Summary
Within the geophysical literature there is shown a group of proceedings concerning analytical continuities of potential fields into the lower half-space. These proceedings are based on the Poisson's formula which gives a solution to the Dirichlet's problem applied to in a plane degenerated spheres, like this:
where (x, y) is the at the surface measured gravity-or magnetic-field; andg(ζ, ξ) is the field within a plane at ah(z=h) elevation.
To discoverg(ζ, ξ) within thez=h plane, the successive approximating method is commonly used.
Within the present paper two proceedings of effectuating analytical continuities by using the aleatory numbers method (the Monte Carlo method) as well as the linear programming algorithmes, are suggested.
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References
S. I. Gass,Linear Programming Methods and Applications (McGraw Hill Books Company, Inc., New York, Toronto, London 1968).
J. M. Hammersley andD. C. Handscomb,Monte Carlo Methods (London 1964).
Gh. Mihoc,Sur l'application de la méthode de Monte-Carlo aux processus pour apprendre, Rev. math. pures et appl.8 (1963).
O. Onicescu,Nombres et systèmes aléatoires (Bukarest-Paris 1964).
M. Ianâs andD. Zorilescu,Some Applications of the Linear Programming within Gravimetry, Pure and Applied Geophysics 72 (1969/I), 5–12.
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Zorilescu, D. Two new proceedings for the analytical continuities of within the lower half-space, by using the Monte Carlo method and the algorithmes of the linear programming. PAGEOPH 73, 19–24 (1969). https://doi.org/10.1007/BF00875117
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DOI: https://doi.org/10.1007/BF00875117