Fundamentals of Gravity Exploration || Front Matter

GEOPHYSICAL MONOGRAPH SERIES NUMBER 17 FUNDAMENTALS OF GRAVITY EXPLORATION Thomas R. LaFehr Misac N. Nabighian Wei Liu, managing editor Edward K. Biegert and Michal Ruder, volume editors The international society of applied geophysics D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ ISBN 978-0-931830-56-3 (Series) ISBN 978-1-56080-298-3 (Volume) Society of Exploration Geophysicists P. O. Box 702740 Tulsa, OK 74170-2740 © 2012 by Society of Exploration Geophysicists All rights reserved. This book or parts hereof may not be reproduced in any form without written permission from the publisher. Published 2012 Printed in the United States of America Cover figure courtesy of Guy Flanagan. Used by permission. Library of Congress Cataloging-in-Publication Data LaFehr, Thomas R., 1934- author. Fundamentals of gravity exploration / Thomas R. LaFehr, Misac N. Nabighian ; Wei Liu, managing editor ; Edward K. Biegert and Michal Ruder, volume editors. pages cm. -- (Geophysical monograph series ; no. 17) Includes bibliographical references and index. ISBN 978-1-56080-298-3 (volume : alk. paper) -- ISBN 978-0-931830-56-3 (series : alk. paper) 1. Gravity--Measurement. I. Nabighian, Misac N., author. II. Liu, Wei, 1969- editor. III. Biegert, Edward K., editor. IV. Ruder, Michal, editor. V. Title. QB334.L34 2012 526’.7--dc23 2012041177D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ Dedicated to our wives, Arlys LaFehr and Aida Nabighian D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ v Contents About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2: Principles of Attraction and Earth’s Gravity Field . . . 5 Gravitational force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Gravitational constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Gravitational potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The earth’s gravity field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 The geoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 The standard International Gravity Formula . . . . . . . . . . . . . . . . . . 11 GPS and the geoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Chapter 3: The Gravitational Potential and Attraction of Mass Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Attraction of a spherical shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Components of attraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Analysis of potential fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Gravity calculations for simple geometries . . . . . . . . . . . . . . . . . . 25 Gravity calculations for 2D geometries . . . . . . . . . . . . . . . . . . . . . . 34 The logarithmic potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Green’s equivalent layer and the problem of ambiguity . . . . . . . . . 44 Chapter 4: Field Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Absolute-gravity measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Relative-gravity instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ vi Fundamentals of Gravity Exploration Gravity gradiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Field operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Measurement uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Ambiguity related to survey design — Aliasing . . . . . . . . . . . . . . . 65 Chapter 5: Rock Density and Gravity Anomalies . . . . . . . . . . . . . . 67 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Typical near-surface rock densities . . . . . . . . . . . . . . . . . . . . . . . . . 67 Density and porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Constituent densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Methods for deriving, measuring, and evaluating density . . . . . . . . 72 Definition of what causes a gravity anomaly . . . . . . . . . . . . . . . . . . 78 Chapter 6: Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Reduction of gravity survey data . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Appendix A — Bullard correction . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Chapter 7: Anomaly Interpretation Guidelines and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Purposes of gravity surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Gravity calculations for an arbitrary model . . . . . . . . . . . . . . . . . . . 102 The fast-Fourier transform for calculating gravity effects . . . . . . . . 105 Anomaly shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Anomaly separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Depth determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Determination of anomalous mass . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Interpretation of borehole gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Reservoir monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Appendix A — The unit half-width circle (2D) and ellipse (3D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Appendix B — Application of Bott and Smith theorems . . . . . . . . 147 Appendix C — Corrections for incomplete integration using Gauss’ theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Appendix D — Borehole-gravity distance/thickness relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ Contents vii Chapter 8: Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Density inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Geometric (boundary) inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Chapter 9: Geologic Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Introduction to interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Location of buried features by filtering and/or modeling . . . . . . . . 173 Example of salt with caprock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Examples of seismic pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Example of borehole gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Borehole gravity in combination with surface gravity . . . . . . . . . . . 181 Integration of seismic and/or magnetic information with gravity data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Mining applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Satellite gravity and satellite-derived gravity . . . . . . . . . . . . . . . . . 190 Appendix A: Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ viii About the Authors Thomas R. LaFehr received an A.B., College of Letters and Science, from the University of California (Berkeley) in 1958; an M.Sc. in geophysics from Colorado School of Mines in 1962 (while working at the U. S. Geological Survey); and a Ph.D. in geo- physics from Stanford University in 1964. He was employed as a geophysicist by Grav- ity Meter Exploration Company in Hous- ton from 1964 to 1969. At CSM from 1969 through 1992, LaFehr was an associate, adjunct, and full professor and George Brown Professor, taking leaves of absence during which he was founder, consultant to, president, and chairman of EDCON. He was also founder, president, chairman, and consultant for LCT. Since 1998, he has been a Distinguished Senior Scientist at Colorado School of Mines. LaFehr has published in Geophysics, the Journal of Geophysical Re- search, the Bulletin of the Geological Society of America, and the Austra- lian Oil and Gas Journal. He won three awards for best presentation at the SEG annual meeting, was the SEG distinguished lecturer in 1971 and editor in 1972–1973, was elected to honorary membership in 1979, was president in 1983–1984, and received the Maurice Ewing Medal in 1997. D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ About the Authors ix Misac N. Nabighian received a B.Sc. (honors) degree in geophysics in 1955 from the Institute of Petrol and Gas in Bucharest, Romania, and a Ph.D. in geophysics in 1967 from Columbia University in New York. He began his career in Romania in 1955, first as a party chief and then as an assistant profes- sor at the Institute of Petrol and Gas. After obtaining his Ph.D., he was employed by Newmont Mining to carry out research and develop new interpretation techniques in various areas of mining geophysics. During Nabighian’s tenure at Newmont, he devel- oped, among others, the concept of the analytic signal for interpreting poten- tial-field data and the “smoke-ring” concept to help interpret time-domain electromagnetic methods. He retired from Newmont in 1997 and since then has been a Distinguished Senior Scientist at Colorado School of Mines. Nabighian is an honorary member of SEG and was the first recipient of the Gerald Hohmann Award for excellence in electromagnetics. He was edi- tor of the two-volume SEG publication Electromagnetic Methods in Applied Geophysics and editor of the special issue of Geophysics devoted to time- domain electromagnetic methods. He also served two terms as an associate editor of Geophysics. D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ xi Preface “Knowledge of the gravity field of the earth is important in the study of our globe,” wrote W. Heiskanen and F. A. Vening Meinesz in 1958. We would add that such knowledge is also very important in the study of local earth features found in mining, petroleum, environmental, and other explo- ration venues. This book is intended to aid all earth scientists engaged in such studies. Where we describe and emphasize analytical techniques, we do so in the firm conviction that in their understanding lies the basis for future economic discoveries and that an understanding of the limitations of techniques is as important as their applicability. As discussed in this book, a rich mathemati- cal substance is the basis for clearer understanding and innovative explora- tion tools, but equations do not replace geologic breadth and scope. No better example of the use of mathematics can be found than the de- scription of the problem of ambiguity, eloquently described by Green’s iden- tities. This eloquence, however, would be lost without a thorough grounding in the acceptable solutions in practical geologic terms. We have tried separately to acknowledge the uncountable sources from which this book is derived. Some of our sources, such as our early teachers and colleagues, living and gone, contributed to the framework with which we view gravity methods and to our appreciation for their limitations. Although many such sources will remain unknown to our readers, everyone can appreciate the concept of community synergism and multiple collabora- tions. We would therefore like to express our thanks to all those who have been involved in our small but dynamic discipline. D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ xiii Acknowledgments Most of the material in this book is based on courses taught by both authors at various times in the Geophysics Department, Colorado School of Mines (CSM). We felt that a proper balance in presenting the gravity method can be achieved by combining one author’s experience in the petro- leum industry (TRL) with the other’s experience in the mining industry (MNN). The final format of the book, however, was strongly influenced by the excellent technical editing provided by Ed Biegert from Shell E&P Technologies and Michal Ruder from Wintermoon Geotechnologies. We are both extremely grateful for their patience and excellent suggestions and for providing additional technical material when needed. We are also indebted to Guy Flanagan of ConocoPhillips, who provided the satellite gravity data and helped in writing the description of the tech- nique. The chapter on inversion could not have been written without the help of Yaoguo Li from CSM, who patiently guided us in streamlining this important chapter. Mike Thomas from the Geological Survey of Canada, Jeremy Cook from Newmont, and Jules Lajoie from Comtek Enterprises Ltd. helped in obtaining some data related to mining applications. Camriel Coleman, a student at CSM, helped in imaging the Heath Steele Stratmat magnetic data, and Dionisio Uendro Carlos from Vale Mining Company helped with sketching an important figure. Mark Ander from Ander Lab- oratory LLC provided valuable information on various aspects of gravity instrumentation. Ed Biegert suggested the inclusion of various summarizing tables in Chapter 3, and they were modeled after similar tables in the Russian gravity handbook Gravirazvedka. Some material was extracted, sometimes verba- tim, from the authors’ paper “Historical development of the gravity method in exploration” (Nabighian et al., 2005), and as such, special thanks are due to the other authors of that publication: Mark Ander, Tien Grauch, Richard Hansen (deceased), Yaoguo Li, William Pearson, John Peirce, Jeff Phillips, and Michal Ruder. The authors also acknowledge the contributions from their cumulative experiences at GMX, EDCON, and LCT (TRL) and New- mont Mining Co. (MNN). D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/ xiv Fundamentals of Gravity Exploration We also thank Ted Bakamjian, Jennifer Cobb, and the rest of the SEG gang, our longtime friend, Jerry Henry, and our newfound buddy, Rowena Mills, who ably performed as special editors. Some of the material in this book is based on innumerable presentations under the auspices of SEG and AAPG. Finally, we would be remiss if we failed to acknowledge the enduring support of our wives, Arlys and Aida, to whom this book is dedicated. D ow nl oa de d 09 /2 7/ 13 to 1 28 .1 13 .2 6. 88 . R ed ist rib ut io n su bje ct to SE G lic en se or co py rig ht; se e T erm s o f U se at htt p:/ /lib rar y.s eg .or g/