Geophysical electromagnetic theory and methods:
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2009
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| Edition: | 1. ed. |
| Series: | Methods in geochemistry and geophysics
43 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 848 S. graph. Darst. 24cm |
| ISBN: | 9780444529633 |
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MARC
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| 100 | 1 | |a Ždanov, Michail S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geophysical electromagnetic theory and methods |c Michael S. Zhdanov |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2009 | |
| 300 | |a XIX, 848 S. |b graph. Darst. |c 24cm | ||
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| 490 | 1 | |a Methods in geochemistry and geophysics |v 43 | |
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| _version_ | 1804140305813864448 |
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| adam_text | Titel: Geophysical electromagnetic theory and methods
Autor: Ždanov, Michail S.
Jahr: 2009
Contents
Preface xvii
Part I Introduction to Field Theory 1
1 Differential Calculus of Vector Fields and Differential Forms 3
1.1 The Basic Differential Relationships of Field Theory 3
1.1.1 Concept of the physical field 3
1.1.2 Dot (scalar) and cross (vector) products of vectors 6
1.1.3 Vector differential Operators 7
1.1.4 Differentiation of the products of scalar and vector fields 11
1.2 The Basic Integral Relationships of Field Theory 12
1.2.1 Concept of work and flux of a field 12
1.2.2 Gauss s theorem and its vector formulations 15
1.2.3 Stokes s theorem and its vector formulations 17
1.2.4 Green s formulas 18
1.3 Differential Forms in Field Theory 19
1.3.1 Concept of the differential form 19
1.3.2 Exterior (wedge) product of the linear forms 23
1.3.3 Canonical representations of the differential forms in
three-dimensional Euclidean Space 24
1.3.4 The exterior derivative 25
References and Recommended Reading 28
2 Foundations of Field Theory 29
2.1 Field Generation 30
2.1.1 Harmonie funetions; Liouville s theorem 30
2.1.2 Uniqueness of determination of the scalar field by its
gradient and the vector field by its divergence and curl 32
2.1.3 Field generation conditions 34
2.1.4 Sources of the field and their physical meaning 36
2.1.5 Vortices of the field and their physical meaning 38
2.1.6 Source field and vortex field 41
2.2 Stationary Fietd Equations and Methods of Their Solutions 42
2.2.1 Poisson s equations for scalar and vector fields 42
2.2.2 Point source; Dirac Singular funetion 44
2.2.3 Fundamental Green s funetion for the Laplace equation 46
vi Contents
2.3 Scalar and Vector Potentials of the Stationary Field 49
2.3.1 Scalar potential of the source field 49
2.3.2 Vector potential of the vortex field 50
2.3.3 Helmholtz theorem and classification of the vector fields 52
2.4 Nonstationary Fields and Differential Forms 54
2.4.1 Nonstationary vector fields and differential forms in
four-dimensional space E4 54
2.4.2 Differential form equations 55
2.4.3 Ampere-type differential forms and a continuity equation 58
2.4.4 Faraday-type differential forms and the four-potential 59
2.4.5 Nonstationary vector field equations 60
References and Recommended Reading 61
Part II Foundations of Electromagnetic Theory 63
3 Electromagnetic Field Equations 65
3.1 Maxwell s Equations and Boundary Conditions 67
3.1.1 Basic equations in the theory of electromagnetic fields 67
3.1.2 Physical interpretation of Maxwell s equations 71
3.1.3 Boundary conditions for the vector field 77
3.1.4 The field in a homogeneous medium 82
3.2 Time-Harmonic Electromagnetic Field 83
3.3 Electromagnetic Energy and Poynting s Theorem 86
3.3.1 Radiation conditions 87
3.3.2 Poynting s theorem in the time domain 87
3.3.3 Energy inequality in the time domain 89
3.3.4 Poynting s theorem in the frequency domain 91
3.4 Electromagnetic Green s Tensors 93
3.4.1 Green s tensors in the frequency domain 93
3.4.2 Green s tensors in the time domain 95
3.5 Reciprocity Relations 96
3.5.1 Lorentz lemma 96
3.5.2 Reciprocity relations for the Green s tensors and
electromagnetic fields 98
3.5.3 Electromagnetic Green s tensor representation theorems 100
References and Recommended Reading 103
4 Models of Electromagnetic Induction in the Earth 105
4.1 Models of Electromagnetic Fields 106
Contents vii
4.2 Static Electromagnetic Fields 107
4.2.1 Electrostatic fields and electrostatic Potentials 108
4.2.2 Boundary conditions for electrostatic potential 111
4.2.3 Calculation of the electrostatic field of a specified Charge
distribution 112
4.2.4 Analogy between constant current fields and electrostatic
fields 113
4.2.5 Direct current flow, associated magnetic field, and the
Biot-Savart law 117
4.2.6 Point and dipole sources on a uniform earth 120
4.2.7 DC potential in an anisotropic earth 126
4.3 Electromagnetic Field Diffusion in Conductive Media 130
4.3.1 Monochromatic quasi-static EM fields 131
4.3.2 Plane electromagnetic waves in a homogeneous
medium 133
4.3.3 Electromagnetic potentials 140
4.3.4 Quasi-stationary field of a dipole source in a homogeneous
medium 142
4.3.5 Spherical electromagnetic waves 146
4.4 Electromagnetic Waves 150
References and Recommended Reading 151
5 Electromagnetic Fields in Horizontally Stratified Media 153
5.1 Plane Wave Propagation in a Layered Earth 154
5.1.1 Plane electromagnetic wave in a horizontally stratified
medium 154
5.1.2 Low-frequency behavior of wave impedance 162
5.1.3 Definition of frequency Windows 165
5.2 Spectral Method of Computing EM Fields in Horizontally Stratified
Media 168
5.2.1 Fourier transform in the spatial domain 168
5.2.2 Point source of the DC field in horizontally stratified
medium 172
5.2.3 Electric field of the point source in a layered earth 183
5.2.4 Electrical dipole source of the DC field in a horizontally
layered medium 187
5.2.5 Expressions for electric fields in a horizontally layered
medium using the Hankel transform 188
viii Contents
5.3 Electromagnetic Field of an Arbitrary System of Magnetospheric
Currents in a Horizontally Homogeneous Medium 191
5.3.1 Spatial frequency-domain (SFD) representation of the
electromagnetic field in a horizontally layered medium 192
5.3.2 Lipskaya-Vanyan formulas concerning impedance ratios 194
5.3.3 Horizontal polarization of the electric field in a
horizontally homogeneous earth, and the reduced spatial
wave number spectrum 197
5.4 Eectromagnetic Fields Generated in Layered Earth by Electric and
Magnetic Dipole Transmitters 200
5.4.1 Spectral representation of the field of a horizontal current
dipole on the surface of a horizontally layered medium 200
5.4.2 Electromagnetic field of a horizontal current dipole at the
surface of a homogeneous half-space 206
5.4.3 Frequency domain representation of the field of a vertical
magnetic dipole above a horizontally stratified medium 210
5.4.4 The magnetic field of a vertical magnetic dipole on the
surface of a uniform half-space 213
5.4.5 Near and far fields 214
5.4.6 Frequency domain method for computing transient fields 217
5.4.7 Transient fields of a dipole source observed in a homo-
geneous medium and on the surface of a homogeneous
conducting half-space; fields in the near and far zones 220
References and Recommended Reading 230
6 Electromagnetic Fields in Inhomogeneous Media 233
6.1 Integral Equation Method 235
6.1.1 Background (normal) and anomalous parts of the
electromagnetic field 235
6.1.2 Poynting s theorem and energy inequality for an
anomalous field 236
6.1.3 Integral equation method in two dimensions 237
6.1.4 Calculation of the first variation (Frechet derivative) of the
electromagnetic field for 2-D models 240
6.1.5 Integral equation method in three dimensions 243
6.1.6 Calculation of the first variation (Frechet derivative) of the
electromagnetic field for 3-D models 244
6.2 Integral Equation Method in Models with Inhomogeneous
Background Conductivity 247
6.2.1 Model with inhomogeneous background conductivity 248
6.2.2 Accuracy control of the IBC IE method 252
Contents
6.3 Family of Linear and Nonlinear Integral Approximations of the
Electromagnetic Field 254
6.3.1 Born and extended Born approximations 255
6.3.2 Quasi-linear approximation and tensor quasi-linear
equation 256
6.3.3 QL approximation using a multigrid approach 257
6.3.4 Quasi-analytical Solutions for a 3-D electromagnetic field 258
6.3.5 Quasi-analytical approximation for a model with variable
background (QAVB) 262
6.3.6 Quasi-analytical Solutions for 2-D electromagnetic fields 265
6.3.7 Localized nonlinear approximation 265
6.3.8 Localized quasi-linear approximation 267
6.4 Differential Equation Methods 270
6.4.1 Field equations and boundary conditions 270
6.4.2 Electromagnetic potential equations and boundary
conditions 274
6.4.3 Finite difference approximation of boundary-value problem 275
6.4.4 Discretization of Maxwell s equations using a
staggered grid 276
6.4.5 Discretization of the second order differential equations
using the balance method 280
6.4.6 Discretization of the electromagnetic potential differential
equations 285
6.4.7 Finite element solution of boundary-value problems 288
References and Recommended Reading 292
Part III Inversion and Imaging of Electromagnetic
Field Data 297
7 Principles of Ill-Posed Inverse Problem Solution 299
7.1 Ill-Posed Inverse Problems 300
7.1.1 Formulation of well-posed and Ill-posed problems 300
7.1.2 Correctness set 301
7.1.3 Quasi-solution of the Ill-posed problem 302
7.2 Foundations of Regularization Theory 303
7.2.1 Definition of misfit functional 303
7.2.2 Regularizing Operators 306
7.2.3 Stabilizing functionais 307
7.2.4 Tikhonov parametric functional 312
x Contents
7.3 Regularization Parameter 313
7.3.1 Tikhonov method of regularization parameter selection 313
7.3.2 L-curve method of regularization parameter selection 316
References and Recommended Reading 319
8 Electromagnetic Inversion 321
8.1 Linear Inversions 322
8.1.1 Born inversion 322
8.1.2 Discrete linear EM inverse problem 323
8.1.3 The Tikhonov regularization method of linear inversion 325
8.1.4 Definition of the weighting matrices for model parameters
and data 326
8.1.5 Approximate regularized solution of linear inverse problem 328
8.1.6 The Levenberg-Marquardt method 331
8.1.7 Conductivity imaging by the Born approximation 331
8.1.8 Iterative Born inversions 336
8.2 Nonlinear Inversion 337
8.2.1 Formulation of the nonlinear EM inverse problem 337
8.2.2 Regularized solution of nonlinear discrete EM inverse
problem 338
8.2.3 The steepest descent method for nonlinear regularized
least-squares inversion 339
8.2.4 The Newton method for nonlinear regularized
least-squares inversion 340
8.2.5 Numerical schemes of the Newton method for nonlinear
regularized least-squares inversion 341
8.2.6 Nonlinear least-squares inversion by the conjugate
gradient method 342
8.2.7 The numerical scheme of the regularized conjugate
gradient method for nonlinear least-squares inversion 343
8.2.8 Frechet derivative calculation 344
8.3 Quasi-Linear Inversion 347
8.3.1 Principles of quasi-linear inversion 347
8.3.2 Localized quasi-linear inversion 348
8.4 Quasi-Analytical Inversion 348
8.4.1 Frechet derivative calculation 349
8.4.2 Inversion based on the quasi-analytical method 350
References and Recommended Reading 351
Contents xi
9 Electromagnetic Migration 353
9.1 Electromagnetic Migration in the Time Domain 354
9.1.1 Physical principles of electromagnetic migration 355
9.1.2 Migration in a model with homogeneous background
conductivity 356
9.1.3 Migration using integral transformation 357
9.2 Analytic Continuation and Migration in the {k, J) Domain 359
9.2.1 Analytic continuation of the EM field 359
9.2.2 Migration as a spectral transformation 361
9.2.3 Convolution form of migration Operator 363
9.2.4 Constructing a digital filter for EM migration 364
9.2.5 Spectrat characteristic of the digital filter 367
9.3 Finite Difference Migration 370
9.3.1 2-D Finite difference migration 370
9.3.2 Finite difference migration of a 3-D EM field 374
9.4 Visualization of Geoelectric Structures by Use of Migration in
the Frequency and Time Domains 377
9.4.1 Migration imaging condition in the frequency domain 377
9.4.2 Migration imaging condition in the time domain 379
9.5 Migration Versus Inversion 381
9.5.1 Formulation of the inverse probtem 381
9.5.2 General concept of the migration anomalous field 382
9.5.3 General migration imaging conditions 384
9.5.4 Regularized iterative migration 387
References and Recommended Reading 390
Part IV Geophysical Electromagnetic Methods 393
10 Electromagnetic Properties of Rocks and Minerals 395
10.1 Properties and Units 396
10.1.1 Electrical conductivity and resistivity 396
10.1.2 Dielectric permittivity 398
10.1.3 Magnetic permeability 399
10.1.4 Wave number 400
10.2 Properties in a Parametric Sense 402
10.2.1 Electric properties of rock-forming minerals and rocks 402
10.2.2 Induced polarization 416
10.2.3 Dielectric properties of rock-forming minerals 420
10.2.4 Magnetic properties of minerals 425
xii Contents
10.3 Effective Conductivity of Heterogeneous Multiphase Rocks 427
10.3.1 Mixture of conductive minerals in a host rock 427
10.3.2 Principles of the effective-medium theory 427
10.3.3 Effective conductivity of heterogeneous medium 433
10.4 Properties in an Existential Sense 435
10.4.1 Concepts of a geoelectric structure and a geoelectric
section 435
10.4.2 Longitudinal conductance and transverse resistance of the
horizontally layered geoelectric section 437
10.5 Properties of Large-Scale Geoelectric Structures 440
10.5.1 Geoelectric mesostructures and megastructures 440
10.5.2 The oceans 442
10.5.3 The atmosphere 444
References and Recommended Reading 446
11 Generation and Measurement of Electromagnetic Fields in
Geophysical Applications 449
11.1 Field Generation 450
11.1.1 Sources of EM fields 450
11.1.2 Cables 453
11.1.3 Grounding structures 454
11.2 Measurement of Electric and Magnetic Fields 459
11.2.1 Voltage, potential, and electric field 459
11.2.2 Sensing the magnetic field 465
11.3 Preprocessing of the Data 478
11.3.1 Sampling in time 478
11.3.2 Analog-to-digital conversion 479
11.3.3 Filtering 481
11.3.4 Stacking 486
11.3.5 Deconvolution 487
References and Recommended Reading 489
12 Direct Current and Induced Polarization Methods 491
12.1 Vertical Electric Sounding and Apparent Resistivity 493
12.1.1 Techniques for vertical electric sounding 494
12.1.2 Three point electrode array 502
12.1.3 Dipole electric sounding 503
Contents xiii
12.2 Induced Polarization (IP) Methods 508
12.2.1 Induced polarization phenomena 508
12.2.2 IP method in the frequency and time domains 509
12.2.3 Resistivity/IP model of a typical porphyry copper system
in the Southwestern U. S. 512
12.3 Physical and Mathematical Models of the IP Phenomenon 515
12.3.1 IP phenomenon in the context of effective-medium theory 516
12.3.2 Effective conductivity of a heterogeneous polarizable
medium 521
12.3.3 Self-consistent approximation for effective conductivity 523
12.3.4 Anisotropy effect in IP data 524
12.3.5 Fundamental IP model: effective resistivity of the isotropic
multiphase heterogeneous medium filled with spherical
inclusions 525
12.4 Nonlinear Regularized Inversion of IP Data Based on the
Cole-Cole Model 530
12.4.1 Forward modeling of induced polarization based
on the LQL approximation 531
12.4.2 Inversion based on the LQL approximation 532
12.4.3 Regularized solution of the material property equation 534
12.4.4 Quantitative interpretation of IP data - The road ahead 537
References and Recommended Reading 538
13 Magnetotelluric and Magnetovariational Methods 543
13.1 Earth EM Field of External Origin 545
13.1.1 Quiet-time magnetic field variations 547
13.1.2 Micropulsations 549
13.1.3 Magnetic storms 552
13.1.4 Substorms 553
13.2 The Tikhonov-Cagniard Model of the MT Field 554
13.2.1 Tikhonov-Cagniard model 554
13.2.2 Concepts of apparent resistivity and sounding 554
13.2.3 Relationships between the MT sounding curve and
the actual l-D resistivity model 556
13.3 Theory of the MT and MV Transfer Functions 564
13.3.1 Magnetotelluric operators: impedance and admittance,
telluric and magnetic 565
13.3.2 Induction vectors and magnetic and electric tippers 568
13.3.3 Spectral magnetotelluric impedances 569
xiv Contents
13.4 Magnetotelluric Fields in Horizontally Inhomogeneous Media 574
13.4.1 Concepts of external and internal, normal and anomalous
parts of an electromagnetic field 574
13.4.2 Anomalous electromagnetic fields and their classification 576
13.4.3 Fields in two-dimensionally inhomogeneous media and the
concepts of E and H polarization 577
13.5 Magnetotelluric and Magnetovariational Surveys 579
13.5.1 The MTS, MTP, and TCM methods 579
13.5.2 MVS and MVP survey methods 582
13.5.3 CGDS survey method 583
13.6 Processing and Analysis of MT and MV Data 583
13.6.1 The least-squares method 584
13.6.2 Remote reference method 592
13.6.3 Robust estimation of magnetotelluric and induction
matrices 593
13.6.4 Graphical presentation of magnetotelluric and induction
matrices 597
13.7 One-Dimensional Interpretation of MT Data 599
13.7.1 Analysis of distorted MTS curves 602
13.7.2 Quick and dirty MTS analysis 608
13.7.3 Quantitative interpretation of MTS curves with one-dimensional
models 612
13.8 Interpretation of MVP and GDS Data 612
13.8.1 Separation of fields into internal and external parts 614
13.8.2 Separation of fields into normal and anomalous parts 618
13.9 Rapid Three-Dimensional Magnetotelturic Inversion Based on
Linear and Quasi-Linear Approximations 619
13.9.1 Iterative Born inversion of magnetotelluric data 620
13.9.2 MT inversion based on the quasi-analytical method 621
13.9.3 Regularized smooth and focusing inversion of MT data 623
13.9.4 Principles of the re-weighted regularized inversion 624
13.9.5 Minimum support nonlinear parameterization 627
13.9.6 Case study 1: inversion of the Voisey s Bay MT data 631
13.9.7 Case study 2: 3-D inversion of MT data collected by
Phoenix Geophysics in Ontario, Canada 634
13.10 Rigorous 3-D Magnetotelluric Inversion 637
13.10.1 Tikhonov regularization in the full MT impedance tensor
inversion 638
13.10.2 Frechet operator and its adjoint for two-component
impedance inversion 639
Contents xv
13.10.3 Frechet operator for the full magnetotelluric impedance
tensor inversion 640
13.10.4 Frechet derivative calculation using quasi-analytical
approximation for a variable background (QAVB) 643
References and Recommended Reading 645
14 Electromagnetic Methods in the Frequency and Time Domains 649
14.1 Electromagnetic Sounding in the Frequency and Time Domains 650
14.1.1 Mutual coupling 654
14.1.2 Theoretical curves for EM sounding in the frequency
domain 658
14.1.3 Time-domain electromagnetic sounding 662
14.1.4 Properties of TDEM sounding curves 672
14.2 Interpretation of Controlled-Source Time Domain EM Data Using
the thin-sheet Approach 677
14.2.1 The Price-Sheinman and Tikhonov-Dmitriev thin-film
models with laterally varying conductance 677
14.2.2 Transient field of a magnetic dipole above a conducting
thin sheet 680
14.2.3 S-lnversion method 686
14.3 Electromagnetic Profile and Array Surveys 689
14.3.1 Profiling with two loops 689
14.3.2 Profiling with large fixed sources 689
14.3.3 Transient electromagnetic techniques: UTEM, LOTEM, and
MTEM methods 690
References and Recommended Reading 691
15 Marine Electromagnetic Methods 695
15.1 Marine Magnetotelluric Method 696
15.1.1 Main characteristic of seafloor EM equipment 697
15.1.2 Comparison between land and sea-bottom electromagnetic
anomalies 700
15.1.3 Case study: marine magnetotellurics in the Gulf of Mexico 701
15.2 Marine Controlled-Source Electromagnetic Methods 704
15.2.1 Electrical exploration in shallow water 705
15.2.2 Electrical exploration beneath deep oceans 707
15.2.3 MCSEM method for offshore petroleum exploration 713
15.2.4 Interpretation of MCSEM data 716
15.2.5 Case study: iterative migration of Troll Gas Province
MCSEM data 727
References and Recommended Reading 73!
xvi Contents
16 Other Platforms, Other Methodologies 735
16.1 Airborne Electromagnetic Methods 736
16.1.1 Frequency domain airborne surveys 737
16.1.2 Airborne transient electromagnetic systems (ATEM) 751
16.1.3 Far field AEM methods 752
16.2 Ground Penetrating Radar (GPR) 756
16.3 Borehole Assisted Methods 764
16.3.1 Borehole-to-surface techniques 764
16.3.2 Cross-well electromagnetic tomography 767
16.4 Other Electromagnetic Methods 774
16.4.1 Piezoelectric method 774
16.4.2 Spontaneous polarization (SP) method 776
References and Recommended Reading 780
A Algebra of Differential Forms 783
A.i Differential Forms in Three-Dimensional Space 784
A.1.1 1-, 2-, and 3-Forms 784
A.i.2 Exterior product of the differential forms 785
A.1.3 Basis of differential forms 786
A.2 Differential Forms in Multidimensional Spaces 790
A.2.1 Euclidean space 790
A.2.2 Differential forms in Euclidean space £„ 792
A.2.3 Differential forms in Minkowskian space M4 794
B Calculus of Differential Forms 799
B.i Exterior Differentiation of the Forms 799
B.1.1 Exterior differential operator in multidimensional space En 800
B.i.2 Exterior differential operator in four-dimensional space N k 802
B.2 Integration of the Forms 806
B.2.1 Three-dimensional space £3 806
B.2.2 Beyond three-dimensional space 808
C Mathematical Notations 811
D Definition of Fields and Units 815
E Linear Operators and Their Matrices 819
Bibliography 823
Index 845
|
| any_adam_object | 1 |
| author | Ždanov, Michail S. |
| author_facet | Ždanov, Michail S. |
| author_role | aut |
| author_sort | Ždanov, Michail S. |
| author_variant | m s ž ms msž |
| building | Verbundindex |
| bvnumber | BV024118832 |
| classification_rvk | UT 1000 |
| ctrlnum | (OCoLC)603836661 (DE-599)GBV598135642 |
| dewey-full | 622.15 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 622 - Mining and related operations |
| dewey-raw | 622.15 |
| dewey-search | 622.15 |
| dewey-sort | 3622.15 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Bergbau / Hüttenwesen |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV024118832 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:57:52Z |
| institution | BVB |
| isbn | 9780444529633 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018335555 |
| oclc_num | 603836661 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XIX, 848 S. graph. Darst. 24cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Elsevier |
| record_format | marc |
| series | Methods in geochemistry and geophysics |
| series2 | Methods in geochemistry and geophysics |
| spelling | Ždanov, Michail S. Verfasser aut Geophysical electromagnetic theory and methods Michael S. Zhdanov 1. ed. Amsterdam [u.a.] Elsevier 2009 XIX, 848 S. graph. Darst. 24cm txt rdacontent n rdamedia nc rdacarrier Methods in geochemistry and geophysics 43 Methods in geochemistry and geophysics 43 (DE-604)BV001889852 43 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018335555&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ždanov, Michail S. Geophysical electromagnetic theory and methods Methods in geochemistry and geophysics |
| title | Geophysical electromagnetic theory and methods |
| title_auth | Geophysical electromagnetic theory and methods |
| title_exact_search | Geophysical electromagnetic theory and methods |
| title_full | Geophysical electromagnetic theory and methods Michael S. Zhdanov |
| title_fullStr | Geophysical electromagnetic theory and methods Michael S. Zhdanov |
| title_full_unstemmed | Geophysical electromagnetic theory and methods Michael S. Zhdanov |
| title_short | Geophysical electromagnetic theory and methods |
| title_sort | geophysical electromagnetic theory and methods |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018335555&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001889852 |
| work_keys_str_mv | AT zdanovmichails geophysicalelectromagnetictheoryandmethods |