Integral transforms in geophysics:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1988
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XXIII, 367 S. |
| ISBN: | 3540177590 |
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| 240 | 1 | 0 | |a Analogii integrala tipa koši v teorii geofizičeskich polej |
| 245 | 1 | 0 | |a Integral transforms in geophysics |c Michael S. Zhdanov |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1988 | |
| 300 | |a XXIII, 367 S. | ||
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MICHAEL S. ZHDANOV INTEGRAL TRANSFORMS IN GEOPHYSICS WITH 71 FIGURES
SPRINGER-VERLAG BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO CONTENTS
PART I CAUCHY-**** INTEGRALS IN THE THEORY OF A PLANE GEOPOTENTIAL FIELD
1 CAUCHY-**** INTEGRAL 3 1.1 DEFINITION 3 1.1.1 CAUCHY INTEGRAL FORMULA
3 1.1.2 CONCEPT OF THE CAUCHY-**** INTEGRAL 4 1.1.3 PIECEWISE ANALYTICAL
FUNCTIONS 6 1.2 MAIN PROPERTIES 7 1.2.1 HOLDER CONDITION 7 1.2.2
CALCULATION OF SINGULAR INTEGRALS IN TERMS OF THE CAUCHY PRINCIPAL VALUE
9 1.2.3 SOKHOTSKY-PLEMELJ FORMULAS 13 1.2.4 GENERALIZATION OF THE
SOKHOTSKY-PLEMELJ FORMULAS FOR PIECEWISE SMOOTH CURVES 14 1.2.5
CAUCHY-TPYE INTEGRALS ALONG THE REAL AXIS 16 1.3 CAUCHY AND HILBERT
INTEGRAL TRANSFORMS 17 1.3.1 INTEGRAL BOUNDARY CONDITIONS FOR ANALYTICAL
FUNCTIONS 17 1.3.2 DETERMINATION OF A PIECEWISE ANALYTICAL FUNCTION FROM
A SPECIFIED DISCONTINUITY 20 1.3.3 INVERSION FORMULAS FOR THE
CAUCHY-**** INTEGRAL (CAUCHY INTEGRAL TRANSFORMS) 20 1.3.4 HILBERT
TRANSFORMS 22 2 REPRESENTATION OF PLANE GEOPOTENTIAL FIELDS IN THE FORM
OF THE CAUCHY-**** INTEGRAL 24 2.1 PLANE POTENTIAL FIELDS AND THEIR
GOVERNING EQUATIONS 24 2.1.1 VECTOR FIELD EQUATIONS 24 2.1.2 CONCEPT OF
A PLANE FIELD 26 2.1.3 PLANE FIELD EQUATIONS 27 2.1.4 PLANE FIELD FLOW
FUNCTION 28 2.2 LOGARITHMIC POTENTIALS AND THE CAUCHY-**** INTEGRAL . 29
2.2.1 LOGARITHMIC POTENTIALS 29 2.2.2 LOGARITHMIC POTENTIALS IN COMPLEX
COORDINATES 32 XII CONTENTS 2.2.3 CAUCHY-**** INTEGRAL AS A SUM OF THE
LOGARITHMIC POTENTIALS OF SIMPLE AND DOUBLE LAYERS 34 2.3 COMPLEX
INTENSITY AND POTENTIAL OF A PLANE FIELD . 35 2.3.1 CONCEPT OF COMPLEX
INTENSITY OF A PLANE FIELD 35 2.3.2 COMPLEX INTENSITY EQUATIONS 36 2.3.3
REPRESENTATION OF COMPLEX INTENSITY IN TERMS OF FIELD SOURCE DENSITY 37
2.3.4 COMPLEX POTENTIAL 38 2.4 DIRECT SOLUTION OF THE EQUATION FOR
COMPLEX FIELD INTENSITY 39 2.4.1 TWO-DIMENSIONAL OSTROGRADSKY-GAUSS
FORMULA IN COMPLEX NOTATION 39 2.4.2 POMPEI FORMULAS 40 2.4.3 SOLUTION
TO THE EQUATION FOR COMPLEX INTENSITY 42 2.5 REPRESENTATION OF THE
GRAVITATIONAL FIELD IN TERMS OF THE CAUCHY-**** INTEGRAL 43 2.5.1
COMPLEX INTENSITY OF THE GRAVITATIONAL FIELD 43 2.5.2 REPRESENTATION OF
THE GRAVITATIONAL FIELD OF A HOMOGENEOUS DOMAIN IN TERMS OF THE
CAUCHY-TYPE INTEGRAL 44 2.5.3 REPRESENTATION OF THE GRAVITATIONAL FIELD
OF A DOMAIN WITH AN ANALYTICAL MASS DISTRIBUTION IN TERMS OF THE
CAUCHY-**** INTEGRAL 46 2.5.4 CASE OF VERTICAL OR HORIZONTAL VARIATIONS
IN THE DENSITY 47 2.5.5 CASE OF LINEAR DENSITY VARIATIONS ALONG THE
COORDINATE AXIS 48 2.5.6 GENERAL CASE OF CONTINUOUS DENSITY DISTRIBUTION
. 49 2.5.7 CALCULATION OF THE GRAVITATIONAL FIELD OF AN INFINITELY
EXTENDED DOMAIN 50 2.6 REPRESENTATION OF A FIXED MAGNETIC FIELD IN TERMS
OF THE CAUCHY-**** INTEGRAL 52 2.6.1 COMPLEX POTENTIAL OF A POLARIZED
SOURCE 52 2.6.2 COMPLEX INTENSITIES AND POTENTIAL OF A MAGNETIC FIELD 53
2.6.3 REPRESENTATION OF THE MAGNETIC POTENTIAL OF A HOMOGENEOUS DOMAIN
IN TERMS OF THE CAUCHY-TYPE INTEGRALS 54 2.6.4 GENERAL CASE OF
MAGNETIZATION DISTRIBUTION 54 2.6.5 ANALYTICAL DISTRIBUTION OF
MAGNETIZATION 55 3 TECHNIQUES FOR SEPARATION OF PLANE FIELDS 56 3.1
SEPARATION OF GEOPOTENTIAL FIELDS INTO EXTERNAL AND INTERNAL PARTS USING
SPECTRAL DECOMPOSITION 56 3.1.1 STATEMENT OF THE PROBLEM OF PLANE FIELD
SEPARATION . 57 3.1.2 SPECTRAL REPRESENTATIONS OF PLANE FIELDS 57
CONTENTS XIII 3.1.3 DETERMINATION OF THE EXTERNAL AND INTERNAL PARTS OF
THE SCALAR POTENTIAL AND FIELD (GAUSS-SCHMIEDT FORMULAS) 59 3.2
KERTZ-SIEBERT TECHNIQUE 60 3.2.1 PROBLEM OF SEPARATION OF FIELD COMPLEX
INTENSITY . 60 3.2.2 FIELD SEPARATION AT ORDINARY POINTS OF THE LINE L
. 61 3.2.3 FIELD SEPARATION AT CORNERS OF THE LINE L 62 3.2.4
KERTZ-SIEBERT FORMULAS 63 3.2.5 EQUIVALENCE BETWEEN THE KERTZ-SIEBERT
AND THE GAUSS- SCHMIEDT FORMULAS 64 4 ANALYTICAL CONTINUATION OF A PLANE
FIELD 66 4.1 FUNDAMENTALS OF ANALYTICAL CONTINUATION 66 4.1.1 TAYLOR
THEOREM 66 4.1.2 UNIQUENESS OF AN ANALYTICAL FUNCTION 68 4.1.3 CONCEPT
OF ANALYTICAL CONTINUATION 70 4.1.4 CONCEPT OF THE RIEMANN SURFACE 71
4.1.5 WEIERSTRASS CONTINUATION OF AN ANALYTICAL FUNCTION . 71 4.1.6
SINGULAR POINTS OF AN ANALYTICAL FUNCTION 72 4.1.7 PENLEVE CONTINUATION
OF AN ANALYTICAL FUNCTION (PRINCIPLE OF CONTINUITY) 73 4.1.8 CONFORMAL
MAPPING 73 4.2 ANALYTICAL CONTINUATION OF THE CAUCHY-TYPE INTEGRAL
THROUGH A PATH OF INTEGRATION 75 4.2.1 ANALYTICAL CONTINUATION OF A REAL
ANALYTICAL FUNCTION OF A REAL VARIABLE 75 4.2.2 CONCEPT OF AN ANALYTICAL
ARC; THE HERGLOTZ-TSIRULSKY EQUATION FOR THE ARC 76 4.2.3 ANALYTICAL
CONTINUATION OF A FUNCTION SPECIFIED ALONG AN ANALYTICAL CURVE 79 4.2.4
CONTINUATION OF THE CAUCHY-TYPE INTEGRAL THROUGH A PATH OF INTEGRATION;
SINGULAR POINTS OF THE CONTINUED FIELD 80 4.3 ANALYTICAL CONTINUATION OF
A PLANE MAGNETIC FIELD INTO A DOMAIN OCCUPIED BY MAGNETIZED MASSES 82
4.3.1 ANALYTICAL CONTINUATION OF A MAGNETIC POTENTIAL INTO A DOMAIN OF
ANALYTICALLY DISTRIBUTED MAGNETIZATION 82 4.3.2 CONTINUATION THROUGH A
ONE-SIDE HERGLOTZ-TSIRULSKY ANALYTICAL ARC 83 4.3.3 ANALYTICITY
CONDITION FOR THE BOUNDARY OF A DOMAIN OCCUPIED BY MAGNETIZED MASSES 84
4.3.4 SINGULAR POINTS OF ANALYTICAL CONTINUATION OF THE MAGNETIC
POTENTIAL 85 4.3.5 DETERMINATION OF COMPLEX MAGNETIZATION OF A BODY FROM
ITS MAGNETIC POTENTIAL 87 XIV CONTENTS 4.4 ANALYTICAL CONTINUATION OF A
PLANE GRAVITATIONAL FIELD INTO A DOMAIN OCCUPIED BY ATTRACTING MASSES .
88 4.4.1 CHARACTERISTICS OF THE GRAVITATIONAL FIELD OF A HOMOGENEOUS
DOMAIN BOUNDED BY AN ANALYTICAL CURVE 88 4.4.2 CONTINUATION OF THE
GRAVITATIONAL FIELD INTO A DO- MAIN WITH AN ANALYTICAL DENSITY
DISTRIBUTION 90 4.4.3 CASE OF A HOMOGENEOUS DOMAIN BOUNDED BY A
PIECEWISE ANALYTICAL CURVE 91 4.4.4 SINGULAR POINTS OF THE CONTINUED
FIELD, LYING ON THE BOUNDARY OF A MATERIAL BODY 92 4.5 INTEGRAL
TECHNIQUES FOR ANALYTICAL CONTINUATION OF PLANE FIELDS 93 4.5.1 FORMS OF
ANALYTICAL CONTINUATION OF PLANE FIELDS IN GEOPHYSICS 93 4.5.2
RECONSTRUCTION OF A FUNCTION ANALYTICAL IN THE UPPER HALF-PLANE FROM ITS
REAL OR IMAGINARY PART 95 4.5.3 ANALYTICAL CONTINUATION OF PLANE FIELDS
INTO A HORIZONTAL LAYER USING SPECTRAL DECOMPOSITION OF THE CAUCHY
KERNEL 98 4.5.4 CASE OF FIELD SPECIFICATION ON THE REAL AXIS. THE
ZAMOREV FORMULAS 101 4.5.5 DOWNWARD ANALYTICAL CONTINUATION OF FUNCTIONS
HAVING SINGULARITIES BOTH IN THE LOWER AND IN THE UPPER HALF-PLANES 103
4.5.6 ANALYTICAL CONTINUATION INTO DOMAINS WITH CURVILINEAR BOUNDARIES
105 4.5.7 BATEMAN FORMULA; CONTINUATION OF COMPLEX INTENSITY OF THE
FIELD INTO THE LOWER HALF-PLANE USING ITS REAL PART 106 PART II
CAUCHY-TYPE INTEGRAL ANALOGS IN THE THEORY OF A THREE-DIMENSIONAL
GEOPOTENTIAL FIELD 5 THREE-DIMENSIONAL CAUCHY-TYPE INTEGRAL ANALOGS .
ILL 5.1 THREE-DIMENSIONAL ANALOG OF THE CAUCHY INTEGRAL FORMULA ILL
5.1.1 VECTOR STATEMENTS OF THE OSTROGRADSKY-GAUSS THEOREM ILL 5.1.2
VECTOR STATEMENTS OF THE STOKES THEOREM 113 5.1.3 ANALOG OF THE
CAUCHY-TYPE INTEGRAL 114 5.1.4 RELATIONSHIP BETWEEN THE
THREE-DIMENSIONAL ANALOG AND THE CLASSICAL CAUCHY INTEGRAL FORMULA 115
5.1.5 GAUSS HARMONIC FUNCTION THEOREM 117 5.1.6 CAUCHY FORMULA ANALOG
FOR AN INFINITE DOMAIN . 118 CONTENTS XV 5.1.7 THREE-DIMENSIONAL
ANALOG OF THE POMPEI FORMULAS . 119 5.2 DEFINITION AND PROPERTIES OF THE
THREE-DIMENSIONAL CAUCHY INTEGRAL ANALOG 120 5.2.1 CONCEPT OF A
THREE-DIMENSIONAL CAUCHY INTEGRAL ANALOG 120 5.2.2 EVALUATION OF
SINGULAR INTEGRALS IN TERMS OF THE CAUCHY PRINCIPAL VALUE 124 5.2.3
THREE-DIMENSIONAL ANALOGS OF THE SOKHOTSKY-PLEMELJ FORMULAS 127 5.3
INTEGRAL TRANSFORMS OF THE LAPLACE VECTOR FIELDS . 128 5.3.1 INTEGRAL
BOUNDARY CONDITIONS FOR THE LAPLACE FIELD . 129 5.3.2 PIECEWISE LAPLACE
VECTOR FIELDS. DETERMINATION OF A PIECEWISE LAPLACE FIELD FROM A
SPECIFIED DISCONTINUITY 132 5.3.3 INVERSION FORMULAS FOR THE
THREE-DIMENSIONAL CAUCHY INTEGRAL ANALOG 133 5.3.4 THREE-DIMENSIONAL
HILBERT TRANSFORMS 134 5.4 CAUCHY INTEGRAL ANALOGS IN MATRIX NOTATION
136 5.4.1 MATRIX REPRESENTATION OF THE DIFFERENTIATION OPERATORS OF
SCALAR AND VECTOR FIELDS 136 5.4.2 MATRIX REPRESENTATIONS OF
THREE-DIMENSIONAL CAUCHY INTEGRAL ANALOGS 138 6 APPLICATION OF CAUCHY
INTEGRAL ANALOGS TO THE THEORY OF A THREE-DIMENSIONAL GEOPOTENTIAL FIELD
. 140 6.1 NEWTON POTENTIAL AND THE THREE-DIMENSIONAL CAUCHY INTEGRAL
ANALOG 140 6.1.1 NEWTON POTENTIAL 140 6.1.2 NEWTON POTENTIAL OF SIMPLE
FIELD SOURCES 141 6.1.3 NEWTON POTENTIAL OF POLARIZED FIELD SOURCES 141
6.1.4 THREE-DIMENSIONAL CAUCHY-TYPE INTEGRAL AS A SUM OF A SIMPLE AND A
DOUBLE LAYER FIELD 143 6.2 REPRESENTATION OF THE GRAVITATIONAL FIELD IN
TERMS OF THE CAUCHY INTEGRAL ANALOG 145 6.2.1 GRAVITATIONAL FIELD
EQUATIONS 145 6.2.2 REPRESENTATION OF THE GRAVITATIONAL FIELD OF A
THREE- DIMENSIONAL HOMOGENEOUS BODY IN TERMS OF THE CAUCHY-TYPE INTEGRAL
146 6.2.3 GRAVITATIONAL FIELD OF A BODY WITH AN ARBITRARY DENSITY
DISTRIBUTION 148 6.2.4 CASE OF VERTICAL OR ONE-DIMENSIONAL HORIZONTAL
VARIATIONS IN THE DENSITY 150 6.2.5 SOME SPECIAL CASES OF DENSITY
DISTRIBUTION 153 6.2.6 CALCULATION OF THE GRAVITATIONAL FIELD OF A
THREE- DIMENSIONAL INFINITELY EXTENDED HOMOGENEOUS DOMAIN 154 XVI
CONTENTS 6.2.7 FIELD OF AN INFINITELY EXTENDED DOMAIN FILLED WITH MASSES
OF A Z-VARIABLE DENSITY 158 6.3 REPRESENTATION OF A FIXED MAGNETIC FIELD
IN TERMS OF THE CAUCHY INTEGRAL ANALOG 159 6.3.1 INTENSITY AND POTENTIAL
OF A FIXED MAGNETIC FIELD . 160 6.3.2 REPRESENTATION OF A MAGNETIC
FIELD WITH AN ARBITRARY DISTRIBUTION OF MAGNETIZED MASSES 160 6.3.3
POTENTIAL DISTRIBUTION OF MAGNETIZATION 162 6.3.4 LAPLACE DISTRIBUTION
OF MAGNETIZATION 163 6.3.5 MAGNETIC FIELD OF A UNIFORMLY MAGNETIZED BODY
. 164 6.4 GENERALIZED KERTZ-SIEBERT TECHNIQUE FOR SEPARATION OF
THREE-DIMENSIONAL GEOPOTENTIAL FIELDS 165 6.4.1 STATEMENT OF THE PROBLEM
OF SEPARATION OF A THREE- DIMENSIONAL FIELD 165 6.4.2 SEPARATION OF
FIELDS AT ORDINARY POINTS OF THE SURFACE 166 6.4.3 SEPARATION OF FIELDS
AT SINGULAR POINTS OF THE SURFACE 168 6.4.4 GENERALIZED KERTZ-SIEBERT
FORMULAS 168 7 ANALYTICAL CONTINUATION OF A THREE-DIMENSIONAL
GEOPOTENTIAL FIELD 170 7.1 FUNDAMENTALS OF ANALYTICAL CONTINUATION OF
THE LAPLACE FIELD 170 7.1.1 ANALYTICAL NATURE OF LAPLACE VECTOR FIELDS
170 7.1.2 UNIQUENESS OF LAPLACE VECTOR FIELDS AND HARMONIC FUNCTIONS 172
7.1.3 CONCEPT OF ANALYTICAL CONTINUATION OF A VECTOR FIELD AND ITS
RIEMANN SPACE 173 7.1.4 CONTINUATION OF THE LAPLACE FIELD USING THE
TAYLOR SERIES 175 7.1.5 STAL THEOREM (PRINCIPLE OF CONTINUITY FOR THE
LAPLACE FIELD) 176 7.2 ANALYTICAL CONTINUATION OF THE THREE-DIMENSIONAL
CAUCHY INTEGRAL ANALOG THROUGH THE INTEGRATION SURFACE 177 7.2.1 CONCEPT
OF AN ANALYTICAL PART OF THE SURFACE; SURFACE EQUATIONS IN A HARMONIC
FORM 177 7.2.2 RELATIONSHIP BETWEEN THE SURFACE EQUATION IN A HARMONIC
FORM AND THE PLANE CURVE EQUATION IN THE HERGLOTZ-TSIRULSKY FORM 181
7.2.3 CONTINUATION OF THE CAUCHY-TYPE INTEGRAL THROUGH THE INTEGRATION
SURFACE 182 7.3 ANALYTICAL CONTINUATION OF A THREE-DIMENSIONAL
GRAVITATIONAL FIELD INTO A HOMOGENEOUS MATERIAL BODY 182 CONTENTS XVII
7.3.1 PROPERTIES OF THE GRAVITATIONAL FIELD OF A BODY BOUNDED BY AN
ANALYTICAL SURFACE 183 7.3.2 RELATIONSHIP BETWEEN THE SHAPE OF THE
SURFACE OF A THREE-DIMENSIONAL HOMOGENEOUS MATERIAL BODY AND THE
LOCATION OF SINGULARITIES OF THE GRAVITATIONAL FIELD CONTINUED
ANALYTICALLY INTO THE BODY 186 7.3.3 DEFINITION OF THE SHAPE OF THE
SURFACE OF THREE- DIMENSIONAL MATERIAL BODIES BY ANALYTICAL CONTINUA-
TION OF THE GRAVITATIONAL FIELD 189 7.4 CONTINUATION OF THE
GRAVITATIONAL AND MAGNETIC FIELDS INTO A DOMAIN WITH AN ARBITRARY
ANALYTICAL DISTRIBUTION OF FIELD SOURCES 190 7.4.1 ANALYTICAL
REPRESENTATIONS OF FIELDS CONTINUED INTO MASSES 191 7.4.2 CASE OF A
DOMAIN BOUNDED BY AN ANALYTICAL SURFACE 192 7.4.3 CASE OF A DOMAIN
BOUNDED BY A PIECEWISE ANALYTICAL SURFACE 193 7.5 INTEGRAL TECHNIQUES
FOR ANALYTICAL CONTINUATION OF THREE-DIMENSIONAL LAPLACE FIELDS 195
7.5.1 ANALYTICAL CONTINUATION OF THE LAPLACE FIELD INTO THE UPPER
HALF-SPACE 195 7.5.2 ANALYTICAL CONTINUATION OF THE LAPLACE FIELD INTO
THE LOWER HALF-SPACE 197 PART III STRATTON-CHU TYPE INTEGRALS IN THE
THEORY OF ELECTROMAGNETIC FIELDS 8 STRATTON-CHU TYPE INTEGRALS 203 8.1
ELECTROMAGNETIC FIELD EQUATIONS 203 8.1.1 MAXWELL EQUATIONS 203 8.1.2
FIELD IN HOMOGENEOUS DOMAINS OF A MEDIUM 204 8.1.3 BOUNDARY CONDITIONS
205 8.1.4 MONOCHROMATIC FIELD EQUATIONS 206 8.1.5 QUASI-STATIONARY
ELECTROMAGNETIC FIELD 207 8.1.6 FIELD WAVE EQUATIONS 208 8.1.7 FIELD
EQUATIONS ALLOWING FOR MAGNETIC CURRENTS AND CHARGES 209 8.1.8
STATIONARY ELECTROMAGNETIC FIELD 210 8.2 INTEGRATION OF EQUATIONS FOR AN
ARBITRARY VECTOR FIELD 211 8.2.1 AUXILIARY INTEGRAL IDENTITIES 211 8.2.2
VECTOR ANALOGS OF THE POMPEI FORMULAS 212 8.3 STRATTON-CHU INTEGRAL
FORMULAS 214 8.3.1 STRATTON-CHU FORMULAS FOR A TRANSIENT ELECTRO-
MAGNETIC FIELD (GENERAL CASE) 214 XVLII CONTENTS 8.3.2 STRATTON-CHU
FORMULAS FOR A QUASI-STATIONARY FIELD . 217 8.3.3 WAVE MODEL OF THE
FIELD 219 8.3.4 CASE OF A STATIONARY FIELD 221 8.3.5 STRATTON-CHU
FORMULAS FOR A MONOCHROMATIC FIELD (GENERAL CASE) 223 8.3.6 MODIFIED
STRATTON-CHU FORMULAS FOR A MONOCHROMATIC FIELD 224 8.3.7
TWO-DIMENSIONAL STRATTON-CHU FORMULAS 226 8.3.8 STRATTON-CHU FORMULAS AS
A CAUCHY FORMULA ANALOG 226 8.4 STRATTON-CHU TYPE INTEGRALS 227 8.4.1
CONCEPT OF THE STRATTON-CHU TYPE INTEGRAL FOR A MONOCHROMATIC FIELD 227
8.4.2 PROPERTIES OF THE STRATTON-CHU TYPE INTEGRALS 228 8.4.3 MODIFIED
STRATTON-CHU TYPE INTEGRALS 231 8.4.4 MATRIX REPRESENTATION 233 8.4.5
STRATTON-CHU TYPE INTEGRALS FOR A QUASI-STATIONARY FIELD 234 8.5
EXTENSION OF THE STRATTON-CHU FORMULAS TO INHOMOGENEOUS MEDIA 236 8.5.1
GREEN ELECTROMAGNETIC TENSORS AND THEIR PROPERTIES . 236 8.5.2
STRATTON-CHU FORMULAS FOR AN INHOMOGENEOUS MEDIUM 238 8.5.3 TRANSITION
TO THE MODEL OF A HOMOGENEOUS MEDIUM 239 8.5.4 STRATTON-CHU TYPE
INTEGRALS IN AN INHOMOGENEOUS MEDIUM AND THEIR PROPERTIES 242 8.6
INTEGRAL TRANSFORMS OF ELECTROMAGNETIC FIELDS 246 8.6.1 INTEGRAL
BOUNDARY CONDITIONS FOR THE ELECTROMAGNETIC FIELD ON THE BOUNDARY OF A
HOMOGENEOUS DOMAIN . 247 8.6.2 INTEGRAL BOUNDARY CONDITIONS FOR THE
ELECTROMAGNETIC FIELD ON THE BOUNDARY OF AN INHOMOGENEOUS DOMAIN 249
8.6.3 DETERMINATION OF THE ELECTROMAGNETIC FIELD FROM A SPECIFIED
DISCONTINUITY 250 8.6.4 INVERSION FORMULAS FOR THE STRATTON-CHU TYPE
INTEGRALS 251 8.6.5 STRATTON-CHU INTEGRAL TRANSFORMS ON A PLANE 253 8.7
TECHNIQUES FOR SEPARATION OF THE EARTH'S ELECTRO- MAGNETIC FIELDS 255
8.7.1 SEPARATION OF THE ELECTROMAGNETIC FIELD INTO EXTERNAL AND INTERNAL
PARTS 255 8.7.2 SEPARATION OF THE ELECTROMAGNETIC FIELD INTO NORMAL AND
ANOMALOUS PARTS 258 9 ANALYTICAL CONTINUATION OF THE ELECTROMAGNETIC
FIELD 262 9.1 GENERAL PRINCIPLES 262 9.1.1 ANALYTICAL NATURE OF THE
ELECTROMAGNETIC FIELD 262 CONTENTS XIX 9.1.2 CONCEPT OF ANALYTICAL
CONTINUATION OF THE ELECTRO- MAGNETIC FIELD 264 9.1.3 EQUATIONS OF
COMPLETE ANALYTICAL FUNCTIONS 265 9.1.4 PRINCIPLE OF CONTINUITY FOR THE
ELECTROMAGNETIC FIELD 265 9.1.5 ELECTROMAGNETIC FIELD IN THE RIEMANN
SPACE 268 9.2 ANALYTICAL CONTINUATION OF THE ELECTROMAGNETIC FIELD INTO
GEOELECTRICAL INHOMOGENEITIES 269 9.2.1 ANALYTICAL CONTINUATION OF THE
STRATTON-CHU TYPE INTEGRAL THROUGH THE INTEGRATION SURFACE 270 9.2.2
ANALYTICAL CONTINUATION OF THE ELECTROMAGNETIC FIELD INTO A HOMOGENEOUS
DOMAIN BOUNDED BY AN ANALYTICAL AND PIECEWISE ANALYTICAL SURFACES 272
9.3 TECHNIQUES FOR ANALYTICAL CONTINUATION OF THE ELECTROMAGNETIC FIELD
274 9.3.1 FORMS OF ANALYTICAL CONTINUATION OF THE ELECTRO- MAGNETIC
FIELD IN GEOELECTRICAL PROBLEMS 274 9.3.2 PROBLEM STATEMENT 276 9.3.3
CONTINUATION OF THE FIELD INTO A LAYER 276 9.3.4 CONTINUATION OF A
TWO-DIMENSIONAL ELECTROMAGNETIC FIELD 281 10 MIGRATION OF THE
ELECTROMAGNETIC FIELD 284 10.1 DEFINITION OF THE CONCEPT OF MIGRATION
284 10.1.1 DEFINITION OF A MIGRATION FIELD 285 10.1.2 SYSTEM OF
MIGRATION TRANSFORMS OF NONSTATIONARY ELECTROMAGNETIC FIELDS 287 10.2
PROPERTIES OF MIGRATION FIELDS 288 10.2.1 EQUATION FOR A MIGRATION FIELD
IN DIRECT TIME 288 10.2.2 ONE-, TWO-, AND THREE-DIMENSIONAL MIGRATIONS
OF ELECTROMAGNETIC SOURCE FIELDS 289 10.2.3 EXTREME VALUES OF MIGRATION
FIELDS 291 10.2.4 MIGRATION OF THEORETICAL AND MODEL ELECTROMAGNETIC
FIELDS 299 PART IV KIRCHHOFF-TYPE INTEGRALS IN THE ELASTIC WAVE THEORY
11 KIRCHHOFF-TYPE INTEGRALS 307 11.1 ELASTIC WAVES IN AN ISOTROPIC
MEDIUM 307 11.1.1 STRESSES AND STRAINS IN ELASTIC BODIES 307 11.1.2
EQUATIONS OF MOTION OF A HOMOGENEOUS ISOTROPIC ELASTIC MEDIUM 310 11.1.3
LONGITUDINAL AND TRANSVERSE WAVES IN A HOMOGENEOUS ISOTROPIC ELASTIC
MEDIUM 311 11.2 GENERALIZED KIRCHHOFF INTEGRAL FORMULA 312 11.2.1 GREEN
TENSOR AND VECTOR FORMULAS 312 XX CONTENTS 11.2.2 KIRCHHOFF INTEGRAL
FORMULAS 314 11.2.3 KIRCHHOFF INTEGRAL FORMULAS FOR A SCALAR WAVE FIELD
. 318 11.2.4 KIRCHHOFF INTEGRAL FORMULAS IN MATRIX NOTATION . 319
11.3 KIRCHHOFF-TYPE INTEGRALS 321 11.3.1 KIRCHHOFF-TYPE INTEGRALS FOR
WAVE FIELDS 321 11.3.2 KIRCHHOFF-TYPE INTEGRALS FOR ELASTIC DISPLACEMENT
FIELDS 323 12 CONTINUATION AND MIGRATION OF ELASTIC WAVE FIELDS . 325
12.1 ANALYTICAL CONTINUATION OF ELASTIC WAVE FIELDS 325 12.1.1
CONTINUATION OF THE ELASTIC DISPLACEMENT FIELD INTO THE UPPER AND LOWER
HALF-SPACES IN A HOMOGENEOUS ISOTROPIC MEDIUM 326 12.1.2 INTEGRAL
FORMULAS FOR CONTINUATION OF THE ELASTIC DISPLACEMENT FIELD INTO THE
LOWER HALF-SPACE FOR A TWO-LAYER MEDIUM 329 12.1.3 CONTINUATION OF
ELASTIC DISPLACEMENT FIELDS SPECIFIED IN A HORIZONTAL PLANE 331 12.1.4
ELABORATION OF REGULARIZING ALGORITHMS FOR WAVE FIELD CONTINUATION 333
12.2 MIGRATION OF WAVE FIELDS ON THE BASIS OF ANALYTICAL CONTINUATION
335 APPENDIX A SPACE ANALOGS OF THE CAUCHY-TYPE INTEGRALS AND THE
QUATERNION THEORY 344 A.1 QUATERNIONS AND OPERATIONS THEREON 344 A.2
MONOGENIC FUNCTIONS 346 A.3 QUATERNION NOTATION OF SPACE ANALOGS OF THE
CAUCHY-TYPE INTEGRAL 348 APPENDIX * GREEN ELECTROMAGNETIC FUNCTIONS FOR
INHOMOGCNEOUS MEDIA AND THEIR PROPERTIES 351 B.L FIELD EQUATIONS 351 B.2
LORENTZ LEMMA FOR AN INHOMOGENEOUS MEDIUM . 352 B.3 RECIPROCAL
RELATIONS 354 B.4 INTEGRAL REPRESENTATIONS OF THE ELECTRIC AND MAGNETIC
FIELDS 355 B.5 SOME FORMULAS AND RULES OF OPERATIONS ON DYADIC TENSOR
FUNCTIONS 357 B.6 TENSOR STATEMENTS OF THE OSTROGRADSKY-GAUSS THEOREM
358 REFERENCES 361 SUBJECT INDEX 365 |
| any_adam_object | 1 |
| author | Ždanov, Michail Semenovič |
| author_GND | (DE-588)1089261241 |
| author_facet | Ždanov, Michail Semenovič |
| author_role | aut |
| author_sort | Ždanov, Michail Semenovič |
| author_variant | m s ž ms msž |
| building | Verbundindex |
| bvnumber | BV001297681 |
| classification_rvk | UT 1150 |
| ctrlnum | (OCoLC)635972529 (DE-599)BVBBV001297681 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV001297681 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-20T09:00:34Z |
| institution | BVB |
| isbn | 3540177590 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000783021 |
| oclc_num | 635972529 |
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| owner | DE-12 DE-83 DE-188 DE-706 |
| owner_facet | DE-12 DE-83 DE-188 DE-706 |
| physical | XXIII, 367 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| spelling | Ždanov, Michail Semenovič Verfasser (DE-588)1089261241 aut Analogii integrala tipa koši v teorii geofizičeskich polej Integral transforms in geophysics Michael S. Zhdanov Berlin u.a. Springer 1988 XXIII, 367 S. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Integraltransformation (DE-588)4027235-7 gnd rswk-swf Geophysik (DE-588)4020252-5 gnd rswk-swf Geophysik (DE-588)4020252-5 s Integraltransformation (DE-588)4027235-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000783021&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ždanov, Michail Semenovič Integral transforms in geophysics Integraltransformation (DE-588)4027235-7 gnd Geophysik (DE-588)4020252-5 gnd |
| subject_GND | (DE-588)4027235-7 (DE-588)4020252-5 |
| title | Integral transforms in geophysics |
| title_alt | Analogii integrala tipa koši v teorii geofizičeskich polej |
| title_auth | Integral transforms in geophysics |
| title_exact_search | Integral transforms in geophysics |
| title_full | Integral transforms in geophysics Michael S. Zhdanov |
| title_fullStr | Integral transforms in geophysics Michael S. Zhdanov |
| title_full_unstemmed | Integral transforms in geophysics Michael S. Zhdanov |
| title_short | Integral transforms in geophysics |
| title_sort | integral transforms in geophysics |
| topic | Integraltransformation (DE-588)4027235-7 gnd Geophysik (DE-588)4020252-5 gnd |
| topic_facet | Integraltransformation Geophysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000783021&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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