APPROXIMATE INVERSE GEOPHYSICAL SCATTERING ON A SMALL BODY

A rigorous theoretical investigation of an inverse geophysical scatter ing problem for a small body D characterized by a real-valued function v(z),z is an element of D subset of R(3), is given. Using this invest igation, a two-step method for an approximate solution of the inverse problem is developed. First, the zeroth moment (total intensity) (v) o ver tilde(D) approximate to S, v(z)dz and the first moment (center of gravity) (z) over tilde((0)) approximate to integral(D) zv(z)dz/integr al(D) v(z)dz of the unknown function v(z) are approximately found. Sec ond, the above moments are refined and the tensor of the second centra l moments of v(z) is found. Using this information, an ellipsoid D and a real constant (v) over tilde are found, such that the inhomogeneity (v) over tilde(z) = (v) over tilde, z is an element of (D) over tilde and (v) over tilde(z) = 0, z is not an element of (D) over tilde, bes t fits the surface data and has the same zeroth, first, and second mom ents. The accuracy of such procedure is established. Both low-frequenc y and fixed-frequency cases are considered. The proposed method is ver y simple numerically and is relatively stable with respect to small pe rturbations of the data. Model numerical experiments showed effectiven ess of the method.