Application in geophysics of analytical continuation of the potential function to the lower half-plane
Authors:
Abstract
In the geological interpretation of geophysical observations, it is often necessary to calculate the potential function in the lower half-plane from its values determined by measurements at the earth's surface. This problem was solved by many researchers, including G. Renbow, who, for example, performed analytical continuation to the lower half-plane of the second derivative of the gravitational potential, with the help of which he determined the interface between two media of different densities.
Область исследования:
(Archived) Without section
Funding:
None
References
- Andreev B. A. Calculations of spatial distribution of potential fields and their use in exploration geophysics. Izvestiya AN SSSR, seriya geografii i geofiziki, 1949, No. 3. (in Russian)
- Andreev B. A. Calculations of Spatial Distribution of Potential Fields and Their Use in Exploration Geophysics. Izvestiya AN SSSR, seriya geofizicheskaya, 1952, No. 2. (in Russian)
- Andreev B. A. Calculations of Spatial Distribution of Potential Fields and Their Use in Exploration Geophysics. Izvestiya AN SSSR, seriya geofizicheskaya, 1954, No. 1. (in Russian)
- Zamorev A. A. Determination of Body Form by Derivatives of External Gravitational Potential. Izvestiya AN SSSR, seriya geografii i geofiziki, 1942, No. 1‑2. (in Russian)
- Kantorovich L. V. and Krylov V. I. Approximate Methods of Higher Analysis. Gostekhteoretizdat, 1941. (in Russian)
- Kantorovich L. V., Krylov V. I., Chernin K. E. Tables for solving boundary value problems. Gostekhteoretizdat, 1956. (in Russian)
- Malkin N. R. Dependence between gradients of the Newtonian potential on the plane in application to the study of gravitational anomalies. Izvestiya AN SSSR, seriya VII, otd. fiz.‑mat. nauk, 1930, No. 8. (in Russian)
- Markushevich V. M. Theory of Analytical Functions. Gostekhteoretizdat, 1950. (in Russian)
- Malovichko A. K. Methods of analytical continuation of gravity anomalies and their applications to gravity survey problems. Gostoptekhizdat, 1956. (in Russian)
- Pudovkin I. M. Application of Neumann's problem to solution of some questions of applied magnetometry.Trudy NIIZM, 1950, issue 5. (in Russian)
- Ryzhik I. M. Tables of integrals, sums, series and products. Gostekhteoretizdat, 1948. (in Russian)
- Smirnov V. I. Course of Higher Mathematics. Vol. III, pt. 2. Gostekhteoretizdat, 1950. (in Russian)
- Sokolov K. P. Geological Interpretation of Magnetic Exploration Data. Gosgeoltekhizdat, 1956. (in Russian)
- Strakhov V. N. Some questions of methodology of interpretation of magnetic anomalies. Izvestiya AN SSSR, seriya geofizicheskaya, 1956, No. 12. (in Russian)
- Tyapkin K. F. To the question of graphical calculation of Vzz from the results of Ag measurements. Sbornik Prikladnaya geofizika, 1957, issue 16. (in Russian)
- Tichmarsh E. Introduction to the theory of Fourier integrals. Gostekhteoretizdat, 1948. (in Russian)
- Fikhtenholtz G. M. Course of Differential and Integral Calculus, vol. II, Gostekhteoretizdat, 1948. (in Russian)
- Shvank O. A. and Liu E. N. Interpretation of Gravitational Observations. Gostoptekhizdat, 1947. (in Russian)
- Yakovlev K. P. Mathematical Processing of Measurement Results. Gostekhteoretizdat, 1953. (in Russian)
- Rainbow N. The Interpretation of Torsion Balance Data. World Petroleum Congress. London, 1933.