Institute of Computational Mathematics and Mathematical Geophysics

Международная Конференция по Математическим Методам в Геофизике «ММГ-2003»

Россия, Новосибирск, Академгородок 8-12 октября 2003 г.

Тезисы докладов

Пленарные доклады

An approach to solving three-dimensional inverse gravity problems

Акимова Е.Н., Мартышко П.С.,Пруткин И.Л., Тимерканова Л.Ю., Васин В.В.

Институт математики и механики Уральского отделения РАН
Институт геофизики УрО РАН (Екатеринбург)

Two inverse gravity problems are investigated:
---selection of gravitational effect from sources in a horizontal layers and finding variable density localized in this layer;
---reconstruction of interface surfaces between layers with different constant densities using gravitational data measured on the ground surface.

In the first case we deal with a linear two-dimensional Fredholm integral equation of the first kind and in the second case we have a nonlinear equation . To solve these integral equations we use the coupled monotone process [1]:

u^(k+1)=u^(k)-beta_(k)[A(u^k)+epsilon_ku^(k)-f]+alpha_k(nu^k-u^k)
u^(k+1)=nu^(k)-beta_(k)[A(nu^k)+epsilon_knu^(k)-f]-alpha_k(nu^k-u^k)

and some another iteratively regularized methods.

In the talk we analyze effectiveness of iterative methods and discuss the numerical results for the inverse problems mentioned above with real gravitational data [2].

[1] Vasin V.V. Iterative regularization of monotonic operator equations in half-ordered B-spaces. Dokl.Akad.Nauk, 1995, vol.341, no.2, pp.151-155.
[2] Vasin V.V., Perestoronina G.Ya., Prutkin I.L., Timerkhanova L.Yu. Solution of gravity and magnetic three-dimensional inverse problems for three-layers medium. Mathematical Modelling, 2003, vol. 15, no. 2, pp. 69-76.

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