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Microfilms International 300N.Zeeb Road Ann Arbor, Ml 48106 THE INFLUENCE OF INDUCED POLARIZATION IN INDUCTIVE METHODS OF ELECTRICAL PROSPECTING. Item Type text; Thesis-Reproduction (electronic) Authors Debroux, Patrick Serge, 1957- Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 28/09/2021 04:46:33 Link to Item http://hdl.handle.net/10150/275348 INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. 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University Microfilms International 300N.Zeeb Road Ann Arbor, Ml 48106 1326200 Debroux, Patrick Serge THE INFLUENCE OF INDUCED POLARIZATION IN INDUCTIVE METHODS OF ELECTRICAL PROSPECTING The University of Arizona M.S. 1985 University Microfilms International 300 N. Zeeb Road, Ann Arbor, Ml 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or pages 2. Colored illustrations, paper or print 3. Photographs with dark background 4. Illustrations are poor copy 5. Pages with black marks, not original copy 6. Print shows through as there is text on both sides of page 7. Indistinct, broken or small print on several pages 8. Print exceeds margin requirements 9. Tightly bound copy with print lost in spine 10. Computer printout pages with indistinct print 11. Page(s) lacking when material received, and not available from school or author. 12. Page(s) seem to be missing in numbering only as text follows. 13. Two pages numbered . Text follows. 14. Curling and wrinkled pages 15. Other University Microfilms Internationa! THE INFLUENCE OF INDUCED POLARIZATION IN INDUCTIVE METHODS OF ELECTRICAL PROSPECTING by Patrick Serge Debroux A Thesis Submitted to the Faculty of the DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE WITH A MAJOR IN ELECTRICAL ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA 19 8 5 STATEMENT BY AUTHOR This thesis has been submitted in partial fulfillment of the requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgement the proposed use of the material is in the interests of scholarship. In all other instances, hpwever, permission must be obtained from the author. SIGNED: / r APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: 0 oa)( James R. Wait Date Professor of Electrical Engineering ACKNOWLEDGMENTS I would like to gratefully acknowledge the help my thesis advisor. Professor J.R. Wait, has given me in plan­ ning and reviewing my research and thesis. I would also like to thank the other members of my examining committee, Professors R.F. Butler and D.G. Dudley for their review of this manuscript and subsequent helpful comments, as well as the University of Arizona Electromagnetics Laboratory for its technical support. Next I would like to acknowledge the financial sup­ port that I have received while in the Master's program. I would like to thank CONOCO for its support, as well as the other companies which have supported me indirectly through Dr. Wait's Geo-Electromagnetics fund. Finally, I would like to thank Anna for her support these last three years, as well as the emotional and financial support of my parents, who have all allowed me to fulfill a long stanciing desire. TABLE OF CONTENTS LIST OF ILLUSTRATIONS vi LIST OF TABLES xviii ABSTRACT xix 1. INTRODUCTION 1 2. INDUCED POLARIZATION 4 Historical Development of Induced Polarization 5 Concepts of Induced Polarization 7 The Effect of Boundary Inhomogeneities and Clay: Membrane Polarization ...12 Classical Parameters of IP 14 Equivalent Circuit Analysis 16 Experimental Data: A Survey of Cole Parameter Range 27 3. ELECTROMAGNETIC INDUCTION SOUNDING 32 Historical Overview 34 Recognition of EM Coupling in IP Studies ... 36 The Hybrid Methods 39 The Results of Hohmann et al, 1970 41 4. INDUCTIVE RESISTIVITY MEASURMENTS IN AND ON A POLARIZABLE MEDIUM 44 Electromagnetic Fields of a Magnetic Dipole in an Infinite Medium . 45 Electromagnetic Fields of a Magnetic Dipole Over a Half-Space 47 Closed-Form Solutions of a Vertical Magnetic Dipole Lying on a Conductive, Polarizable Half-Space 52 iv V TABLE OP CONTENTS—Continued Closed-Form Expressions of the Electro­ magnetic Field Components Without Using the Quasi-Static Approximation . 58 Data Measurment: the Physics of the Receivers . 59 A Geophysical Measure: The Mutual Impedance . 61 The Mutual Impedance of Various Dipole Configurations 61 Inclusion of Ground Polarization: The Cole Relaxation Model 69 Presentation of Numerical Results 71 5. THE MAGNETIC DIPOLE INDUCED IN A PERMEABLE SPHERE BURIED IN AN INFINITE, CONDUCTIVE MEDIUM 116 Scattering From a Polarizable Sphere Buried in a Homogenous, Infinite, and Conductive Medium 117 Inclusion of Ground Polarizability: The Cole model 127 Presentation of Numerical Results 128 CONCLUSIONS 138 APPENDIX A: ANALYTIC LIMITING FORMS. .149 APPENDIX B: ADDITIONAL MUTUAL IMPEDANCE PLOTS OP INTEREST 153 APPENDIX C: ANALYSIS OF THE VALIDITY OF USING THE QUASI- STATIC APPROXIMATION IN THIS WORK 158 APPENDIX D: COMPUTER PROGRAMS „ 162 Computer Program to Compute the Mutual Impedance of the First Four Dipole Configurations .... 163 PASCAL Program to Calculate Scheme F ... 168 GLOSSARY OP INDUCED POLARIZATION TERMS 176 REFERENCES 180 LIST OF ILLUSTRATIONS Figure Page 1. A possible electro-chemical reaction involving a copper particle in an electrolytic pore fluid 10 2. An equivalent circuit modeling the electrical behavior of a metal- electrolyte interface. 19 3. An equivalent circuit model for a general mineralized rock (after Madden and Cantwel 1, 1967) 19 4. Empirical equivalent circuit for the Cole polarization model. ... 20 5. Amplitude of the Cole model (frequency dependent resistivity), dispersion exponent=0.25. Curve A: m=0.0, curve B: m=0.2, curve C: m=0.4, curve D: m=0.6, curve E: m=0.8. 23 6. Phase of the Ccle model. k=0.25. Curve A: m=0.0, curve B: ji=0.2, curve C: m=0.4, curve D: m=0.6, curve E: m=0.8. 24 7. Amplitude of the Cole model. k=0.50. Curve A: m=0.0, curve B: m=0.2, curve C: m=0.4, curve D: m=0.6, curve E: m=0.8. 25 8. Phase of the Cole model. k=0.50. Curve A: m=0.0, curve B: m=0.2 curve C: m=0.4, curve D: m=0.6, curve E: m=0.8. 26 9. Comparison between coupling and true IP response as a function of transmitter/receiver spacing. After Hohmann (1973). 38 10. Comparison between coupling and true IP response as a function of transmitter/receiver spacing. After Hohmann (1973). 38 vi vii LIST OP ILLUSTRATIONS—Continued Figure Page 11. Coordinate system used to solve for the fields of a magnetic dipole in an infinite medium. 48 12. Geometry and coordinate system used in solving for the fields of a magnetic dipole over a half-space. 48 13. Schematic configurations of transmitter/receiver pairs considered. ... 63 14. The amplitude of the normalized mutual impedance of coaxial magnetic dipoles in an infinite medium using published Cole parameter data (Pelton 1977) 76 15. The phase of the normalized mutual impedance of coaxial magnetic dipoles in an infinite medium using published Cole parameter data (Pelton 1977) 77 16.
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