ON THE PROBLEM OF DETERMINATION OF MASS INHOMOGENEITY WITH MULTI - CONNECTED DOMAIN IN GRAVIMETRY

Abstract

In this paper, we consider the problem of determining the shape of an object in the interior of the Earth, the density of which differs from that of the surrounding medium Consider the flat earth model, the problem is that of finding a domain in the half plane z ≤ H, H > 0, represented by: Ω ={ (x,z):σo (ꭓ) ≤ z ≤ σ1 (ꭓ), 0 ≤ ꭓ ≤ 1; 0, σo (ꭓ) ≤ z ≤ σ2 (ꭓ), 2 ≤ ꭓ ≤ 3 } Where σo, is given and σ1, σ2 satisfies a non linear integrl equation of the first kind. Uniqeness is proved, the non linear integral is approximated by a linear moment equation. Solution of the linear moment equation is rgularized by Tikhonov method.