The Inverse Problem For An Acoustic Equation In A Weakly Horizontally Inhomogeneous Medium

摘要

The inverse problem of reconstructing the coefficients A and B in the equation AU_(tt) =div(B grad U) in the half-plane z > 0 is considered. It is assumed that an instantaneous point source at z = 0 generates a wave field U(t,z,x), which is known on the boundary. It is also known that the coefficients A and B can be represented in the form A = A(z,εx) = A_0(z) + εxA_1(z) + O(ε~2), B= B(z,εx) = B_0(z) + εxB_1(z) + O(ε~2). Here e is a small parameter. An algorithm for determinating the coefficients A_0, B_0, A_1, and B_1 with accuracy O(e~2) is constructed.