Potential theory in applied geophysics:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
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| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XXIII, 651 S. graph. Darst. |
| ISBN: | 9783540720898 |
Internformat
MARC
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| 020 | |a 9783540720898 |c Gb. : EUR 149.75 (freier Pr.), sfr 229.50 (freier Pr.) |9 978-3-540-72089-8 | ||
| 035 | |a (OCoLC)255965282 | ||
| 035 | |a (DE-599)DNB983522359 | ||
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| 084 | |a GEO 500f |2 stub | ||
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| 084 | |a 16,13 |2 ssgn | ||
| 100 | 1 | |a Roy, Kalyan K. |d 1940- |e Verfasser |0 (DE-588)121083276 |4 aut | |
| 245 | 1 | 0 | |a Potential theory in applied geophysics |c Kalyan Kumar Roy |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XXIII, 651 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Angewandte Geophysik - Potenzialtheorie | |
| 650 | 4 | |a Geophysics | |
| 650 | 4 | |a Potential theory (Mathematics) | |
| 650 | 0 | 7 | |a Angewandte Geophysik |0 (DE-588)4122049-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Potenzialtheorie |0 (DE-588)4046939-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Angewandte Geophysik |0 (DE-588)4122049-3 |D s |
| 689 | 0 | 1 | |a Potenzialtheorie |0 (DE-588)4046939-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=2931514&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m OEBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015696624&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-015696624 | |
Datensatz im Suchindex
| _version_ | 1805089120916078592 |
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| adam_text |
ELEMENTS OF VECTOR ANALYSIS 1 1.1 SCALAR & VECTOR 1 1.2 PROPERTIES OF
VECTORS 1 1.3 GRADIENT OF A SCALAR 4 1.4 DIVERGENCE OF A VECTOR 6 1.5
SURFACE INTEGRAL 7 1.6 GAUSS'S DIVERGENCE THEOREM 8 1.7 LINE INTEGRAL 10
1.8 CURL OF A VECTOR 11 1.9 LINE INTEGRAL IN A PLANE (STOKE'S THEOREM)
12 1.10 SUCCESSIVE APPLICATION OF THE OPERATOR V 14 1.11 IMPORTANT
RELATIONS IN VECTOR ALGEBRA 15 INTRODUCTORY RENIARKS 17 2.1 FIELD OF
FORCE 17 2.2 CLASSIFICATION OF FIELDS 19 2.2.1 TYPE A CLASSIFICATION 19
2.2.2 TYPE B CLASSIFICATION 19 2.2.3 TYPE C CLASSIFICATION 20 2.2.4 TYPE
D CLASSIFICATION 20 2.2.5 TYPE E CLASSIFICATION 20 2.2.6 TYPE F
CLASSIFICATION 21 2.2.7 TYPE G CLASSIFICATION 21 2.2.8 TYPE H
CLASSIFICATION 22 2.2.9 TYPE I CLASSIFICATION 23 2.2.10 TYPE 3
CLASSIFICATION 24 2.2.11 TYPE K CLASSIFICATION 25 2.3 CONCEPT OF
POTENTIAL 25 2.4 FIELD MAPPING 27 2.5 NATURE OF A SOLID MEDIUM 31 2.6
TENSORS 32 XIV CONTENTS 2.7 BOUNDARY VALUE PROBLEMS 34 2.7.1 DIRICHLET'S
PROBLEM 34 2.7.2 NEUMAIM PROBLEM 36 2.7.3 MIXED PROBLEM 36 2.8 DIMENSION
OF A PROBLEM AND ITS SOLVABILITY 36 2.9 EQUATIONS 38 2.9.1 DIFFERENTIAL
EQUATIONS 38 2.9.2 INTEGRAL EQUATIONS 40 2.10 DOMAIN OF GEOPHYSICS IN
POTENTIAL THEORY 41 3 GRAVITATIONAL POTENTIAL AND FIELD 43 3.1
INTRODUCTION 43 3.2 NEWTON'S LAW OF GRAVITATION 44 3.3 GRAVITY FIELD AT
A POINT DUE TO NUMBER OF POINT SOURCES . 46 3.4 GRAVITATIONAL FIELD
FOR A LARGE BODY 47 3.5 GRAVITATIONAL FIELD DUE TO A LINE SOUREE 48 3.6
GRAVITATIONAL POTENTIAL DUE TO A FINITE LINE SOUREE 50 3.7 GRAVITATIONAL
ATTRACTION DUE TO A BURIED CYLINDER 53 3.8 GRAVITATIONAL FIELD DUE TO A
PLANE SHEET .* 54 3.9 GRAVITATIONAL FIELD DUE TO A CIRCULAR PLATE 55
3.10 GRAVITY FIELD AT A POINT OUTSIDE ON THE AXIS OF A VERTICAL CYLINDER
56 3.11 GRAVITATIONAL POTENTIAL AT A POINT DUE TO A SPHERICAL BODY .
58 3.12 GRAVITATIONAL ATTRAETION ON THE SURFACE DUE TO A BURIED SPHERE
62 3.13 GRAVITATIONAL ANOMALY DUE TO A BODY OF TRAPEZOIDAL CROSS SECTION
63 3.13.1 SPECIAL CASES 64 3.14 GRAVITY FIELD OF THE EARTH 69 3.14.1
FREE AIR CORRECTION 70 3.14.2 BOUGUER CORREETION 70 3.14.3 TERRAIN
CORRECTION 70 3.14.4 LATITUDE CORRECTION 70 3.14.5 TIDAL CORRECTION 71
3.14.6 ISOSTATIC CORRECTION 71 3.15 UNITS 72 3.16 BASIC EQUATION 72 4
ELECTROSTATICS 75 4.1 INTRODUCTION 75 4.2 COULOMB" LAW 7FI 4.3
ELECTROSTATIC POTENTIAL 76 4.4 ELECTRICAL PERMITTIVITY AND ELCCTRICAL
FORCE FIELD 77 4.5 ELECTRIC FLUX 79 4.6 ELECTRIC DISPLACEMENT Y AND THE
DISPLACCMENT VCCTOR D 79 4.7 GAUSS'S THEOREM 80 4.8 FIELE! DUE TO AN
ELECTROSTATIC DIPOLE 82 4.9 POISSON AND LAPLACE EQUATIONS 85 4.10
ELECTROSTATIC ENERGY 86 4.11 BOUNDARY CONDITIONS 87 4.12 BASIC EQUATIONS
IN ELECTROSTATIC FIELD 88 MAGNETOST ATICS 91 5.1 INTRODUCTION 91 5.2
COULOMB'S LAW 98 5.3 MAGNETIC PROPERTIES 98 5.3.1 MAGNETIC DIPOLE MOMENT
98 5.3.2 INTENSITY OF MAGNETISATION 98 5.3.3 MAGNETIC SUSCEPTIBILITY
(INDUCED MAGNETISM) 99 5.3.4 FERROMAGNETIC, PARAMAGNETIC AND DIAMAGNETIC
SUBSTANCES 100 5.4 MAGNETIC INDUCTION B 102 5.5 MAGNETIC FIELD INTENSITY
H 104 5.6 FARADAY'S LAW 104 5.7 BIOT AND SAVART'S LAW 7 106 5.8 LORENTZ
FORCE 108 5.9 AMPERE'S FORCE LAW 109 5.10 MAGNETIC FIELD ON THE AXIS OF
A MAGNETIC DIPOLE 110 5.11 MAGNETOMOTIVE FORCE (MMF) 112 5.12 AMPERE'S
LAW 112 5.13 DIV B = 0 113 5.14 MAGNETIC VECTOR POTENTIAL 114 5.15
MAGNETIC SCALAR POTENTIAL 115 5.16 POISSON'S RELATION 116 5.17
MAGNETOSTATIC ENERGY 117 5.18 GEOMAGNETIC FIELD 118 5.18.1 GEOMAGNETIC
FIELD VARIATIONS 121 5.19 APPLICATION OF MAGNETIC FIELD MEASUREMENT IN
GEOPHYSICS . . . 123 5.20 UNITS 124 5.21 BASIC EQUATIONS IN
MAGNETOSTATICS 124 DIRECT CURRENT FLOW FIELD 127 6.1 INTRODUCTION 127
6.2 DIRECT CURRENT FLOW 131 6.3 DIFFERENTIAL FORM OF THE OHM'S LAW 131
6.4 EQUATION OF CONTINUITY 132 6.5 ANISOTROPY IN ELECTRICAL CONDUCTIVITY
133 6.6 POTENTIAL AT A POINT DUE TO A POINT SOURCE 134 6.7 POTENTIAL FOR
LINE ELECTRODC CONFIGURATION 136 6.7.1 POTENTIAL DUE TO A FINITE LINE
ELECTRODC 138 XVI CONTENTS 6.8 CURRENT FLOW INSIDE THE EARTH 139 6.9
REFRACTION OF CURRENT LINES 143 6.10 DIPOLE FIELD 144 6.11 BASIC
EQUATIONS IN DIRECT CURRENT FLOW FIELD 149 6.12 UNITS 150 7 SOLUTION OF
LAPLACE EQUATION 151 7.1 EQUATIONS OF POISSON AND LAPLACE 151 7.2
LAPLACE EQUATION IN DIREET CURRENT FLOW DOMAIN 152 7.3 LAPLACE EQUATION
IN GENERALISED CURVILINEAR COORDINATES . 153 7.4 LAPLACE EQUATION IN
CARTESIAN COORDINATES 156 7.4.1 WHEN POTENTIAL IS A FUNCTION OF VERTICAL
AXIS Z, I.E., = F(Z) 156 7.4.2 WHEN POTENTIAL IS A FUNCTION OF BOTH X
AND Y, I.E. 4 = F(X.Y) 157 7.4.3 SOLUTION OF BOUNDARY VALUE PROBLEMS
IN CARTISIAN COORDINATES BY THE METHOD OF SEPARATION OF VARIABLES 158
7.5 LAPLACE EQUATION IN CYLINDRICAL POLAR COORDINATES 162 7.5.1 WHEN
POTENTIAL IS A FUNCTION OLZ .I.E., (J * F(Z) 164 7.5.2 WHEN POTENTIAL
IS A FUNCTION OF AZIMUTHAI ANGLE ONLY I.E. § = F(Y) 164 7.5.3 WHEN THE
POTENTIAL IS A FUNCTION OF RADIAL DISTANCE, I.E., = F(P ) 164 7.5.4 WHEN
POTENTIAL IS A FUNCTION OF BOTH P AND \J/, I.E. (]) = F(P. \JR) 165
7.5.5 WHEN POTENTIAL IS A FUNCTION OF ALL THE THREE COORDINATES. I.E.
* F(P,\|/. Z) 171 7.5.6 BESSEL EQUATION AND BESSEL'S FUNCTIONS 172 7.5.7
MODIFIED BESSEL'S FUNCTIONS 177 7.5.8 SOME RELATION OF BESSEL'S FUNCTION
181 7.6 SOLUTION OF LAPLACE EQUATION IN SPHERICAL POLAR CO-ORDINATES .
183 7.6.1 WHEN POTENTIAL IS A FUNCTION OF RADIAL DISTANCE R I.E., =
F(R) 183 7.6.2 WHEN POTENTIAL IS A FUNCTION OF POLAR ANGLE, I.E. 0 =
F(9) 184 7.6.3 WHEN POTENTIAL IS A FUNCTION OF AZIMUTHAI ANGLE I.E., IP
= F(Y) 185 7.6.4 WHEN POTENTIAL IS A FUNCTION OF BOTH THE RADIAL
DISTANCE AND POLAR ANGLE I.E., - F(R, 0) 185 7.6.5 LEGENDER'» EQUATION
AND LEGENDER'S POLYNOMIAL 187 7.6.6 WHEN POTENTIAL IS A FUNCTION OF ALL
THE THREE COORDINATES VIZ, RADIAL DISTANCE, POLAR ANGLE AND AZIMUTHAI
ANGLE,I.E., (J = F(R,OE,\|/) 198 7.6.7 ASSOCIATED LEGENDRE POLYNOMIAL
200 7.7 SPHERICAL HARMONICS 201 7.7.1 ZONAL, SECTORAL AND TESSERAL
HARMONICS 202 DIRECT CURRENT FIELD RELATED POTENTIAL PROBLEMS 207 8.1
LAYERED EARTH PROBLEM IN A DIRECT CURRENT DOMAIN 207 8.1.1 CRAMER'S RULE
211 8.1.2 TWO LAYERED EARTH MODEL 211 8.1.3 THREE LAYERED EARTH MODEL
213 8.1.4 GENERAL EXPRESSIONS FOR THE SURFACE AND SUBSURFACE KERNELS FOR
AN N-LAYERED EARTH 217 8.1.5 KERNELS IN DIFFERENT LAYERS FOR A FIVE
LAYERED EARTH . . 219 8.1.6 POTENTIALS IN DIFFERENT MEDIA 221 8.2
POTENTIAL DUE TO A POINT SOURCE IN A BOREHOLE WITH CYLINDRICAL COAXIAL
BOUNDARIES 223 8.3 POTENTIAL FOR A TRANSITIONAL EARTH 232 8.3.1
POTENTIAL FOR A MEDIUM WHCRC PHYSICAL PROPERTY VARIES CONTINUOUSLY WITH
DISTANCE 232 8.3.2 POTENTIAL FOR A LAYERED EARTH WITH A SANDWITCHED
TRANSITIONAL LAYER 240 8.3.3 POTENTIAL WITH MEDIA HAVING COAXIAL
CYLINDRICAL SYMMETRY WITH A TRANSITIONAL LAYER IN BETWEEN 243 8.4
GEOELECTRICAL POTENTIAL FOR A DIPPING INTERFACE 253 8.5 GEOELECTRICAL
POTENTIALS FOR AN ANISOTROPIE MEDIUM 257 8.5.1 GENERAL NATURE OF THE
BASIC EQUATIONS 257 8.5.2 GENERAL SOLUTION OF LAPLACE EQUATION FOR AN
ANISOTROPIE EARTH 260 COMPLEX VARIABLES AND CONFORMAL TRANSFORMATION IN
POTENTIAL THEORY 263 9.1 DEFINITION OF ANALYTIC FUNCTION 263 9.2 COMPLEX
FUNCTIONS AND THEIR DERIVATIVES 264 9.3 CONFORMAL MAPPING 267 9.4
TRANSFORMAT IONS 269 9.4.1 SIMPLE TRANSFORMATIONS 270 9.5 SCHWARZ
CHRISTOFFEL TRANSFORMATION 274 9.5.1 INTRODUCTION 274 9.5.2
SCHWARZ-CHRISTOFFEL TRANSFORMATION OF THE INTERIOR OF A POLYGON 274
9.5.3 DETERMINATION OF UNKNOWN CONSTANTS 276 9.5.4 S-C TRANSFORMATION
THEOREM 276 9.6 GEOPHYSICAL PROBLEMS ON S-C TRANSFORMATION 278 9.6.1
PROBLEM 1 CONFORMAL TRANSFORMATION FOR A SUBSTRATUM OF FINITE THIEKNESS
278 9.6.2 PROBLEM 2 TELLURIC FIELD OVER A VERTICAL BASEMENT FAULT 280
9.6.3 PROBLEM 3 TELLURIC FIELD AND APPARENT RESISTIVITY OVER AN
ANTICLINE 284 9.6.4 PROBLEM 4 TELLURIC FIELD OVER A FAULTED BASEMENT
(HORST) 290 9.7 ELLIPTIC INTEGRALS AND ELLIPTIC FUNCTIONS 297 9.7.1
LEGENDRE'S EQUATION 297 9.7.2 COMPLETE INTEGRALS 297 9.7.3 ELLIPTIC
FUNCTIONS 300 9.7.4 JACOBI'S ZETA FUNCTION 302 9.7.5 JACOBI'S THETA
FUNCTION 302 9.7.G JACOBI'S ELLIPTIC INTEGRAL OF THE THIRD KIND 303 10
GREEN'S THEOREM IN POTENTIAL THEORY 307 10.1 GREEN'S FIRST. IDENTITY 307
10-2 HARMONIE FUNCTION 308 10.3 COROLLARIES OF GREEN'S THEOREM 309 10.4
REGULAER FUNCTION 311 10.5 GREEN'S FORMULA 312 10.6 SOME SPECIAL CASES IN
GREEN'S FORMULA 315 10.7 POISSON'S EQUATION F'ROM GREEN'S THEOREM 316
10.8 GAUSS'S THEOREM OF TOTAL NORMAL INDUCTION IN GRAVITY FIELD . 316
10.9 ESTIMATION OF MASS IN GRAVITY FIELD ". 317 10.10 GREEN'S THEOREM
FOR ANALYTICAL CONTINUATION 318 10.11 GREEN'S THEOREM FOR TWO
DIMENSIONAL PROBLEMS 320 10.12 THREE TO TWO DIMENSIONAL CONVERSION 321
10.13 GREEN'S EQUIVALENT LAYCRS 322 10.14 UNIQUE SURFACE DISTRIBUTION
324 10.15 VECTOR GREEN'S THEOREM 326 11 ELECTRICAL IMAGES IN POTENTIAL
THEORY 329 11.1 INTRODUCTION 329 11.2 COMPUTATION OF POTENTIAL USING
IMAGES (TWO MEDIA) 329 11.3 COMPUTATION OF POTENTIAL USING IMAGES (FOR
THREE MEDIA) . . . 332 11.4 GENERAL EXPRESSIONS FOR POTENTIALS USING
IMAGES 334 11.5 EXPRESSIONS FOR POTENTIALS FOR TWO ELECTRODE
CONFIGURATION . . 336 11.6 EXPRESSIONS FOR POTENTIALS FOR THREE
ELECTRODE CONFIGURATION . 338 11.7 EXPRESSION FOR POTENTIALS FOR SEVEN
ELECTRODE CONFIGURATIONS . 341 12 ELECTROMAGNETIC THEORY (VECTOR
POTENTIALS) 349 12.1 INTRODUCTION 349 12.2 ELEMENTAR)' WAVELET 354 12.3
ELLIPTIC POLARISATION OF ELECTROMAGNETIC WAVES 356 12.4 MUTUAL
INDUCTANCE 358 12.4.1 MUTUAL INDUCTANCE BETWEEN ANY TWO ARBITRARY COILS
. 359 12.4.2 SIMPLE MUTUAL INDUCTANCE MODEL IN GEOPHYSICS 361 12.5
MAXWELL'S EQUATIONS 363 12.5-1 INTEGRAL FORM OF MAXWELL'S EQUATIONS 366
12.6 HELMHOLTZ ELECTROMAGNETIC WAVE EQUATIONS 366 12.7 HERTZ AND
FITZERALD VECTORS 369 12.8 BOUNDARY CONDITIONS IN ELECTROMAGNETICS 371
12.8.1 NORMAL COMPONENT OF THE MAGNETIC INDUCTION B IS CONTINUOUS ACROSS
THE BOUNDARY IN A CONDUCTOR . 371 12.8.2 KORMAL COMPONENT OF THE
ELECTRIC DISPLACEMENT IS CONTINUOUS ACROSS THE BOUNDARY 371 12.8.3
TANGENTIAL COMPONENT OF E IS CONTINUOUS ACROSS THE BOUNDARY 373 12.8.4
TANGENTIAL COMPONENT OF H IS CONTINUOUS ACROSS THE BOUNDARY 373 12.8.5
NORMAL COMPONENT OF THE CURRENT DENSITY IS CONTHMOUS ACROSS THE BOUNDARY
374 12.8.6 SCALAR POTENTIALS ARE CONTINUOUS ACROSS THE BOUNDARY 375 12.9
POYNTING VECTOR 376 13 ELECTROMAGNETIC WAVC PROPAGATION PROBLEMS RELATCD
TO GEOPHYSICS 381 13.1 PLANE WAVE PROPAGATION 381 13.1.1 ADVANCING
ELCCTROMAGNETIC WAVE 384 13.1.2 PLANE WAVE INCIDENCE ON THE SURFACE OF
THE EARTH . 385 13.2 SKIN DEPTH 387 13.3 PERTURBATION CENTROID
FREQUCNCY 388 13.4 MAGNETOTELLURIC RESPONSE FOR A LAYERED EARTH MODEL
389 13.5 ELECTROMAGNETIC FIELD DUE TO A VCRTICAL OSEILLATING ELECTRIC
DIPOLE 394 13.6 ELECTROMAGNETIC FIELD DUE TO AN OSCILLATING VERTICAL
MAGNETIC DIPOLE PLACCD ON THE SURFACE OF THE EARTH 399 13.7
ELCCTROMAGNETIC FIELD DUE TO AN OSCILLATING HORIZONTAL MAGNETIC DIPOLE
PLACED ON THE SURFACE OF THE EARTH 108 13.8 ELECTROMAGNETIC FIELD DUE TO
A LONG LINE CABLC PLACED IN AN INFINITE AND HOMOGENOUS MEDIUM 416 13.9
ELECTROMAGNETIC FIELD DUE TO A LONG CABLE ON THE SURFACE OF A
HOMOGENCOUS EARTH 421 13.10 ELECTROMAGNETIC INDUCTION DUE TO AN INFINITE
CYLINDER IN AU UNIFORM FIELD 428 13.10.1EFICCT OF CHANGE IN FREQUENCY ON
THE RESPONSE PARAMETER 432 13.11 ELECTROMAGNETIC RESPONSE DUE TO A
SPHERE IN THE FIELD OF A VERTICALLY OSCILLATING MAGNETIC DIPOLE 434
13.12 PRINCIPLE OF ELECTRODYNAMIC SIMILITUDE 441 14 GREEN'S FUNCTION 445
14.1 INTRODUCTION 445 14.2 DELTA FUNCTION 447 14.3 OPERATORS 448 14.4
ADJOINT AND SEIF ADJOINT OPERATOR 449 14.5 DEFINITION OF A GREEN'S
FUNCTION 449 14.6 FREE SPACE GREEN'S FUNCTION 451 14.7 GREEN'S FUNCTION
IS A POTENTIAL DUC TO A CHARGE OF UNIT STRENGTH IN ELECTROSTATICS 452
14.8 GREEN'S FUNCTION CAN REDUCE THE NUMBER OF UNKNOWNS TO BE DETERMINED
IN A POTENTIAL PROBLEM 453 14.9 GREEN'S FUNCTION HAS SOME RELATION WITH
THE CONCEPT OF IMAGE IN POTENTIAL THEORY 454 14.10 RECIPROCITY RELATION
OF GREEN'S FUNCTION 456 14.11 GREEN'S FUNCTION AS A KERNEL FUNCTION IN
AN INTEGRAL EQUATION 457 14.12 POISSON'S EQUATION AND GREEN'S FUNCTION
460 14.13 PROBLEM 1 461 14.14 PROBLEIN 2 463 14.15 PROBLEM 3 465 14.16
DYADICS 466 NUMERICAL METHODS IN POTENTIAL THEORY 471 15.1 INTRODUCTION
471 15.2 FINITE DIFFERENCE FORMULATION/DIRECT, CURRENT DOMAIN (SURFACE
GEOPHYSICS) 473 15.2.1 INTRODUCTION 473 15.2.2 FORMULATION OF THE
PROBLEM 476 15.2.3 BOUNDARY CONDITIONS 477 15.2.4 STRUCTURE OF THE FD
BOUNDARY VALUE PROBLEM 478 15.2.5 INVERSE FOURIER COSINE TRANSFORM 480
15.2.6 CALIBRATION 481 15.3 FINITE DIFFERENCE FORMULATION DOMAIN WITH
CYLINDRICAL SYMMETRY DC FIELD BOREHOLE GEOPHYSICS 482 15.3.1
INTRODUCTION 482 15.3.2 FORMULATION OF THE PROBLEM 483 15.3.3 BOUNDARY
CONDITIONS 483 15.3.4 GRID GENERATION FOR DISCRETIZATION 483 15.3.5
FINITE DIFFERENCE EQUATIONS 484 15.3.6 CURRENT DENSITY FACTOR Q AT THE
SOURCE 488 15.3.7 EVALUATION OF THE POTENTIAL 489 15.4 FINITE DIFFERENCE
FORMULATION PLANE WAVE ELECTROMAGNETICS MAGNETOTELLURICS 490 15.4.1
BOUNDARY CONDITIONS 495 15.5 FINITE ELEMENT FORMULATION DIRECT CURRENT
RESISTIVITY DOMAIN 496 15.5.1 INTRODUCTION 496 15.5.2 DERIVATION OF THE
FUNCTIONAL FROM POWER CONSIDERATIONS 497 15.5.3 EQUIVALENCE BETWEEN
POISSON'S EQUATION AND THE MINIMIZATION OF POWER 499 15.5.4 FINITE
ELEMENT FORMULATION 500 15.5.5 MINIMISATION OF THE POWER 503 15.6 3D
MODEL 507 15.7 FINITE ELEMENT FORMULATION GALERKIN'S APPROACH
MAGNETOTELLURICS 509 15.7.1 INTRODUCTION 509 15.7.2 FINITE ELEMENT
FORMULATION FOR HELMHOLTZ WAVE EQUATIONS 510 15.7.3 ELEMENT EQUATIONS
512 15.8 FINITE ELEMENT FORMULATION GALERKIN'S APPROACH ISOPARAMETRIC
ELEMENTS MAGNETOTELLURICS 515 15.8.1 INTRODUCTION 515 15.8.2 FINITE
ELEMENT FORMULATION 517 15.8.3 SHAPE FUNCTIONS USING NATURAL COORDINATES
(.??) . 522 15.8.4 COORDINATE TRANSFORMATION 524 15.9 INTEGRAL
EQUATION METHOD 528 15.9.1 INTRODUCTION 528 15.9.2 FORMULATION OF AN
ELECTROMAGNETIC BOUNDARY VALUE PROBLEM 529 16 ANALYTICAL CONTINUATION OF
POTENTIAL FIELD 535 16.1 INTRODUCTION 535 16.2 DOWNWARD CONTINUATION BY
HARMONIE ANALYSIS OF GRAVITY FIELD 536 16.3 TAYLOR'S SERIES EXPANSION
AND FINITE DIFFERENCE APPROACH FOR DOWNWARD CONTINUATION 537 16.3.1
APPROACH A 537 16.3.2 APPROACH B 538 16.3.3 AN EXAMPLE OF ANALYTICAL
CONTINUATION BASCD ON SYNTHETIC DATA 539 16.4 GREEN 1 THEOREM AND
INTEGRAL EQUATIONS FOR ANALYTICAL CONTINUATION 541 16.5 ANALYTICAL
CONTINUATION USING INTEGRAL EQUATION AND TAKING AREAL AVERAGES 544
16.5.1 UPWARD CONTINUATION OF POTENTIAL FIELD 544 16.5.2 DOWNWARD
CONTINUATION OF POTENTIAL FIELD (PETERS APPROACH) 547 16.6 UPWARD AND
DOWNWARD CONTINUATION USING INTEGRAL EQUATION AND LAGRANGE INTERPOLATION
FORMULA 550 16.7 DOWNWARD CONTINUATION OF TELLURIC CURRENT DATA 551 XXII
CONTENTS 16.8 UPWARD AND DOWNWARD CONTINUATION OF ELECTRORNAGNETIC FIELD
DATA 552 1.6.9 DOWNWARD CONTINUATION OF ELECTROMAGNETIC FIELD 556 16.9.1
DOWNWARD CONTINUATION OF H Z 559 17 INVERSION OF POTENTIAL FIELD DATA
561 17.1 INTRODUCTION 561 17.2 WELLPOSED AND ILLPOSED PROBLEMS 57UE 17.3
TIKHNOV'S REGULARISATION 571 17.4 ABSTRACT SPACES 571 17.4.1 N
DIMENSIONAL VCCTOR SPACE 571 17.4.2 NORM OF A VECTOR 572 17.4.3 METRIC
SPACE 573 17.4.4 LINEAR SYSTEM 573 17.4.5 NORMED SPACE 573 17.4.6 LINEAR
DCPENDCNCE AND INDEPENDENCE 574 17.4.7 INNER PRODUCT SPACE 574 17.4.8
HUBERT SPACE 574 17.5 SOME PROPCRTIES OF A MATRIX . . ._ 575 17.5.1 RANK
OF A MATRIX '. 575 17.5.2 EIGEN VALUES AND EIGEN VECTORS 576 17.5.3
PROPERTIES OF THE EIGEN VALUES 577 "17.G LAGRANGE MULTIPLIER 578 1.7.7
SINGULAR VALUC DECOMPOSITION (SVD) 578 17.8 LEAST SQUARES ESTIMATOR 584
17.9 RIDGE REGRESSION ESTIMATOR 586 17.10 WEIGHTCD RIDGE REGRESSION 587
17.11 MINIMUM NORM ALGORITMN FOR AN UNDER DETERMINCD PROBLEM 589
17.11.INORM 589 17.11.2MINIMUM NORM ESTIMATOR 590 17.12 BACHUS - GILBERT
INVERSION 592 17.12.1 INTRODUCTION 592 17.12.2B-G FORMULATION 593 17.13
STOCHASTIC INVERSION 597 17.13.1 INTRODUCTION 597 17.13.2 CONJUNCTION OF
THE STATE OF INFORMATION 600 17.13.3MAXIMUM LIKELYHOOD POINT 600 17.14
OCCAM'S INVERSION 6UE2 17.15 GLOBAL OPTIMIZATION 603 17.15.1 INTRODUCTION
603 17.15.2MONTE CARLO INVERSION 605 17.15.3SIMULATED ANNEALING 606
17.15.4GENETIC ALGORITHM 611 17.16 NEURAL NETWORK 616 CONTENTS XXIII
17.16.1INTRODUCTION 616 17.16.2OPTIMIZATION PROBLEM 618 17.17 JOINT
INVERSION 621 REFERENCES 625 LIST OF SYMBOLS 641 INDEX 647 |
| adam_txt |
ELEMENTS OF VECTOR ANALYSIS 1 1.1 SCALAR & VECTOR 1 1.2 PROPERTIES OF
VECTORS 1 1.3 GRADIENT OF A SCALAR 4 1.4 DIVERGENCE OF A VECTOR 6 1.5
SURFACE INTEGRAL 7 1.6 GAUSS'S DIVERGENCE THEOREM 8 1.7 LINE INTEGRAL 10
1.8 CURL OF A VECTOR 11 1.9 LINE INTEGRAL IN A PLANE (STOKE'S THEOREM)
12 1.10 SUCCESSIVE APPLICATION OF THE OPERATOR V 14 1.11 IMPORTANT
RELATIONS IN VECTOR ALGEBRA 15 INTRODUCTORY RENIARKS 17 2.1 FIELD OF
FORCE 17 2.2 CLASSIFICATION OF FIELDS 19 2.2.1 TYPE A CLASSIFICATION 19
2.2.2 TYPE B CLASSIFICATION 19 2.2.3 TYPE C CLASSIFICATION 20 2.2.4 TYPE
D CLASSIFICATION 20 2.2.5 TYPE E CLASSIFICATION 20 2.2.6 TYPE F
CLASSIFICATION 21 2.2.7 TYPE G CLASSIFICATION 21 2.2.8 TYPE H
CLASSIFICATION 22 2.2.9 TYPE I CLASSIFICATION 23 2.2.10 TYPE 3
CLASSIFICATION 24 2.2.11 TYPE K CLASSIFICATION 25 2.3 CONCEPT OF
POTENTIAL 25 2.4 FIELD MAPPING 27 2.5 NATURE OF A SOLID MEDIUM 31 2.6
TENSORS 32 XIV CONTENTS 2.7 BOUNDARY VALUE PROBLEMS 34 2.7.1 DIRICHLET'S
PROBLEM 34 2.7.2 NEUMAIM PROBLEM 36 2.7.3 MIXED PROBLEM 36 2.8 DIMENSION
OF A PROBLEM AND ITS SOLVABILITY 36 2.9 EQUATIONS 38 2.9.1 DIFFERENTIAL
EQUATIONS 38 2.9.2 INTEGRAL EQUATIONS 40 2.10 DOMAIN OF GEOPHYSICS IN
POTENTIAL THEORY 41 3 GRAVITATIONAL POTENTIAL AND FIELD 43 3.1
INTRODUCTION 43 3.2 NEWTON'S LAW OF GRAVITATION 44 3.3 GRAVITY FIELD AT
A POINT DUE TO NUMBER OF POINT SOURCES . 46 3.4 GRAVITATIONAL FIELD
FOR A LARGE BODY 47 3.5 GRAVITATIONAL FIELD DUE TO A LINE SOUREE 48 3.6
GRAVITATIONAL POTENTIAL DUE TO A FINITE LINE SOUREE 50 3.7 GRAVITATIONAL
ATTRACTION DUE TO A BURIED CYLINDER 53 3.8 GRAVITATIONAL FIELD DUE TO A
PLANE SHEET .* 54 3.9 GRAVITATIONAL FIELD DUE TO A CIRCULAR PLATE 55
3.10 GRAVITY FIELD AT A POINT OUTSIDE ON THE AXIS OF A VERTICAL CYLINDER
56 3.11 GRAVITATIONAL POTENTIAL AT A POINT DUE TO A SPHERICAL BODY .
58 3.12 GRAVITATIONAL ATTRAETION ON THE SURFACE DUE TO A BURIED SPHERE
62 3.13 GRAVITATIONAL ANOMALY DUE TO A BODY OF TRAPEZOIDAL CROSS SECTION
63 3.13.1 SPECIAL CASES 64 3.14 GRAVITY FIELD OF THE EARTH 69 3.14.1
FREE AIR CORRECTION 70 3.14.2 BOUGUER CORREETION 70 3.14.3 TERRAIN
CORRECTION 70 3.14.4 LATITUDE CORRECTION 70 3.14.5 TIDAL CORRECTION 71
3.14.6 ISOSTATIC CORRECTION 71 3.15 UNITS 72 3.16 BASIC EQUATION 72 4
ELECTROSTATICS 75 4.1 INTRODUCTION 75 4.2 COULOMB" LAW 7FI 4.3
ELECTROSTATIC POTENTIAL 76 4.4 ELECTRICAL PERMITTIVITY AND ELCCTRICAL
FORCE FIELD 77 4.5 ELECTRIC FLUX 79 4.6 ELECTRIC DISPLACEMENT Y AND THE
DISPLACCMENT VCCTOR D 79 4.7 GAUSS'S THEOREM 80 4.8 FIELE! DUE TO AN
ELECTROSTATIC DIPOLE 82 4.9 POISSON AND LAPLACE EQUATIONS 85 4.10
ELECTROSTATIC ENERGY 86 4.11 BOUNDARY CONDITIONS 87 4.12 BASIC EQUATIONS
IN ELECTROSTATIC FIELD 88 MAGNETOST ATICS 91 5.1 INTRODUCTION 91 5.2
COULOMB'S LAW 98 5.3 MAGNETIC PROPERTIES 98 5.3.1 MAGNETIC DIPOLE MOMENT
98 5.3.2 INTENSITY OF MAGNETISATION 98 5.3.3 MAGNETIC SUSCEPTIBILITY
(INDUCED MAGNETISM) 99 5.3.4 FERROMAGNETIC, PARAMAGNETIC AND DIAMAGNETIC
SUBSTANCES 100 5.4 MAGNETIC INDUCTION B 102 5.5 MAGNETIC FIELD INTENSITY
H 104 5.6 FARADAY'S LAW 104 5.7 BIOT AND SAVART'S LAW 7 106 5.8 LORENTZ
FORCE 108 5.9 AMPERE'S FORCE LAW 109 5.10 MAGNETIC FIELD ON THE AXIS OF
A MAGNETIC DIPOLE 110 5.11 MAGNETOMOTIVE FORCE (MMF) 112 5.12 AMPERE'S
LAW 112 5.13 DIV B = 0 113 5.14 MAGNETIC VECTOR POTENTIAL 114 5.15
MAGNETIC SCALAR POTENTIAL 115 5.16 POISSON'S RELATION 116 5.17
MAGNETOSTATIC ENERGY 117 5.18 GEOMAGNETIC FIELD 118 5.18.1 GEOMAGNETIC
FIELD VARIATIONS 121 5.19 APPLICATION OF MAGNETIC FIELD MEASUREMENT IN
GEOPHYSICS . . . 123 5.20 UNITS 124 5.21 BASIC EQUATIONS IN
MAGNETOSTATICS 124 DIRECT CURRENT FLOW FIELD 127 6.1 INTRODUCTION 127
6.2 DIRECT CURRENT FLOW 131 6.3 DIFFERENTIAL FORM OF THE OHM'S LAW 131
6.4 EQUATION OF CONTINUITY 132 6.5 ANISOTROPY IN ELECTRICAL CONDUCTIVITY
133 6.6 POTENTIAL AT A POINT DUE TO A POINT SOURCE 134 6.7 POTENTIAL FOR
LINE ELECTRODC CONFIGURATION 136 6.7.1 POTENTIAL DUE TO A FINITE LINE
ELECTRODC 138 XVI CONTENTS 6.8 CURRENT FLOW INSIDE THE EARTH 139 6.9
REFRACTION OF CURRENT LINES 143 6.10 DIPOLE FIELD 144 6.11 BASIC
EQUATIONS IN DIRECT CURRENT FLOW FIELD 149 6.12 UNITS 150 7 SOLUTION OF
LAPLACE EQUATION 151 7.1 EQUATIONS OF POISSON AND LAPLACE 151 7.2
LAPLACE EQUATION IN DIREET CURRENT FLOW DOMAIN 152 7.3 LAPLACE EQUATION
IN GENERALISED CURVILINEAR COORDINATES . 153 7.4 LAPLACE EQUATION IN
CARTESIAN COORDINATES 156 7.4.1 WHEN POTENTIAL IS A FUNCTION OF VERTICAL
AXIS Z, I.E., = F(Z) 156 7.4.2 WHEN POTENTIAL IS A FUNCTION OF BOTH X
AND Y, I.E. 4 = F(X.Y) 157 7.4.3 SOLUTION OF BOUNDARY VALUE PROBLEMS
IN CARTISIAN COORDINATES BY THE METHOD OF SEPARATION OF VARIABLES 158
7.5 LAPLACE EQUATION IN CYLINDRICAL POLAR COORDINATES 162 7.5.1 WHEN
POTENTIAL IS A FUNCTION OLZ .I.E., (J * F(Z) 164 7.5.2 WHEN POTENTIAL
IS A FUNCTION OF AZIMUTHAI ANGLE ONLY I.E. § = F(Y) 164 7.5.3 WHEN THE
POTENTIAL IS A FUNCTION OF RADIAL DISTANCE, I.E., = F(P ) 164 7.5.4 WHEN
POTENTIAL IS A FUNCTION OF BOTH P AND \J/, I.E. (]) = F(P. \JR) 165
7.5.5 WHEN POTENTIAL IS A FUNCTION OF ALL THE THREE COORDINATES. I.E.
* F(P,\|/. Z) 171 7.5.6 BESSEL EQUATION AND BESSEL'S FUNCTIONS 172 7.5.7
MODIFIED BESSEL'S FUNCTIONS 177 7.5.8 SOME RELATION OF BESSEL'S FUNCTION
181 7.6 SOLUTION OF LAPLACE EQUATION IN SPHERICAL POLAR CO-ORDINATES .
183 7.6.1 WHEN POTENTIAL IS A FUNCTION OF RADIAL DISTANCE R I.E., =
F(R) 183 7.6.2 WHEN POTENTIAL IS A FUNCTION OF POLAR ANGLE, I.E. 0 =
F(9) 184 7.6.3 WHEN POTENTIAL IS A FUNCTION OF AZIMUTHAI ANGLE I.E., IP
= F(Y) 185 7.6.4 WHEN POTENTIAL IS A FUNCTION OF BOTH THE RADIAL
DISTANCE AND POLAR ANGLE I.E., - F(R, 0) 185 7.6.5 LEGENDER'» EQUATION
AND LEGENDER'S POLYNOMIAL 187 7.6.6 WHEN POTENTIAL IS A FUNCTION OF ALL
THE THREE COORDINATES VIZ, RADIAL DISTANCE, POLAR ANGLE AND AZIMUTHAI
ANGLE,I.E., (J = F(R,OE,\|/) 198 7.6.7 ASSOCIATED LEGENDRE POLYNOMIAL
200 7.7 SPHERICAL HARMONICS 201 7.7.1 ZONAL, SECTORAL AND TESSERAL
HARMONICS 202 DIRECT CURRENT FIELD RELATED POTENTIAL PROBLEMS 207 8.1
LAYERED EARTH PROBLEM IN A DIRECT CURRENT DOMAIN 207 8.1.1 CRAMER'S RULE
211 8.1.2 TWO LAYERED EARTH MODEL 211 8.1.3 THREE LAYERED EARTH MODEL
213 8.1.4 GENERAL EXPRESSIONS FOR THE SURFACE AND SUBSURFACE KERNELS FOR
AN N-LAYERED EARTH 217 8.1.5 KERNELS IN DIFFERENT LAYERS FOR A FIVE
LAYERED EARTH . . 219 8.1.6 POTENTIALS IN DIFFERENT MEDIA 221 8.2
POTENTIAL DUE TO A POINT SOURCE IN A BOREHOLE WITH CYLINDRICAL COAXIAL
BOUNDARIES 223 8.3 POTENTIAL FOR A TRANSITIONAL EARTH 232 8.3.1
POTENTIAL FOR A MEDIUM WHCRC PHYSICAL PROPERTY VARIES CONTINUOUSLY WITH
DISTANCE 232 8.3.2 POTENTIAL FOR A LAYERED EARTH WITH A SANDWITCHED
TRANSITIONAL LAYER 240 8.3.3 POTENTIAL WITH MEDIA HAVING COAXIAL
CYLINDRICAL SYMMETRY WITH A TRANSITIONAL LAYER IN BETWEEN 243 8.4
GEOELECTRICAL POTENTIAL FOR A DIPPING INTERFACE 253 8.5 GEOELECTRICAL
POTENTIALS FOR AN ANISOTROPIE MEDIUM 257 8.5.1 GENERAL NATURE OF THE
BASIC EQUATIONS 257 8.5.2 GENERAL SOLUTION OF LAPLACE EQUATION FOR AN
ANISOTROPIE EARTH 260 COMPLEX VARIABLES AND CONFORMAL TRANSFORMATION IN
POTENTIAL THEORY 263 9.1 DEFINITION OF ANALYTIC FUNCTION 263 9.2 COMPLEX
FUNCTIONS AND THEIR DERIVATIVES 264 9.3 CONFORMAL MAPPING 267 9.4
TRANSFORMAT IONS 269 9.4.1 SIMPLE TRANSFORMATIONS 270 9.5 SCHWARZ
CHRISTOFFEL TRANSFORMATION 274 9.5.1 INTRODUCTION 274 9.5.2
SCHWARZ-CHRISTOFFEL TRANSFORMATION OF THE INTERIOR OF A POLYGON 274
9.5.3 DETERMINATION OF UNKNOWN CONSTANTS 276 9.5.4 S-C TRANSFORMATION
THEOREM 276 9.6 GEOPHYSICAL PROBLEMS ON S-C TRANSFORMATION 278 9.6.1
PROBLEM 1 CONFORMAL TRANSFORMATION FOR A SUBSTRATUM OF FINITE THIEKNESS
278 9.6.2 PROBLEM 2 TELLURIC FIELD OVER A VERTICAL BASEMENT FAULT 280
9.6.3 PROBLEM 3 TELLURIC FIELD AND APPARENT RESISTIVITY OVER AN
ANTICLINE 284 9.6.4 PROBLEM 4 TELLURIC FIELD OVER A FAULTED BASEMENT
(HORST) 290 9.7 ELLIPTIC INTEGRALS AND ELLIPTIC FUNCTIONS 297 9.7.1
LEGENDRE'S EQUATION 297 9.7.2 COMPLETE INTEGRALS 297 9.7.3 ELLIPTIC
FUNCTIONS 300 9.7.4 JACOBI'S ZETA FUNCTION 302 9.7.5 JACOBI'S THETA
FUNCTION 302 9.7.G JACOBI'S ELLIPTIC INTEGRAL OF THE THIRD KIND 303 10
GREEN'S THEOREM IN POTENTIAL THEORY 307 10.1 GREEN'S FIRST. IDENTITY 307
10-2 HARMONIE FUNCTION 308 10.3 COROLLARIES OF GREEN'S THEOREM 309 10.4
REGULAER FUNCTION 311 10.5 GREEN'S FORMULA 312 10.6 SOME SPECIAL CASES IN
GREEN'S FORMULA 315 10.7 POISSON'S EQUATION F'ROM GREEN'S THEOREM 316
10.8 GAUSS'S THEOREM OF TOTAL NORMAL INDUCTION IN GRAVITY FIELD . 316
10.9 ESTIMATION OF MASS IN GRAVITY FIELD ". 317 10.10 GREEN'S THEOREM
FOR ANALYTICAL CONTINUATION 318 10.11 GREEN'S THEOREM FOR TWO
DIMENSIONAL PROBLEMS 320 10.12 THREE TO TWO DIMENSIONAL CONVERSION 321
10.13 GREEN'S EQUIVALENT LAYCRS 322 10.14 UNIQUE SURFACE DISTRIBUTION
324 10.15 VECTOR GREEN'S THEOREM 326 11 ELECTRICAL IMAGES IN POTENTIAL
THEORY 329 11.1 INTRODUCTION 329 11.2 COMPUTATION OF POTENTIAL USING
IMAGES (TWO MEDIA) 329 11.3 COMPUTATION OF POTENTIAL USING IMAGES (FOR
THREE MEDIA) . . . 332 11.4 GENERAL EXPRESSIONS FOR POTENTIALS USING
IMAGES 334 11.5 EXPRESSIONS FOR POTENTIALS FOR TWO ELECTRODE
CONFIGURATION . . 336 11.6 EXPRESSIONS FOR POTENTIALS FOR THREE
ELECTRODE CONFIGURATION . 338 11.7 EXPRESSION FOR POTENTIALS FOR SEVEN
ELECTRODE CONFIGURATIONS . 341 12 ELECTROMAGNETIC THEORY (VECTOR
POTENTIALS) 349 12.1 INTRODUCTION 349 12.2 ELEMENTAR)' WAVELET 354 12.3
ELLIPTIC POLARISATION OF ELECTROMAGNETIC WAVES 356 12.4 MUTUAL
INDUCTANCE 358 12.4.1 MUTUAL INDUCTANCE BETWEEN ANY TWO ARBITRARY COILS
. 359 12.4.2 SIMPLE MUTUAL INDUCTANCE MODEL IN GEOPHYSICS 361 12.5
MAXWELL'S EQUATIONS 363 12.5-1 INTEGRAL FORM OF MAXWELL'S EQUATIONS 366
12.6 HELMHOLTZ ELECTROMAGNETIC WAVE EQUATIONS 366 12.7 HERTZ AND
FITZERALD VECTORS 369 12.8 BOUNDARY CONDITIONS IN ELECTROMAGNETICS 371
12.8.1 NORMAL COMPONENT OF THE MAGNETIC INDUCTION B IS CONTINUOUS ACROSS
THE BOUNDARY IN A CONDUCTOR . 371 12.8.2 KORMAL COMPONENT OF THE
ELECTRIC DISPLACEMENT IS CONTINUOUS ACROSS THE BOUNDARY 371 12.8.3
TANGENTIAL COMPONENT OF E IS CONTINUOUS ACROSS THE BOUNDARY 373 12.8.4
TANGENTIAL COMPONENT OF H IS CONTINUOUS ACROSS THE BOUNDARY 373 12.8.5
NORMAL COMPONENT OF THE CURRENT DENSITY IS CONTHMOUS ACROSS THE BOUNDARY
374 12.8.6 SCALAR POTENTIALS ARE CONTINUOUS ACROSS THE BOUNDARY 375 12.9
POYNTING VECTOR 376 13 ELECTROMAGNETIC WAVC PROPAGATION PROBLEMS RELATCD
TO GEOPHYSICS 381 13.1 PLANE WAVE PROPAGATION 381 13.1.1 ADVANCING
ELCCTROMAGNETIC WAVE 384 13.1.2 PLANE WAVE INCIDENCE ON THE SURFACE OF
THE EARTH . 385 13.2 SKIN DEPTH 387 13.3 PERTURBATION CENTROID
FREQUCNCY 388 13.4 MAGNETOTELLURIC RESPONSE FOR A LAYERED EARTH MODEL
389 13.5 ELECTROMAGNETIC FIELD DUE TO A VCRTICAL OSEILLATING ELECTRIC
DIPOLE 394 13.6 ELECTROMAGNETIC FIELD DUE TO AN OSCILLATING VERTICAL
MAGNETIC DIPOLE PLACCD ON THE SURFACE OF THE EARTH 399 13.7
ELCCTROMAGNETIC FIELD DUE TO AN OSCILLATING HORIZONTAL MAGNETIC DIPOLE
PLACED ON THE SURFACE OF THE EARTH 108 13.8 ELECTROMAGNETIC FIELD DUE TO
A LONG LINE CABLC PLACED IN AN INFINITE AND HOMOGENOUS MEDIUM 416 13.9
ELECTROMAGNETIC FIELD DUE TO A LONG CABLE ON THE SURFACE OF A
HOMOGENCOUS EARTH 421 13.10 ELECTROMAGNETIC INDUCTION DUE TO AN INFINITE
CYLINDER IN AU UNIFORM FIELD 428 13.10.1EFICCT OF CHANGE IN FREQUENCY ON
THE RESPONSE PARAMETER 432 13.11 ELECTROMAGNETIC RESPONSE DUE TO A
SPHERE IN THE FIELD OF A VERTICALLY OSCILLATING MAGNETIC DIPOLE 434
13.12 PRINCIPLE OF ELECTRODYNAMIC SIMILITUDE 441 14 GREEN'S FUNCTION 445
14.1 INTRODUCTION 445 14.2 DELTA FUNCTION 447 14.3 OPERATORS 448 14.4
ADJOINT AND SEIF ADJOINT OPERATOR 449 14.5 DEFINITION OF A GREEN'S
FUNCTION 449 14.6 FREE SPACE GREEN'S FUNCTION 451 14.7 GREEN'S FUNCTION
IS A POTENTIAL DUC TO A CHARGE OF UNIT STRENGTH IN ELECTROSTATICS 452
14.8 GREEN'S FUNCTION CAN REDUCE THE NUMBER OF UNKNOWNS TO BE DETERMINED
IN A POTENTIAL PROBLEM 453 14.9 GREEN'S FUNCTION HAS SOME RELATION WITH
THE CONCEPT OF IMAGE IN POTENTIAL THEORY 454 14.10 RECIPROCITY RELATION
OF GREEN'S FUNCTION 456 14.11 GREEN'S FUNCTION AS A KERNEL FUNCTION IN
AN INTEGRAL EQUATION 457 14.12 POISSON'S EQUATION AND GREEN'S FUNCTION
460 14.13 PROBLEM 1 461 14.14 PROBLEIN 2 463 14.15 PROBLEM 3 465 14.16
DYADICS 466 NUMERICAL METHODS IN POTENTIAL THEORY 471 15.1 INTRODUCTION
471 15.2 FINITE DIFFERENCE FORMULATION/DIRECT, CURRENT DOMAIN (SURFACE
GEOPHYSICS) 473 15.2.1 INTRODUCTION 473 15.2.2 FORMULATION OF THE
PROBLEM 476 15.2.3 BOUNDARY CONDITIONS 477 15.2.4 STRUCTURE OF THE FD
BOUNDARY VALUE PROBLEM 478 15.2.5 INVERSE FOURIER COSINE TRANSFORM 480
15.2.6 CALIBRATION 481 15.3 FINITE DIFFERENCE FORMULATION DOMAIN WITH
CYLINDRICAL SYMMETRY DC FIELD BOREHOLE GEOPHYSICS 482 15.3.1
INTRODUCTION 482 15.3.2 FORMULATION OF THE PROBLEM 483 15.3.3 BOUNDARY
CONDITIONS 483 15.3.4 GRID GENERATION FOR DISCRETIZATION 483 15.3.5
FINITE DIFFERENCE EQUATIONS 484 15.3.6 CURRENT DENSITY FACTOR Q AT THE
SOURCE 488 15.3.7 EVALUATION OF THE POTENTIAL 489 15.4 FINITE DIFFERENCE
FORMULATION PLANE WAVE ELECTROMAGNETICS MAGNETOTELLURICS 490 15.4.1
BOUNDARY CONDITIONS 495 15.5 FINITE ELEMENT FORMULATION DIRECT CURRENT
RESISTIVITY DOMAIN 496 15.5.1 INTRODUCTION 496 15.5.2 DERIVATION OF THE
FUNCTIONAL FROM POWER CONSIDERATIONS 497 15.5.3 EQUIVALENCE BETWEEN
POISSON'S EQUATION AND THE MINIMIZATION OF POWER 499 15.5.4 FINITE
ELEMENT FORMULATION 500 15.5.5 MINIMISATION OF THE POWER 503 15.6 3D
MODEL 507 15.7 FINITE ELEMENT FORMULATION GALERKIN'S APPROACH
MAGNETOTELLURICS 509 15.7.1 INTRODUCTION 509 15.7.2 FINITE ELEMENT
FORMULATION FOR HELMHOLTZ WAVE EQUATIONS 510 15.7.3 ELEMENT EQUATIONS
512 15.8 FINITE ELEMENT FORMULATION GALERKIN'S APPROACH ISOPARAMETRIC
ELEMENTS MAGNETOTELLURICS 515 15.8.1 INTRODUCTION 515 15.8.2 FINITE
ELEMENT FORMULATION 517 15.8.3 SHAPE FUNCTIONS USING NATURAL COORDINATES
(.??) . 522 15.8.4 COORDINATE TRANSFORMATION 524 15.9 INTEGRAL
EQUATION METHOD 528 15.9.1 INTRODUCTION 528 15.9.2 FORMULATION OF AN
ELECTROMAGNETIC BOUNDARY VALUE PROBLEM 529 16 ANALYTICAL CONTINUATION OF
POTENTIAL FIELD 535 16.1 INTRODUCTION 535 16.2 DOWNWARD CONTINUATION BY
HARMONIE ANALYSIS OF GRAVITY FIELD 536 16.3 TAYLOR'S SERIES EXPANSION
AND FINITE DIFFERENCE APPROACH FOR DOWNWARD CONTINUATION 537 16.3.1
APPROACH A 537 16.3.2 APPROACH B 538 16.3.3 AN EXAMPLE OF ANALYTICAL
CONTINUATION BASCD ON SYNTHETIC DATA 539 16.4 GREEN 1 THEOREM AND
INTEGRAL EQUATIONS FOR ANALYTICAL CONTINUATION 541 16.5 ANALYTICAL
CONTINUATION USING INTEGRAL EQUATION AND TAKING AREAL AVERAGES 544
16.5.1 UPWARD CONTINUATION OF POTENTIAL FIELD 544 16.5.2 DOWNWARD
CONTINUATION OF POTENTIAL FIELD (PETERS APPROACH) 547 16.6 UPWARD AND
DOWNWARD CONTINUATION USING INTEGRAL EQUATION AND LAGRANGE INTERPOLATION
FORMULA 550 16.7 DOWNWARD CONTINUATION OF TELLURIC CURRENT DATA 551 XXII
CONTENTS 16.8 UPWARD AND DOWNWARD CONTINUATION OF ELECTRORNAGNETIC FIELD
DATA 552 1.6.9 DOWNWARD CONTINUATION OF ELECTROMAGNETIC FIELD 556 16.9.1
DOWNWARD CONTINUATION OF H Z 559 17 INVERSION OF POTENTIAL FIELD DATA
561 17.1 INTRODUCTION 561 17.2 WELLPOSED AND ILLPOSED PROBLEMS 57UE 17.3
TIKHNOV'S REGULARISATION 571 17.4 ABSTRACT SPACES 571 17.4.1 N
DIMENSIONAL VCCTOR SPACE 571 17.4.2 NORM OF A VECTOR 572 17.4.3 METRIC
SPACE 573 17.4.4 LINEAR SYSTEM 573 17.4.5 NORMED SPACE 573 17.4.6 LINEAR
DCPENDCNCE AND INDEPENDENCE 574 17.4.7 INNER PRODUCT SPACE 574 17.4.8
HUBERT SPACE 574 17.5 SOME PROPCRTIES OF A MATRIX . . ._ 575 17.5.1 RANK
OF A MATRIX '. 575 17.5.2 EIGEN VALUES AND EIGEN VECTORS 576 17.5.3
PROPERTIES OF THE EIGEN VALUES 577 "17.G LAGRANGE MULTIPLIER 578 1.7.7
SINGULAR VALUC DECOMPOSITION (SVD) 578 17.8 LEAST SQUARES ESTIMATOR 584
17.9 RIDGE REGRESSION ESTIMATOR 586 17.10 WEIGHTCD RIDGE REGRESSION 587
17.11 MINIMUM NORM ALGORITMN FOR AN UNDER DETERMINCD PROBLEM 589
17.11.INORM 589 17.11.2MINIMUM NORM ESTIMATOR 590 17.12 BACHUS - GILBERT
INVERSION 592 17.12.1 INTRODUCTION 592 17.12.2B-G FORMULATION 593 17.13
STOCHASTIC INVERSION 597 17.13.1 INTRODUCTION 597 17.13.2 CONJUNCTION OF
THE STATE OF INFORMATION 600 17.13.3MAXIMUM LIKELYHOOD POINT 600 17.14
OCCAM'S INVERSION 6UE2 17.15 GLOBAL OPTIMIZATION 603 17.15.1 INTRODUCTION
603 17.15.2MONTE CARLO INVERSION 605 17.15.3SIMULATED ANNEALING 606
17.15.4GENETIC ALGORITHM 611 17.16 NEURAL NETWORK 616 CONTENTS XXIII
17.16.1INTRODUCTION 616 17.16.2OPTIMIZATION PROBLEM 618 17.17 JOINT
INVERSION 621 REFERENCES 625 LIST OF SYMBOLS 641 INDEX 647 |
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| author | Roy, Kalyan K. 1940- |
| author_GND | (DE-588)121083276 |
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| ctrlnum | (OCoLC)255965282 (DE-599)DNB983522359 |
| dewey-full | 551 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
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| dewey-sort | 3551 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geowissenschaften Geologie / Paläontologie Physik Geographie |
| discipline_str_mv | Geowissenschaften Geologie / Paläontologie Physik Geographie |
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| id | DE-604.BV022489391 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:51:17Z |
| indexdate | 2024-07-20T09:18:52Z |
| institution | BVB |
| isbn | 9783540720898 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015696624 |
| oclc_num | 255965282 |
| open_access_boolean | |
| owner | DE-29 DE-1028 DE-824 |
| owner_facet | DE-29 DE-1028 DE-824 |
| physical | XXIII, 651 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Roy, Kalyan K. 1940- Verfasser (DE-588)121083276 aut Potential theory in applied geophysics Kalyan Kumar Roy Berlin [u.a.] Springer 2008 XXIII, 651 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Angewandte Geophysik - Potenzialtheorie Geophysics Potential theory (Mathematics) Angewandte Geophysik (DE-588)4122049-3 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Angewandte Geophysik (DE-588)4122049-3 s Potenzialtheorie (DE-588)4046939-6 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2931514&prov=M&dok_var=1&dok_ext=htm Inhaltstext OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015696624&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roy, Kalyan K. 1940- Potential theory in applied geophysics Angewandte Geophysik - Potenzialtheorie Geophysics Potential theory (Mathematics) Angewandte Geophysik (DE-588)4122049-3 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4122049-3 (DE-588)4046939-6 |
| title | Potential theory in applied geophysics |
| title_auth | Potential theory in applied geophysics |
| title_exact_search | Potential theory in applied geophysics |
| title_exact_search_txtP | Potential theory in applied geophysics |
| title_full | Potential theory in applied geophysics Kalyan Kumar Roy |
| title_fullStr | Potential theory in applied geophysics Kalyan Kumar Roy |
| title_full_unstemmed | Potential theory in applied geophysics Kalyan Kumar Roy |
| title_short | Potential theory in applied geophysics |
| title_sort | potential theory in applied geophysics |
| topic | Angewandte Geophysik - Potenzialtheorie Geophysics Potential theory (Mathematics) Angewandte Geophysik (DE-588)4122049-3 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Angewandte Geophysik - Potenzialtheorie Geophysics Potential theory (Mathematics) Angewandte Geophysik Potenzialtheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2931514&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015696624&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT roykalyank potentialtheoryinappliedgeophysics |