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

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:

$$\begin{gathered} \bar g(x,y) = \frac{h}{{2\pi }}\smallint \smallint \frac{{g(\xi ,\zeta )}}{{[(\xi - x)^2 + (\zeta - y)^2 + h^2 ]^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}d\xi d\zeta \hfill \\ R^2 \hfill \\ \end{gathered} $$

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.