Potential fields and their transformations in applied geophysics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Borntraeger
1975
|
| Series: | Geoexploration monographs
Series 1 ; 6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 121 Seiten graphische Darstellungen |
| ISBN: | 3443130089 |
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MARC
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| 100 | 1 | |a Baranov, Vladimir I. |d 1892-1972 |0 (DE-588)123774535 |4 aut | |
| 245 | 1 | 0 | |a Potential fields and their transformations in applied geophysics |c by Wladimir Baranov |
| 264 | 1 | |a Berlin [u.a.] |b Borntraeger |c 1975 | |
| 300 | |a XV, 121 Seiten |b graphische Darstellungen | ||
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| 650 | 4 | |a Magnetic anomalies | |
| 650 | 4 | |a Prospecting |x Geophysical methods | |
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Record in the Search Index
| _version_ | 1804116541243916288 |
|---|---|
| adam_text | Titel: Potential fields and their transformations in applied geophysics
Autor: Baranov, Vladimir
Jahr: 1975
Contents
Preface by the Editors....................IX
Foreword ........................XI
List of Principal Symbols...................XIII
I Physics of Fields and Potentials................................1
1 Fields and Potentials......................................1
1.1 Fields which Derive from a Potential........................1
1.2 Force at a Distance....................................2
1.3 Newtonian Potential....................................3
1.4 Continuity of Newtonian Potential and the Field................4
1.5 Laplacian of the Reciprocal Distance........................5
1.6 Poisson s Equation....................................7
1.7 Potential due to a Sheet or a Simple Layer.........
1.8 Potential due to a Double Laye:
:r
10
2 Integral Formulae and Harmonic Functions............12
2.1 The Divergence Theorem................................^
2.2 Green s Theorem...................^
2.3 Gauss Theorem...................^
2.4 A Fundamental Theorem for Harmonic Functions . . ,......15
3 Meaning of the Equation for Harmonic Functions in Applied Geophysics . . 16
3.1 Infinite Harmonic Regions................16
3.2 Continuation Formulae in Applied Geophysics.........18
4 Magnetism in Applied Geophysics...............21
4.1 Magnetic Potential and Magnetization............21
4.2 Magnetic Density and Induction..............22
4.3 Potential, Field and Magnetization in Applied Geophysics.....24
II Functional Transformations in Applied Geophysics.........26
5 Solution of Laplace s Equation................26
5.1 Separation of Variables in Cartesian Coordinates........26
5.2 Dirichlet s Problem for z 0...............28
5.3 A Double Fourier Series as a Solution to Dirichlet s Problem? .... 29
5.4 Separation of Variables in Cylindrical Coordinates.......30
5.5 Possibility for Downward Continuation...........32
6 Function with Limited Spectra................34
6.1 General Expression for a Function with Bounded Spectra in One
Dimension.....................34
6.2 Convolution, Scalar Products, and Sampling Functions......36
6.3 Convergence....................37
6.4 Case of a Finite Interval of Definition............40
6.5 Functions with Bounded Spectra in Two Variables........41
7 Filtering and Functional Transformations............42
7.1 Decomposition of Transformations in Applied Geophysics.....42
7.2 Filtering Proper...................44
7.3 Filter Coefficients...................46
7.4 Examples of Filtering.................46
7.5 The Composition of Transformations............47
8 Continuation of Harmonic Functions..............48
8.1 Calculation of Coefficients...............51
8.2 Example of Continuation Coefficients............51
8.3 Coefficients for Downward Continuation — Discussion of Errors . . . 53
9 Reduction of Magnetic Anomalies to the Pole...........57
9.1 Principles......................57
9.2 Expression for Coefficients for Reduction to the Pole.......60
9.3 Practical Method to Calculate Coefficients for the Reduction .... 61
9.4 Vertical Derivative Reduced to the Pole...........64
9.5 Limitations and Examples................64
10 Derivatives of Harmonic Functions...............70
10.1 Usefulness of Vertical Derivatives.............70
10.2 Vertical Derivatives and Square Grids............71
10.3 First Vertical Derivative as a Function of the Second......72
10.4 Use of a Triangular Grid................73
10.5 Horizontal Derivatives of the Potential and Deviation from the Vertical 76
10.6 Calculation of Magnetic Field Components..........79
10.7 Numerical Example of the Vertical Derivative.........81
11 Establishing a Regular Grid.................82
11.1 Manual, Graphic Method................82
11.2 LaPorte s Method...................82
11.3 Regularizaron using Sampling Functions...........84
11.4 Numerical Example of Interpolation............87
Contents VII
Appendix A. Note on the Fourier Transform............90
A.l Fourier Transform and its Inversion............90
A.2 Facts about Distributions................91
A.3 Fourier Transform of a Polynomial.............92
A.4 Convolution....................93
Appendix B. Cylindrical Structures...............93
B.l Logarithmic Potential.................93
B.2 Integral Formulae in the Plane..............95
B.3 Harmonic Functions in the Plane.............97
B.4 Solutions to Laplace s Equation in Two Variables.......98
B.5 Magnetized Structures.................99
Appendix C. Fields due to Simple Geometric Bodies..........100
C.l Attraction of a Sphere.................101
C.2 Magnetic Potential and Field due to a Magnetized Sphere.....102
C.3 Attraction of a Circular Cylinder.............102
C.4 Magnetic Field of a Magnetized Circular Cylinder........103
C.5 Influence of Thin Magnetic Layers.............104
C.6 Construction of some Vertical Master Curves........104
Appendix D. Review of Computer Programs............109
Appendix E. Bibliographic and Historical Notes...........116
Index.............................120
|
| any_adam_object | 1 |
| author | Baranov, Vladimir I. 1892-1972 |
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| author_facet | Baranov, Vladimir I. 1892-1972 |
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| dewey-ones | 526 - Mathematical geography 622 - Mining and related operations |
| dewey-raw | 526/.7 622/.15/08 |
| dewey-search | 526/.7 622/.15/08 |
| dewey-sort | 3526 17 |
| dewey-tens | 520 - Astronomy and allied sciences 620 - Engineering and allied operations |
| discipline | Physik Bergbau / Hüttenwesen |
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| id | DE-604.BV002089586 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:40:09Z |
| institution | BVB |
| isbn | 3443130089 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001368447 |
| oclc_num | 4465588 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-83 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-83 DE-188 |
| physical | XV, 121 Seiten graphische Darstellungen |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Borntraeger |
| record_format | marc |
| series | Geoexploration monographs |
| series2 | Geoexploration monographs : Series 1 |
| spelling | Baranov, Vladimir I. 1892-1972 (DE-588)123774535 aut Potential fields and their transformations in applied geophysics by Wladimir Baranov Berlin [u.a.] Borntraeger 1975 XV, 121 Seiten graphische Darstellungen txt rdacontent n rdamedia nc rdacarrier Geoexploration monographs : Series 1 6 Prospection géophysique ram Gravity anomalies Magnetic anomalies Prospecting Geophysical methods Geoexploration monographs Series 1 ; 6 (DE-604)BV001902204 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001368447&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baranov, Vladimir I. 1892-1972 Potential fields and their transformations in applied geophysics Geoexploration monographs Prospection géophysique ram Gravity anomalies Magnetic anomalies Prospecting Geophysical methods |
| title | Potential fields and their transformations in applied geophysics |
| title_auth | Potential fields and their transformations in applied geophysics |
| title_exact_search | Potential fields and their transformations in applied geophysics |
| title_full | Potential fields and their transformations in applied geophysics by Wladimir Baranov |
| title_fullStr | Potential fields and their transformations in applied geophysics by Wladimir Baranov |
| title_full_unstemmed | Potential fields and their transformations in applied geophysics by Wladimir Baranov |
| title_short | Potential fields and their transformations in applied geophysics |
| title_sort | potential fields and their transformations in applied geophysics |
| topic | Prospection géophysique ram Gravity anomalies Magnetic anomalies Prospecting Geophysical methods |
| topic_facet | Prospection géophysique Gravity anomalies Magnetic anomalies Prospecting Geophysical methods |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001368447&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902204 |
| work_keys_str_mv | AT baranovvladimiri potentialfieldsandtheirtransformationsinappliedgeophysics |