Geophysical Field Theory and Method: Gravitational, Electric, and Magnetic Fields PDF
Preview Geophysical Field Theory and Method: Gravitational, Electric, and Magnetic Fields
Geophysical Field Theory and Method Part A This is Volume 49,Part A in the INTERNATIONAL GEOPHYSICS SERIES A series of monographs and textbooks Edited by RENATA pMOWSKA and JAMES R. HOLTON A complete listofthe booksinthis series appears at the end ofthisvolume. Geophysical Field Theory and Method Part A Gravitational, Electric, and Magnetic Fields AlexanderA. Kaufman. DEPARTMENTOF GEOPHYSICS COLORADO SCHOOLOF MINES GOLDEN, COLORADO ACADEMIC PRESS, INC. HarcourtBrace Jovanovich, Publishers San Diego New York Boston London Sydney Tokyo Toronto Frontcoverphotograph:Apollo 16Earthview.Courtesyof©NASA. e Thisbookisprintedonacid-freepaper. Copyright© 1992byACADEMICPRESS, INC. AllRightsReserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyany means,electronicormechanical, including photocopy, recording, oranyinformation storageandretrievalsystem,withoutpermissioninwritingfromthepublisher. Academic Press, Inc. 1250SixthAvenue,SanDiego,California92101-4311 UnitedKingdomEditionpublishedby AcademicPressLimited 24-28OvalRoad,LondonNWI 7DX LibraryofCongress Cataloging-in-PublicationData Kaufman,AlexanderA.,date GeophysicalfieldtheoryandmethodsIAlexanderA.Kaufman. p. em.- (International geophysics series;v.49A) Includesbibliographical references. Contents: v.I. Gravitational, electric,andmagnetic fields ISBN 0-12-402041-0(vol. I).- ISBN 0-12-402042-9(vol.2).- ISBN 0-12-402043-7(vol.3). I.Fieldtheory(Physics) 2.Magneticfields. 3.Electric fields. 4.Gravitationalfields. 5.Prospecting-Geophysical methods. I.Title. II.Series. QC173.7.K38 1992 550'.1'53014--dc20 91-48245 CIP PRINTEDINTIlEUNITEDSTATESOFAMERICA 92 93 94 95 96 97 BC 9 8 7 6 5 4 3 2 I To my wife Irina This page intentionally left blank Contents ~a ~ Acknowledgments xi ListofSymbols xiii Chapter I Fields and Their Generators 1.1 Scalars and Vectors, SystemsofCoordinates 1 1.2 The SolidAngle 12 1.3 Fields 22 104 Scalar Field and Gradient 23 1.5 GeometricModel ofaField 36 1.6 Flux,Divergence, Gauss' Theorem 40 1.7 Voltage, Circulation, Curl, Stokes' Theorem 52 1.8 TwoTypesofFields and TheirGenerators: Field Equations 66 1.9 •HarmonicFields 81 1.10Source Fields 100 1.11 Vortex Fields 123 References 136 Chapter II The Gravitational Field 11.1 Newton's LawofAttraction and the GravitationalField 139 II.2 Determination of the GravitationalField 157 II.3 Systemof Equations of the Gravitational Field and Upward Continuation 178 References 199 Chapter III Electric Fields III.1 Coulomb's Law 200 III.2 SystemofEquationsfor the Time-InvariantElectricField and Potential 213 III.3 The Electric Field inthe Presence ofDielectrics 238 lIlA Electric Current, Conductivity,and Ohm's Law 251 vii Vlll Contents I1I.5 Electric Chargesina Conducting Medium 265 I1I.6 Resistance 274 IlL7 The ExtraneousField and Its Electromotive Force 286 IlL8 The Work ofCoulomb and Extraneous Forces, Joule's Law 299 Ill.9 Determination ofthe Electric Field ina Conducting Medium 304 Ill.lO Behavior of the Electric Field ina Conducting Medium 326 References 396 Chapter IV Magnetic Fields IV.! Interaction ofCurrents, Biot-Savart's Law,the Magnetic Field 398 IV.2 The Vector Potential of the Magnetic Field 405 IV.3 The Systemof Equations of the Magnetic Field B Caused byConduction Currents 425 IVA Determinationofthe Magnetic Field BCaused byConduction Currents 432 IV.5 Behavior ofthe Magnetic Field Caused byConduction Currents 444 IV.6 Magnetizationand Molecular Currents: The Field H and Its Relation tothe Magnetic Field B 481 IV.7 SystemsofEquations forthe Magnetic Field Band the Field H 493 IV.8 Behavior ofthe Magnetic Field Caused byCurrents inthe Earth 511 References 565 Index 567 International GeophysicsSeries 579 Preface In this monograph I describe the theory of fields as applied to gravita- tional, electrical, and magnetic exploration methods. The next volumes willbe devoted to the theory of fields applied to electromagnetic, seismic, nuclear, and geothermal methods. Geophysical methods are applied in a wide variety of areas. They are used for oil and mineral prospecting, for solving groundwater and engi- neering problems, and in logging. And, of course, geophysics plays a fundamental role in studies of the earth's deep layers. In every geophysical method it is useful to distinguish several elements, such as theory of the method, principles and methods of measuring the field, systems of survey parameters, data processing, and solving the inverse problem and performing geological interpretation. . All of these elements together form a geophysical method and every one of them is of great practical importance. The theory of a specific method, however, has a large influence on the main features of other elements. In fact, the basis of all geophysical methods are physical laws. The choice of distances between observation points along profiles, as well as the distance between profiles and survey parameters, is usually made based on an understanding of field behavior. Regardless of the method, we always measure a signal which consists of several parts. One of these parts contains useful information about certain structures of the earth, such as layers and confined bodies. Other parts are man-made noise and geologic noise and they have to be reduced as much as possible. In separating the useful signal from the noise, which is the main goal of data processing, knowledge of field behavior as a function of coordinates, frequency, and time is extremely important. Finally, the solution of the inverse problem is in essence based on a comparison between the useful signal and the results of field modeling. ix
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