Reconstruction of density and wave velocity from reflection and transmission data

摘要

Consider an inverse problem of reconstructing the coefficient in a linear wave equation on an inhomogeneous slab with density ρ(z) and wave velocity c(z). The inversion input information is the reflection and transmission data corresponding to a point source. By applying the characteristic theory for hyperbolic equations, we establish an integral system from which ρ(z) and c(z) can be recovered simultaneously. In contrast to some known results, our inverse approach is carried out for depth variable, rather than for travel-time variable. Therefore inversion results in this paper are more appropriate for the physical interpretation of a medium slab.