Institute of Computational Mathematics and Mathematical Geophysics

International Conference on Mathematical Methods in Geophysics «MMG-2003»

Akademgorodok, Novosibirsk, Russia, October 8-12, 2003

Abstracts

Plenary reports

An approach to solving three-dimensional inverse gravity problems

Akimova E.N., P.S.Martyshko P.S.,Prutkin I.L.,Timerkhanova L.Yu., Vasin V.V.

Institute of Mathematics and Mechanics UB RAS
Institute of Geophysics UB of RAS (Ekaterinburg)

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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