Abstract

The authors consider the problem of determining by gravimetric methods the shape of an object in the interior of the Earth, the density of which differs from that of the surrounding medium. Assuming a flat earth model, the problem is that of finding a domain in the half-plane \(z\leq H\), \(H>0\), represented by \(0\leq\sigma (x)<H\), \(0\leq x\leq 1\), where \(\sigma\) satisfies a nonlinear integral equation of the first kind. Uniqueness is proved and the integral equation is approximated by a linear moment problem.