Wladimir Baranov:

Potential fields and their transformations in applied geophysics

1975. XV, 121 pages, 32 figures, 18 tables, 17x24cm, 450 g
Language: English

(Geoexploration Monographs, Number 6)

ISBN 978-3-443-13008-4, bound, price: 33.00 €

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geophysical techniquespractisegeoexplorationmeasurement


Content Description top ↑

Several excellent text books exist which cover the subject of Applied Geophysics but the degree of specialisation and sophistication of present geophysical techniques inevitably means that they have insufficient detail to be used other than as a general introduction. GA intends to provide a series of monographs with sufficient detail to be of use to the practising geophysicist and with sufficient discussion of the scientific fundamentals to be suitable for the student and the research worker.

Essentially, the monographs will be critical reviews of the aims, methods and status of the various techniques covering the whole range of instrumentation, operation and interpretation. They will each be written by a practising geophysicist of considerable experience. The monographs will appeal to advanced students in geoexploration at Universities and Technological Universities as well as to geophysicists and others engaged in geophysical exploration.

The author of this monograph is to be included among the most eminent geophysicists of our age. He merits this consideration as much for his inventive genius as for his energy and tenaceous will to carry the development of his ideas to the point of efficient application. He combines insight and mathematical reason to the end that he has an exceptionally clear understanding of the nature of the geophysical measurements upon which we operate. Moreover, unlike so many respectable theoreticians, he is never satisfied to present the solution of a problem on page after page of formulas spiced with mathematical symbols; he always explains it in terms of practical application including numerical examples and computer programs which he writes himself. This book is dedicated essentially to the functional transformations of gravity and magnetic anomalies. The first chapters present a general elementary view of potentials and the fields which are derived from potentials. We also discuss the principal properties of harmonic functions useful in geophysics. In the following two chapters, these principles are specialized for use in applied geophysics.

Contents top ↑

I Physics of fields and potentials 1
1 Fields and potentials 1
2 Integral formulae and harmonic functions 12
3 Meaning of the equation for harmonic functions in applied geophysics 16
4 Magnetism in applied geophysics 21
II Functional transformation in applied geophysics 26
5 Solution of Laplace's equation 26
Separation of variables in Cartesian coordinates — Dirichlet's problem for z > 0 — A double Fourier series as a solution to Dirichlet's problem? — Separation of variables in cylindrical coordinates — Possibility for downward continuation
6 Functions with limited spectra 34
General expression for a function with bounded spectra in one dimension — Convolution, scalar products, and sampling functions — Convergence — Case of a finite interval of definition — Functions with bounded spectra in two variables
7 Filtering and functional transformations 42
Decomposition of transformations in applied geophysics — Filtering proper — Filter coefficients — Examples — The composition of transformations
8 Continuation of harmonic functions 48
Calculation of coefficients — Example — Coefficients for downward continuation
9 Reduction of magnetic anomalies to the pole 57
Principles — Expression for coefficients for reduction to the pole — Practical method to calculate coefficients for the reduction — Vertical derivative reduced to the pole — Limitations and examples
10 Derivatives of harmonic functions 70
Usefulness of vertical derivatives — Vertical derivatives and square grids — First vertical derivative as a function of the second — Use of a triangular grid — Horizontal derivatives of the potential and deviation from the vertical — Calculation of magnetic field components — Numerical example
11 Establishing a regular grid 82
Manual, graphic method — LaPorte's method — Regularization using sampling functions — Numerical example of interpolation
Appendices: 90—121
Note on the Fourier transform / Cylindrical Structures / Fields due to simple geometric bodies / Review of computer programs / Bibliographic and historical notes / Index