Numerical recovery of the layered medium from the surface data

摘要

In this paper an inverse problem is formulated and its numerical solution is given. The problem is of interest, for example, in geophysics. Numerical results show that the algorithm is efficient for noisy data. Practical recommendations are given. The problem consists of finding n(z), the refraction coefficient of the medium, given the surface data u(x, k), ∀x ϵ P = {x: x3 = 0} and all k ϵ (0, k0), where k0 > 0 is an arbitrary small wave number. The governing equation is [∇2 + k2n(z)]u = − δ(x), x = (x1, x2, z). Analytical solution to this inverse problem is given, a numerical implementation is suggested and the results of the numerical experiments are reported.