation between an anomaly and the corresponding topographic feature. For example, a 0.1 mgal anomaly would be created by a A0 foot high topographic feature if the density assumed in the Bouguer reduction was 0.2 gm/cc too low. Previous Work The importance of the elevation factor in gravity surveying has been stressed in many published papers and a variety of techniques have been developed to minimize this error in the reduction of gravity data. The most significant of these methods are reviewed to provide background for the method developed in this study. Nettleton (1939) was the first to publish a method for obtaining a local representative elevation factor from the gravity data. His approach involved . . . making a special traverse of gravimeter stations across a topographic feature, reducing these stations for several different densities, and finding the density value for which the re- duced curve had a minimum correlation with the topography. In this method, the sample is an entire tOpographic unit and the value obtained is the average density of all material within the elevation range of the gravity traverse. l5 n U540: mzo_h<._.m zo_h<>m...m m>_._.<._um on u>Fh. >120 x unojom ~ 0 s 0 0000. n 0000 n 0000 n a 0 o 7.. cozxw -o_x A moduli! a". kkka .EQUVQQ stk u>x§Vth»_mzwo z. ~-o_ o. a s T TI 0 o o 0. I oooo 0000 .lv 1 rl r: r .nlllollll‘ C. u¢30.u tommw x.uu\Eou. 0 n v n ' 9 O~ 0*. O? 00 1833838 3AI1V'IDN03 Cu 00. O mango: nnJSggozhca mucouo maoqm 02.1 0000." taktm \C>$$303>§ NuQQ! O .u o .u C ‘ O o '0 O O 0 0 _ O O _ _ . . o . . O W O 0 O 'O ‘O O m m ... m m m m m f uQEoNN 0 00 O o—o~c~on ON _ ._ .N ON ON 00 ._ ‘0 N n n - s... m: n- N. N: n o . o o a- it w m- ~.- ? ? ~39??? WW??? .°‘°O°.°.° 0° 0° ‘0 '0 '0 oo so ' 0 0° '0 '0 0° 0° 0° 0° 0° 00 0°00 .0 000° .0 00.0 .0 0° .0 ‘0 .|fi!AIIIIIII.2§Eo:wIIIIIII'. 27 o. manna—m 70x 8330s: I% mu 44.20259. umxowo coco." m:.o<¢ sz QOQQM x k3 Stb xx QC Nu m. 0 0° 0° '0 .o 0° 0° 0° .0 .0 -0 0° 0° 0° 0° 0° 0° ’ O 00 0° 00 0° CO 0° 00 0° '0 0° ’0 5&ku «Rxb‘db QISQOx—‘S «INQQ: m _ ... ... ... ... ... ..- _- m. ... ml” _ uo\E)N.N ~O ‘0 .0 00 “I m: 4......m4mmtswse a _ mu m m . _.. . ... .. ... ... «.umtn'nu.oo_.a_umvmv .1. m ... ._ ... .1 0.. 0 O t s s .-.-.m.._...m....m....... NI 0 .w v 0 O m ._ ... .. m ... Nnmnoauvnmo_onw”-n.v n. ... m. .._ o .w .._ 1- m. n. .u 0 ..-m-m_..._w.__mmwm... IXI on): o _.N IIt'. 28 0° .0 no 00 0° .0 no .0 0° 0° 0° lo I CALCULATED GRAVITY EFFECT OF RIVER CHANNEL (”GAL/X/O" CI = o.Io MGAL 00 ET FIGURE ll 29 with a third and fifth degree polynomial. A radius of 6, 8, and 10 thousand feet was used for each degree polynomial. The difference between the known station density and the density obtained from the calculated elevation factor, along with the difference between the known and calculated station gravity are shown in graphic form in Figures l2-a and 12-h for a third de- gree polynomial. Similar values for the fifth degree polynomial are shown in Figures 13—a and 13—b. These figures indicate that a 10,000 foot ring radius produces the most accurate results, and for that ring radius there is very little difference in accuracy between the third and fifth degree polynomial. The error in station den— sity for a third and fifth degree polynomial and 10,000 foot ring radius is shown in Figures 1A and 15. The associated errors in gravity are shown in Figures 16 and 17. The graphs for both the third and fifth degree polynomial and various ring sizes show the 10,000 foot radius produces the most accurate results, with the third degree slightly more accurate than the fifth. There is, however, a marked decrease in accuracy when compared to the model involving only density variations in the drift. The maps showing the error in the calcu- lated station density and gravity for the fifth degree polynomial and ring size of 10,000 feet reveal that o. o o A o a c n u j C O Q 0 O I O O I I I 0 0000. n u 24 I coo. n a cone n . I c o T r- I‘.\W In. Ulnar; CN- u3:¢.u uh>¢<§§0 QMSE‘ Qhk‘bfi 9.“ txs <30 14% .35) QQsts 430‘ 5.3;; «wagon a. 22:3 ~.o; .m449.44.a a. O l O. 3M1V'I 0.03 1 833838 Os >»_mzmo z. coccu ~-9 x.oo\Eo«. o A o n o oooo. n x coo. n o oooo n . a a "s 1 8 luaouad JAIivwnnna 1 2 .nloo. 31 O. In. ucao: (I. u¢30.u NW§§§Q khxtk 93ka 9Joa wmxwwo 0000." maodm 02.x ~-o?< 33$: gkkh Fat—Stu >6th0 ”I 2 an: o E .mgssu khxtt QNBSQ. 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C u N 0 b v 0 o o o o o o a 32;. ..N I 2 mean: NM§§V§Q th>\k tht§fi Q)“ kkxkfi q‘xb‘a My: 0>Q>QQ>§x uhQQ! 35 sm%%o Gan.”..._-n..m-¢-.,-.~_mmn.mm_mmm.~ n" 44.56259. ummemo - - oooo. u . was: 9.5 m u m _ m. n- .- _ a o ~0°\k\fl‘g§\ o I o 0 o n- u- N o o QOQQM xxg‘ka §QR¢RM . . . . . m- pr u m- o _- _- c. s- s. u- c- n- n- _- _- n- o- o- o- o- ~ ~ _ ~ _ o o _- _- o m t. u- . n- o u o a- a- m- t . o m- c... mu v. _. w n- m- n- ~ a .. _- _- _- 1 s- v- n- o. o- o- .- m- s- :. a- v- n n. n c _ _ m m u m _ .w ..- m. . m m o o- ~- c c u o o- _- o n _ o v. o a o n. o o o o .- o 7 n- a- _. o m .- _- a- u. o. s c c o v a n n a a o . a- o a v ~ o o m n. u . o o o u. a o o o o v. o . o o o o o o . o o _ o o o .- o o u. a. : n. o. o s s h a n .? 3233 XIII 025:“ Ill... 36 these errors are associated with both the river channel and the density contrast zone in the drift. Gravity Model of the Glacial Drift and Reef Structure.--The reef structure was buried 2,500 feet beneath the glacial drift and assigned a positive den- sity contrast of o.u5 gm/cc. The gravity effect of this structure was calculated at the surface elevations by the same method used for calculating the effect of the river channel. The associated anomaly is shown in Figure 18 and closely approximates the magnitude and shape of the observed anomaly (Servos, 1965). The combined observed gravity values for the river channel and reef were studied with third and fifth degree polynomials for ring sizes 6, 8, and 10 thousand feet. Figures 19-a and l9—b are graphs of the error in density and gravity for the third degree polynomial and various ring sizes. Figures 20-a and 20-b are similar graphs for the fifth degree polynomial. Figures 21 and 22 are maps showing station density and gravity errors for the third degree polynomial with 10,000 foot ring radius. 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Q Q 0 ll! 52 nun w¢30.u >t><¢o cuzuaoo z. coxzu (an acne: WQNQQ). ksshthkkxfi Nth 3k hkqxfivflk k0 tomsnx‘QQb ~-O.xam4¢0_44.!fl. ~uo. O. o O h A o . a Q n N . o O. o O N G O o O O o o O O I I. o o 0 o 0 a fl 1 l o. .l 1| 1 ON .I r . tic coco. « 1.8 1 {Eu v 2.3.32. 38. x o {.553 .I 2 n 'l {:3 3:25.... 52¢ 88. o M E36 .6225 52.. 1 I r.._8..._uu¢...uzz§o 52¢ 38. . \ 1 on u I tic ....uuc 33.238 5:: z \ M 3 o T \ LWOO d .I 3 \AV 8 3 T l 2 u I \\\\. x\\\\ 1 .l. ! \ l T o\ \u 8 \I\ I \. \\.\I. 1 a I ‘I‘Okalllu‘. «ul‘u Auv.a\\\u.\\\ g 00. I r h .mzua 2. coxcu x 335...: ‘ n ¢ 0°09 8° 0. 0000. 008. X I, N O o 4 W 1N39I3d amu'lnuna Os OO- 53 bedrock channel are closely associated and distinctly less accurate than the results for the models which in- volve the glacial drift and reef. Increasing the Density Contrast Within the Drift.-- The previous discussion shows that the errors in the calculated elevation factor are directly associated with near surface density contrasts. This source of error was further investigated by reprocessing the glacial drift and bedrock channel model with a fifth degree polynomial after increasing the density contrast within the drift from 0.1 gm/cc to 0.3 gm/cc. The error in density values for a 6, 8, and 10 thousand foot radius is shown in Figure 33-a, with the corresponding error in gravity shown in Figure 33—b. Although the density contrast was increased threefold, a ring radius of 8,000 feet or greater, results in 87 per cent of the density values and 8M per cent of the gravity values having errors less than 0.1 gm/cc and 0.1 mgal. The areal distribution of the station density and gravity errors for the 10,000 foot ring radius are shown in Figures 3M and 35. Decreasing the Station Spacing.--There are a definite number of data points required to satisfy any given degree polynomial, and thus the station spacing will dictate the minimum ring radius required to insure these data points. For example, a first degree equation requires only 4 data points whereas a fifth degree requires 22 data points. 54 on» 0830: 4n» 0.30.; qh>§< «Sb khzxk QMESQ Q); kkxs q‘xb‘flfi Bk: 40) >2 QMQQ‘ $.33 :33- ... .355 >233 .... ..occu 72:33:43.1 ~-o_ x .oo\an. o. o o . s . o . a c n ~ . o o. o o s o o o n ~ . j 0 O O O o o O O I J 0 fl 0 0 o o O o o O O I .Io_ I 00\Eo V.N d) 0 0\Eo ..N hm<¢h200 >._..m2wo 00\ Eo ¢.N a) ue\..:o _.N hm5..ng 1 4.: I . . x r oooo. n x 8 I 33. a x ooo. a o \\\\p. a . oooo a o I oooo a . x.\\\}.¥ M I oooo a . u o \\\\ m \\\\o 1 x o\:. on W. I z a x o\ a. \x \ .l \ \o l 0. d I u\6 0\ 3 \O \O \n\o U x\u x . a , . 1 \ \o\ I as 3 .I x\o\ \o II. 0 Vi“. ak. . .V.\ .HI\OIIII‘O\O I. 8 T. \Kfl\o . uu\\\\~ n\ “a I 1.! _nu““umv\\ \ - . . a... i- 3 uaoud amn'muna 2 55 in ”.50: Shin-Io cowl fluxes-20250.» uwmwuu 0000." -mzaqm 02.x «..ka \uQEu\ QQQQN \meihQ §ka. 33. ..... .. n m .. .iw ... ... 0 m. 0.00 ... s _ 0 ...sm Ii 0' 'V figsv‘tb O '0 .“o' .. $93k thkxufi Qi‘ kkxkfi mwm- omv mm... N..m so". 'N 0. ON 0' 0. ON on d‘xu 3.0 9530635 ##8! ..- o- o.. a- a- ...- 0.7 M1. +. m- .....- «.... BI ...- a- ._- m- .m- . a- on- ..I. t! h. oo\Eo ..N OI 'I | 56 an Utao; 000» ooo~ 000. o by u u nu ..d.§oz>JOa wmxowo 0009 u mgodm 02.1 .13». 3on toot-a .2526 aotEm .- ..- _- ..- - o -o .0, o -0 -o -0 o o ‘- ' O omzkuto «8% 333% S5. bog 43..» 3o offloés «moot o._-o «- o o ..-s-z-zuvwvnflg on ....w n- . I «N N on n - o. o ...- ...- .. V ... ..- m- ... ..- NI no 0- n- .I NI 0: ..I 0? GI ”T n. O h 0 V ... .I O O O O O O ..- . m- ... w OmI «I n.“ . 5.- m- ... _ m- i- ... o v- o- o- o-a- n- m-s-ou-nT r..- o. .o o o. .a .... ..- J- m ..- w- ... m ...- ..- . ... . m- _I m. a O ..I {I N.- _I .... My 1.- NI 0.- ~..I mm C.— _.. W ... .n .0 ..- m. o m ..- ... .... .. 0 n.» on m 8 on 0 o o 0 °-‘ ”T V '3 .8. '5 '3 h 3235'- [XI-ll aux-co ..N .0 “I «- QI on '7 -o ‘0 '0 -o 'O on I, It 57 If the data set encompasses a complex gravity field, then a higher degree polynomial will be required to satisfactorily fit the data. Increasing the number of data points per unit area will permit the use of a smaller ring size and decrease the complexity of the gravity field in the data set. The result of this com— bined effect is demonstrated in the following study. The model involving the glacial drift and buried river channel was processed after calculating the data on a 1,000 foot grid spacing. The calculated density values shown in Figure 36 were obtained from using a first degree polynomial and 1,200 foot ring radius. The excellent results were obtained even though the density values in the glacial drift changed from 2.2 gm/cc to 2.6 gm/cc. Altering the Elevation Datum.—-Vajk (1956) has shown that the variable datum to which the observed gravity values are reduced through the use of a local representative elevation factor should be subject to geological considerations. A study was undertaken to find what effect the elevation datum had on the calcu— lated elevation factor. The observed gravity values for the model involving all of the sources were calculated at the station ele- vations. The elevation datum was raised 100 feet, pro- ducing both positive and negative values as shown in 58 on 952... «$ka 53% on: 95‘ too .3318 $349.): $8: 00%0 O‘cflomflarflhmflflflcfloflcflcflahflfiflONcNONoNONWaHNaoNONUNONoNaoNONoNfiNONONONHN .....Szozfioa mmmomo 334803143on awoum 8m 3w 8w 8.» 8w 8w 8w om“ 8w 8w 8w 3w cam.» . 354m 025. oo..~ 8m 8w Rm showdown omuomu omu omuoam oum 81on oflm 8..“ on.“ on.“ oam .oauu \00\Eu\ _ OJNOOHNOOHNNMN .fl." aoflawawflzw 00..“ SWONhflafluflawoaanfl 8.." 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Sm ou..~ 8% 8w 8.» 8w. on.“ 803w ofiu o«.~ o~.~ ow.“ omd endow.“ 8w oo..~ Swoow o...» oonu o...» new 330..“ Bung-m oumouw ouw 8..~ on." cam 8m 3w 8..~ ow.“ 8w on.“ on." Bu 8% 8w 8w cow 8w 3..qu oowoow 8w on.» 8o 8% on.“ own 8w 8w on.“ 8w 3.3% 8w 8% ow~ o~.~ cam on." 8w. 8.» 8w 3m 8w oo..~ 8..“ on? o3 o3 o3 8w 8m 8w own 5 own and 8d own 88 oz o3 o3 own and . . . o . . . . . o o . . . . . Swoomoow o3 o3 o3 oouoaaooa .38“ caucus as 82.38“ owuoua 8.... 8a o-o-o- o- o- and o O O 0 O O 0 O 0 0 o O 0 0 0 I 0 0 0 0 O I 0 O T 0350 00.0 x . 0350 00.0 I 59 Figure 37. These values along with the previously calcu- lated observed gravity values were used in calculating the station elevation factor. The results, along with the results obtained when the elevation datum was lowered from the original by 100 feet, matched exactly the values obtained from the original complete model study. This study shows the calculated elevation factor is a function of the elevation differences, and not a function of the absolute station elevation. Summary of the Model Studies An individual elevation factor can be obtained at each station in the survey through the use of the pro- posed least squares process. The use of the observed gravity and elevation values of the surrounding stations negates the need for making preliminary data reductions. Evaluation of the assets and limitations of the method through the model studies indicate the following: 1. Rapid variations in the surface topography do not affect the calculated elevation factor when the topographic expression is not associated with a near surface density change. This eliminates the possibility of creating anomalies which are tOpographically associated. 2. An intermediate density value is obtained in the immediate vicinity of a sharp near surface density change. 6O p. u.=.:_ “case‘s sazu.ceuom. qu zpfimcov :oaudum UmpmHSoHMO on» .6 com .mcofium>oam Hmsofiwon on» A0 .houomm soapw>mao nonnasoawo ocu Eopm zpfi>mpw poswsom on» An .oo\Ew m.m mo mpfimcov m wcflm: Eopm zpfi>mpw Loswsom on» Am no . *‘Ngfi 1 I2 ' \ . W , A . Vim-9‘." s " _._ :i_ \ \\X\\ SW! ”‘5 \ a. N \. \\\ x K //_\4'5\\ A 9 ; .... \ V V w \' pg \q) j .- 6/ CI = 0.10 mgal 1' 'r T FIGURE u2.--Bouguer gravity map after employing the variable elevation factor. METHODS OF DATA ANALYSIS One of the major differences between geological and gravitational interpretational methods is the geo- logical desire to recapture, through the use of surface fitting methods, the three dimensional expression of the mapped parameter. Gravitational interpretations, on the other hand, are usually manifested in deviations from a predicted surface. The primary reason for this difference is the direct nature of geological infor- mation as opposed to the indirect nature of gravitational data. Furthermore, the clustered nature of well data does not lend itself to residual analysis, whereas, the inexpensive gathering of gravity data permits the ac- quisition of more evenly distributed information. Unlike the geological situation, where each inter— val or formation conveys specific information and is a measurable entity, the Bouguer gravity map contains in- formation from or caused by geological conditions extend- ing from the surface down to and including the basement complex. Since the mapped parameter is a composite, it becomes necessary to extract and display those signals which may be caused by or related to some known or hypothesized geological situation. 68 69 The extraction or isolation of selected infor- mation from the Bouguer gravity map may be accomplished by several different methods. The methods used in this study include polynomial analysis, double Fourier series analysis, and linear filtering methods. The latter two methods were selected for their ability to quantify the type of information to be extracted from the total map. Furthermore, the parameters of the desired information can be ascertained from geological and geophysical model studies. Polynomial analysis has been widely used as an interpretational technique in the State of Michigan and is included as a standard of comparison. Polynomial Approximations to the Bouguer Surface Polynomial approximations to the Bouguer gravity surface using the least squares criterion are generally used for the removal of the long wavelength regional component. The degree of the approximation polynomial which will satisfactorily represent the regional is subject to personal interpretation and is influenced by the distribution and spacing of the data points, the complexity of the regional, and the size of the map area. The major limitation of the polynomial approach is the inability to specify the range of wavelengths to be isolated. Signal extraction thus takes the form of 70 increasing the degree of the polynomial until the residual values display either known local geological situations, or hypothesized conditions. If an anomaly can be associated with a specific known geological entity, then predictions concerning the occurrence of similar features in the map area can be made on a comparison basis.‘ The other approach is to compare the residual anomalies with an expected anomaly, where the magnitude and configuration of the expected anomaly is obtained through model studies employing theoretical bodies. The seventh degree polynomial representation of the regional resulted in the residual values for profile A—A' shown in Figure 43 and for the map area shown in Figure HM. Double Fourier Series Analysis The recent use of the double Fourier series for surface fitting of irregularly spaced geological data has been described by James (1966). In the present in- stance, the purpose is to represent the Bouguer gravity (Gba) as a function of the two coordinates x and y. This. function may be considered to be oscillatory in these two mutually perpendicular directions and representable by the equation Gba = r (xJ). 71 n. acne: .pfie HassocsHOQ amuse ass was pom modam> Hmsofimmp who Ao ocm .mufi>mzm Loswsom msu.Am mo .<|< maflmopm KAV,.\\// . in/\ C 20.903001.“ ... o - m..- (mm. E 3 nvn~.o no; ...uuu SWV9I1'1IW All/\VU9 'IVnOlSBH S‘wefi'lm ' 8309008 ALIAVUO 72 FIGURE hu.—-Map of the residual values from the 7th degree polynomial approximation to the Bouguer surface. 73 If the function is considered to have a fundamental wavelength of 2L along the x direction and 2H along the y direction, then the double Fourier series is: z m n nmx nny Gba - Z Z Cm,n [am,n Cos —f— Cos H m=0 n=O + bm,n Sin 1%5 Cos 1&1 (11) + cm,n Cos lfli Sin 121 L H + dm,n Sin REE Sin 121- L H where Cm,n = l/U m = n = O Cm,n = l/2 m = O, n > O, or m > O, n = O Cm,n = l m > O, n > O The series is linear with respect to its coeffici- ents and thus the least squares method may be used to calculate these coefficients in a manner similar to that used in calculating the coefficients for the polynomial functions. The A matrix is now composed of the sums of squares and cross-products of the Fourier series terms, the B matrix is the column vector of coefficients, and the C matrix is a column vector of sums of products of observed values and individual Fourier series terms. 7“ The double Fourier series has an advantage over polynomial analysis in that specific wavelengths may be included in the regional values. A present limitation is the large computer memory requirements which prevent calculating coefficients for other than the fundamental wavelengths, and the first five harmonics in both directions. These limitations prevented the calcu— lation in the regional expression of wavelengths less .than 20,000 feet in the x direction and 2U,000 feet in the y direction. The residual values shown in profile A-A' of Figure US were obtained by removing from the Bouguer gravity map a fundamental wavelength in both directions of 120,000 feet, along with the first five harmonics in the x direction and the first four harmonics in the y direction. Figure “6 is a map of the residual values. Linear Filtering Methods Digital filtering of space oriented data has be- come a powerful tool for interpreting gravity data. This study makes use of the approach presented by Fraser, Fuller, and Ward (1966) which employs various filters on profile data to either enhance or eliminate anomalies of specified characteristics. The theory underlying the filtering methods used in this report is presented in the following section. n a. UKDIK mcp pom monam> HmSUflmmp An Ucm .mpfl>mzw pmsmzom one Am mo .<|< maflmopm m I; > \/\/ >> ?> .pflm mmflpmm pmflzzom maozoo ll. 1 1.. Fl ‘| . C C 20:883.; no (u¢( [Cd m... V l (Km. . v a u . o ngxbuuu S‘IV9I'1'HH AlIAVHS WVOOISBH S'IVOIT'HH unonou ALIAVHS 76 FIGURE N6.-—Map of the residual values from the double Fourier series approximation to the Bouguer surface. 77 Theory The input to a linear filter ¢(x) is related to the output ¢'(x) by the convolution of the filter with the data ¢'(x) = of0 (b (x - I) W(T)d1 (12) where the weighting function W(T) is the response of the filter to an impulse. Dean (1958) has shown that a digital representation of a continuous time domain filter, expressed here as a distance domain filter, can be represented by the equation ¢(x) E E W(kAx) ¢(x - kAx)Ax (13) where the smooth variable I has been replaced by the discrete variable kAx, with Ax representing the data increment. The problem of building a filter with the desired frequency response is accomplished through the use of Fourier transforms. The Fourier integral representation of a general filtering function can be expressed in the form g(x) = f F(o) e27“X do (in) —CD where 78 -2wiox F(o) = f g(x) e dx . I (15) -m F(o) is the density function which describes the amount of the frequency that is present in the function g(x) and is called the transform of g(x). The Fourier integral thus decomposes the distance domain function g(x) into frequencies of intensity F(o). When the desired frequency response of a filter is specified, the filtering function g(x) may be obtained from the inverse transform of F(o). For example, the ideal rectangular filter will pass frequencies in the band (Fo - AF) :_F i (F0 + AF)) without distortion, and reject all frequencies outside of this band. The inverse transform of F(o) is g(x) and may be expressed as g(x) = f F(o) Cos 2noxdo + i f F(o) Sin 2noxdo. (16) By specifying F(o) as a real, even function, g(x) is con— strained to be real and even, thus avoiding a space phase shift. These constraints cause the second integral to drop out, resulting in FO+AF f Cos 2woxdo Fo-AF g(x) (17) = %;[Sin 2n(Fo + AF) x - Sin 2w(Fo - Af)x]. 79 After applying the addition and subtraction formulas to the sine function, the filtering function takes the form g(x) = #% Cos 2w Fox Sin 2nAfx. (18) This infinite length filter is shortened to a finite length by applying the banning function (Blackman and Tukey, 1958), l/2(l + Cos %¥ IXI < T S(x) = (19) 0 IX] 3_T where 2 T is the desired filter length in units of dis- tance. In practice, it was found necessary to include the Lancos sigma factor to compensate for the Gibbs phenomenon (Hamming, 1962). The weighting function used in this study now becomes W(k) = g(kAx) S (kAx) sigma (kAX)Ax (20) where the Lancos sigma factor is expressed as Sigma (k) = [Sin ¥§J/§§- . (21) The frequency response of this modified filter is calculated from the Fourier transform of the weighting function: 80 T ~2niox f g(x) s(x) Lancos (x)e III F(o) dx, (22) which may be expressed in summation form as III 2 k w(k) Cos 2wokAx. (23) O F(o) "Mi-3 The above presentation follows that of Fraser, Fuller, and Ward (1966) with the exception of the Lancos sigma factor. The response of both low pass and band pass filters used in the study are shown in Figure N7. The requirement of using evenly spaced data was met by contouring the Bouguer gravity and interpolating onto a 500 foot spacing in the x direction for lines 1,000 feet apart in the y direction. The program ex- tended the ends of the lines the necessary number of data points so that the number of filtered stations equaled the number of input points. The extended values were projected through the use of the mean slope of the end ten stations. Band Pass Filtering The ideal band pass filter will pass without ampli- tude or phase distortion all information which has a frequency within a specified range, and reject all other information. For example, the filter with a center frequency equivalent to a 5,000 foot half wavelength 81 Amplitude Amplitude LO ,- .5 '- O 1 ii 1 l 1 l I 1 _J o 2 A 6 8 lo l2 L4 I5 L8 20 Frequency/Center Frequency LO 5 I— 0 u— Frequency/Cut Off Frequency Frequency response of the band pass and low pass filters. FIGURE 47 82 and a band pass of half the center frequency will pass all information with half wavelengths between 2,500 and 7,500 feet. Each data line was processed with band pass fil- ters having center frequencies equivalent to half wave- lengths of 20,000, 10,000, and 5,000 feet with band widths of half the center frequency. Profile A-A' in Figure U8 presents: (a) the Bouguer gravity, and the associated anomalies with half wavelengths between, (b) 10,000 and 30,000 feet, (0) 5,000 and 15,000 feet, (d) 2,500 and 7,500 feet, and (e) 1,250 and 3,750 feet. The maps associated with the first three filters are shown in Figures 49 through 51. The anomalies associ- ated with the fourth filter are too small in magnitude and random in shape to be geologically significant. Low Pass Filters That Include the Regional‘ Low pass filters were used in the analysis to emphasize the longer wavelength information. This was accomplished by passing all information with half wave- lengths from infinity to 20,000 feet, 10,000 feet, 5,000 feet, and 2,500 feet. The effect of including the pro- gressively shorter wavelength anomalies in the regional is shown in profile A—A' of Figure 52, and in map form in Figures 53 through 56. 83 gonzo: .pmmm om>.m cam omm.a Amv pew .pmom ooman sea oom.m Aav .pmmc ooo.ma sea ooo.m on .pmme ooo.om sea 000.0H ADV .emmspmp mcumcoam>m3 mam: Sufi: mmHHmEocm ocm qufi>maw hmzwsom mzp Adv mo . a < > K ( > ? ”will 1' . > > > ) L T ( i K ( um m0n~_o no. X bwwu l I zogoaooma ...O (my: 0m r I .0“! g I S‘IVSI'HIW Ail/W89 8309008 All/WHO 'WO 0 ISZH 8M : gel 5 FIGURE H9.--Residual map of half wavelengths from 10,000 to 30,000 feet. 85 FIGURE 50.--Residua1 map of half wavelengths from 5,000 to 15,000 feet. 86 FIGURE 51.—-Residual map of half wavelengths from 2,500 to 7,500 feet. 87 Na umaoE .pmmc oom.m Amv new .pmmc ooo.m Aav . . . . o csoo uflcflmcfl Eonm pooh ooo OH on pmmw ooo om ADV u mcpmcoam>m3 damn spfiz moHHmEocm ocm .zpfl>maw poswsom mcp Adv mo .—< . I /_'_\~\ C'V I) — -‘ . ’{ _\\ _ .. - - .-.-.~-_- ":7 hfi ‘K'l . . - - "or '11 .:1 x mm "-1- x "I” "1“ w an 1 FIGURE 56.--Residual map of half wavelengths from infinity to 2,500 feet. 92 High Pass Filters That Exclude the Regional High pass filters may be used to display the shorter wavelength anomalies in the same way as low pass filters are used to bring forth the long wave— lengths. The high regional gradients that predominate in the results of the low pass filter are now effectively removed by convolving the data with filters that elimi- nate anomalies with half wavelengths greater than 20,000 feet, 10,000 feet, and 5,000 feet. These results are shown in profile form in Figure 57, and in map form in Figures 58 through 60. Combining High and Low Pass Filters A selective combination of high and low pass filters will result in a band pass representation. This process of data evaluation was accomplished by using a low pass filter to remove all half wavelengths greater than 20,000 feet and then re-evaluating the residuals with filters that removed half wavelengths less than 10,000 feet, 5,000 feet, and 2,500 feet. The anomalies shown in pro- file A—A' of Figure 61 represent half wavelengths be- tween (a) 10,000 and 20,000 feet, (b) 5,000 and 20,000 feet, and (0) 2,500 and 20,000 feet. The residual maps from using these filters are shown in Figures 62 through 6“. 93 ha manor. .ummc ooo.m Aav was .pmmc ooo.oa on .pmmc ooo.om ADV swap mmma wcpwcmao>m3 mam: Sufi: mmHHmEocm ocm .mpw>mpw posmsom on» Amv mo .’ m..- lllk‘41.474. IIleo (‘ < C N . n0. X hwwk n. n.- o n. I o 0 ON 0.0 mi 6.0 06 SWVSIWWIW All/\Vfls 'lVflOlSBél S'WQIT'IIW Ail/W39 ‘8309008 9n. FIGURE 58.--Residua1 map of half wavelengths less than 20,000 feet. 95 .1. ..1 ..1. .1. .1... .1... _. nae—l 3- (...- A j '6” <1 ._ i- 3 it u $33» 3 _ 3 : 1// W__ . 3 . oqo . 0 3 CI = 0.10 mgal w *— 1 1 j '1" '1" w?" FIGURE 59.--Residua1 map of half anelengths less than 10,000 feet. 96 FIGURE 60.—-Residua1 map of half wavelenghts less than 5,000 feet. 97 .0 02:0: .pmme ooo.om ecm oom.m Aev new .pmme ooo.om new ooo.m on .pmmm ooo.om new ooo.oH ADV cmmzpmn mgpmcmfim>m3 mamz spa: mmflHmEocm ucm .mpH>MLw pmswzom m5» Amv mo . m... AVRS ' ' W —# . A3 + __3 .._ A 3 FIGURE 6U.-—Residual map of half wavelengths from 2,500 to 20,000 feet. INTERPRETATION Detectable gravity anomalies which may be associ- ated with the Scipio Oil Field have two possible origins. The first source is the density contrast between the producing dolomite and the non-producing dolomitic limestone. The other is lithologic or structural changes within the basement complex. The magnitude and shape of the anomalies which could be expected from the density contrast directly associated with the producing body were delineated by model studies. Model Study of thé Scipio 011 Field The geometrical form for the model was obtained by spotting all wells in the survey area and outlining the limits of production. A 610 foot thick three dimen- sional body was constructed, with vertical sides con- forming to the irregular shape of the outlined pro— duction. The density contrast between the producing and non-producing lithologies is governed by their con— trasting composition and porosities. Core analysis from wells in the Scipio Field provided by the McClure Oil Company indicate a l per cent porosity for the dolomitic lOl 102 limestone, and a u per cent average value for the dolo- mite. These porosity values were associated with density values through the use of a graph presented by Roth (1965). This graph, which gives the relationship be- tween the density and porosity of water saturated dolo— mite and limestone, produced density values of 2.73 gm/cc for the dolomitic limestone and 2.79 gm/cc for the dolomite. The body was given a northwest plunge equivalent to the regional dip of the Trenton Formation and the gravity effect was calculated at the surface elevations. The magnitude and configuration of the anomaly, calcu- lated through the method described by Talwani and Ewing (1960), is shown in Figure 65. Geological Factors Which Will Distort the Anomaly Geological factors in the Trenton-Black River sequence and higher in the section in the Niagaran sequence will cause distortions in the gravity anomaly now shown by the model study. The 4 per cent porosity value associated with the Scipio Field is an average value and may not represent local conditions. Table 1 shows the porosity values obtained from core analysis for six different wells in the field. These values range from 6.4 per cent down to 1.5 per cent, and would produce density values from 103 r. ~1 .3 4m —-4 i . u I ‘ u' l u 1 l. ; c- 1 1'. . 1 g 1 o ' J 9 3 I ' 1. I a | I 0 '° 1 3 i ‘ 3 Wis—q I a u no u n‘ n n I I. n " ! | l p—m T f W!!— I I I n In 0 0 ‘ I I o 0 m {+- 5 “ID— . U n ', u- u- y—m ”Tr aw "T: 11‘ *1 .q 9—1 FIGURE 65.--Calculated gravity anomaly of the Scipio Oil Field for a density contrast of 0.05 gm/cc between the dolomite and dolomitic limestone. 1011 «a 897an 22.2mm» :6 mm 8 in" 2493.. «a 83 I. won» zopzu E to 83:33 :3sz 3» we 3 efiom n.» omonIan 54.5 Izopzmmp on 82733 52¢ 54.6 a.» nomnIo~on 22.55 3» mm m ~I< m30m§ 9. 8.81.3» 2322: ~.~ 397.25.. 3 Soc I93 «mam 54.6 3» mo n... mfizzqs H: n.» «can Imam» E. 82. I ~03. 52m xofim E 6am I 03.» zopzumh 3 mm. : I» mmmzmam .... 03». I can zo» zuc» axe .ozm m3» .omm Cacao“. 3309. 20.2.2 mod 22:80.. 3.22 flu; m0< .mfimmamcm whoo Eopm Umsfiwpno mmSHm> zpfimopomlI.H mam¢e 105 2.75 gm/cc to 2.85 gm/cc. This density range would result in density contrasts between the dolomite and the host rock from the low value of 0.02 gm/cc up to 0.12 gm/cc, with associated non-measurable anomalies up to anomalies with magnitudes in excess of 0.2 mgals. For example, an average density contrast of 0.125 gm/cc would result in the anomaly shown in Figure 66. A further complicating factor is that all producing wells do not contain a complete dolomite section. Ells (1962) points out that ". . . the amount of dolomiti- zation of Trenton-Black River rocks along the Trend varies vertically and laterally within the section, and is by no means consistent throughout." Reefing conditions in the Niagaran rocks will cause further distortions in the observed anomaly when the reefal deveIOpment is directly associated with the geo- graphical location of the production. Ells believes the ". . . association of the reefs with the folds is probably entirely coincidence since reefs and reef like masses are found throughout the Niagaran complex of this region." He does, however, say that ". . . the orien- tation, shape, and size of the reefs may be directly related to the lineation and deformational patterns of the Trend." Ferris proposes that the Trend is a direct result of the reefs, but the studies by Ells and Bishop fail to reveal any reefal pattern consistent with the Trenton-Black River production. 106 IIIIII FIGURE 66.--Calculated gravity anomaly of the Scipio Oil Field for a density contrast of 0.125 gm/cc between the dolomite and the dolo- mitic limestone. 107 Residual Map Interpretation Model studies of the Scipio Field indicate anomalies originating within the geological section of the Trenton- Black River sequence will be characterized by E-w anomaly widths between 5,000 and 10,000 feet and range in magni- tude from zero to greater than 0.2 milligals. Least Squares Residuals Least squares residuals obtained from the seventh degree polynomial approximation to the station gravity values indicate the complexity of the Bouguer surface in the map area excludes the objective use of polynomial analysis. The residual values shown in Figure nu do not conform to the expected pattern indicated by the model study. The residual pattern is similar to that obtained through high pass filtering methods when anomalies with widths greater than 20,000 feet are removed. This pattern is evidenced by comparing Figures HM and 58. Double Fourier Series Residuals Double Fourier series residuals presented in Figure 46 were also obtained from operating on the station gravity values and begin to display the expected anomaly pattern. Curtailing the N-S wavelength dimension has resulted in the circular anomaly pattern observed in the lower portion of the map. The personal interpre— tation involved in the hand contouring of the residual 108 values causes some of the discrepancies observed when comparing this map with the gridded machine contoured residual values resulting from band pass and high pass filtering methods involving similar wavelengths. A re-evaluation of the double Fourier series approach would provide more useful results. Band Pass Filtering Band pass filtering with the band pass limited to the expected half wavelength range is successful in delineating linear patterns which coincide with the general pattern of production. E-w anomaly widths be- tween 5,000 and 15,000 feet shown in Figure 50 demon- strate the ability of extracting selected pertinent information from the Bouguer gravity map. Anomalies ranging from 2,500 to 7,500 feet in width shown in Figure 51 further refine the anomaly pattern. High Pass Filtering High pass filtering also delineates the linear anomalies associated with the outlined production. Figures 59 and 60 include anomalies up to 10,000 feet and 5,000 feet respectively. The inclusion of the shorter wavelengths has the negative effect of showing non-pertinent information which locally distorts the anomaly pattern. 109 The geographical distribution of the well data does not permit quantitative evaluation of linear anomalies depicted but not associated with the pro— duction. The similarity in magnitude and shape of these anomalies and the anomalies associated with the production indicate that geological conditions exempli- fying the producing zone may exist elsewhere in the map area. Regional Interpretation Ells (1962, 1966) has speculated that the lineation and interconnection of the synclines associated with the Albion-Scipio Field is controlled by slight lateral move— ment along a basement fault. Basement control for this same feature is also suggested by Rudman, Summerson, and Hinze (l965) on the basis of correlative regional gravity anomaly trends which primarily originate from structural and lithologic variations within the basement rocks. In order to investigate the correlation between the basement and the Albion-Scipio Field, a representative regional gravity profile shown in Figure 67 has been drawn from the southern part of Branch County through Hillsdale County to the center of Jackson County. The profile strikes northeast approximately perpendicular to the strike of the "Trend" and the regional gravity contours. The source of the gravity profile is unpub- lished gravity surveys which have observations at one— fourth mile intervals along all roads. 110 8 8 9 o FTIIIIIIIIIIIIIIII] LIIJLLIIIIIIIIIIIIJ s a 9 ° .1NIW'III FIGURE .7 MICHIGAN GRAVITY PROFILE TI-ROUGH BRANCH, HILLSDALE AND JACKSON COUNTIES. 111 The dominant aspect of the profile is the negative gradient to the northeast. This negative gradient is on the southwestern edge of the gravity minimum which borders the Mid-Michigan Gravity High. This large posi- tive gravity feature and its bordering negatives has a marked similarity to the Mid—Continent Gravity High which extends from Lake Superior southward into Kansas (Thiruvathukal, 1963). Bacon (1957) on the basis of gravity data and Hinze, O'Hara, Trow, and Secor (1966) from aeromagnetic data suggest that this feature extends through Lake Superior and connects with the Mid-Michigan Gravity High. Thiruvathukal (1963) has modeled several possible geological sources for the regional gravity high and its parallel minimums. He suggests that the gravity lows may be due to clastic wedges similar to those ob- served associated with the gravity minimums of the Mid- Continent gravity feature at the western end of Lake Superior. An alternative interpretation offered by him involves a downward flexure of the crust beneath the Mid-Michigan gravity feature. White (1966) also suggests this as a possible source for the minimum gravity ano- malies associated with the Mid-Continent Gravity High in the Lake Superior region. The Bouguer gravity anomaly map of the survey area shown in Figure U2 indicates a marked change in the re- gional gradient along the strike of the outlined pro- duction. This is more clearly shown in Figure 53 which 112 includes gravity anomalies of half wavelengths from 20,000 feet to infinity. This change in gradient is illustrated on the regional gravity profile of Figure 67 as a flattening of the gradient east of the Albion- Scipio Field. Approximately four miles further east the gradient increases and coincides with the gradient observed to the west of the "Trend." Detailed magnetic data is unavailable for this area, but the regional vertical magnetic intensity anomaly map (Hinze, 1963) does not display a similar anomaly. The decrease in the gravity gradient east of the Albion-Scipio Field is interpreted to be the result of a positive gravity anomaly which interrupts the normal gradient and originates from a semi-infinite slab or fault source. The gradients of the ioslated positive anomaly suggests that the center of the anomalous mass is at a depth of approximately one mile. This depth would place the source of the anomaly at or near the basement surface (Cohee, 19U5). This type of anomaly could be attributed to topographic relief on the basement surface with a scarp located approximately one-half mile east of the Albion-Scipio Field. Assuming that the Cambrian sandstones which butt up against and overlie this feature have a density of 2.A5 gm/cc and the base- ment rocks have a density of 2.70 gm/cc, the 2.5 mgal anomaly would necessitate having around 800 feet relief on the basement scarp. 113 This interpreted basement feature may be either a fault or fault line scarp which parallels the Albion- Scipio Field. Reactivation of this feature in Paleozoic time could have fractured the overlying competent sedi- ments and provided the necessary conditions for the development of the Albion—Scipio reservoir. Summary of Interpretation Residual Three different methods were used in removing the regional effects from the Bouguer anomaly map. The poly- nomial and double Fourier series methods mathematically approximate the gravity surface, and the residuals are obtained by taking the difference between the station value and the approximated surface at the data point. The complexity of the Bouguer surface in the survey area rendered both of these methods to be unsatisfactory. Fourier analysis Operates on data which has been interpolated onto a uniform spacing. The band pass and high pass filters displayed all data having wavelengths within a predetermined band or range. These filters were successful in delineating linear anomalies coinci- dent with the outlined production. The anomalies are similar to the 0.2 mgal anomalies theoretically calcu- lated from a gravity model of the producing zone. 11“ Regional All of the regional maps display a change in the regional gravity gradient paralleling the outlined pro- duction. A regional profile striking northeast into the basin reveals this to be a displacement in the regional gradient. Basement topographic relief in the form of a fault—line scarp is postulated as the cause of this displacement, and renewed activity associated with this zone may have provided the necessary condi- tions for the deveIOpment of the Albion-Scipio Field. CONCLUSIONS A detailed gravity survey was conducted in the north central portion of Hillsdale County, Michigan, for the purpose of delineating gravity anomalies associ— ated with the Scipio Oil Field. A method was developed and tested with theoretical model studies, whereby a station elevation factor can be calculated for each station in the survey. This method involved using a polynomial function of the elvation and station coordi- nates to obtain the desired elevation factor. Conclusions drawn from the model studies associ- ated with the variable elevation factor: 1. Rapid variations in the surface topography do not affect the calculated elevation factor when the tOpographic expression is not associated with a near-surface density change. This eliminates the possibility of creating anomalies which are tOpographically associ- ated. 2. An intermediate density value is obtained in the immediate vicinity of a sharp near-surface density change. 115 116 3. Steep gravity gradients caused by near-surface sources have a negative effect on the accuracy. A. The magnitude and lateral extent of the nega- tive effect caused by sharp density changes and steep gravity gradients related to near surface sources is greatly reduced by de- creasing the station spacing. 5. The calculated elevation factor, being a function of the station elevation differences within the data set, permits the reduction of the data to some geologically significant non— horizontal datum with the calculated elevation factor, and then to a horizontal datum with a pre-selected elevation factor. Conclusions related to the field data studies: The field data was corrected with a calculated individual station elevation factor and three different approaches used in removing the regional effects from the Bouguer anomaly map. The polynomial and double Fourier series methods were not effective in adequately removing the complex regional component present in the study area. Band pass and high pass filtering of the gridded Bouguer map effectively isolated elongate dis; continuous anomalies coincident with the outline of the production. These anomalies are similar in magnitude and shape to theoretical anomalies calculated from a 117 gravity model of the producing zone which employs poro- sity and density values obtained from core analysis. Conclusions related to the regional profile: A regional profile striking northeast into the basin reveals a displacement in the uniform gravity I gradient. This displacement occurs along the Albion- Scipio Field and is interpreted to originate from base- ment tOpographic relief in the form of a fault-line scarp. Renewed activity along the fault associated scarp may have established the conditions necessary for the development of the linear Albion-Scipio Field. REFERENCES BACON, L. O. (1957) Relationship of gravity to geologic structure in Michigan's upper peninsula: Insti- tute on Lake Superior Geology, p. 5H. BISHOP, W. C. (1967) Study of the Albion-Scipio Field of Michigan: Masters Thesis, Michigan State Uni- versity. BLACKMAN, R. B., and TUKEY, J. W. (1958) Power spectra: New York, Dover. COHEE, G. V. (1945) Oil and gas investigation prelimi- nary: U. S. Department of the Interior, Geo- logical Survey, Chart 9. DEAN, W. C. (1958) Frequency analysis for gravity and magnetic interpretation: Geophysics, v. 23, p. 97. ELLS, G. D. (1962) Structures associated with the Albion- Scipio Oil Field trend: Michigan Department of Conservation, Geological Survey Division. FERRIS, C. (1962) Gravity can find another Albion- Scipio: Oil and Gas Journal, October. FRASER, D. C., FULLER, B. D., and WARD, S. H. (1966) Some numerical techniques for application in mining exploration: Geophysics, v. 31, no. 6, p. 1066. GRANT, F. S., and ELSAHARTY, A. F. (1962) Bouguer gravity corrections using a variable density: Geophysics, v. 27, p. 616. HAMMING, R. W. (1962) Numerical methods for scientists and engineers: McGraw-Hill, New York. HINZE, W. J., O'HARA, N. W., TROW, J. W., and SECOR, G. B. 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(1966) Geologic evidence for crustal structure in the western Lake Superior basin: American Geophysical Union Mon. 10, p. 28. "IIIIIIIIIIIIIIIIIIIII