Nonlinear inversion of the SH wave equation in a half-space for density and shear modulus determination

This paper deals with the problem of multi-parameter nonlinear inversion of the SH wave equation in an elastic half-space. A numerical approach combining Born iteration and a regularizing technique is presented for simultaneously reconstructing 2-D distributions of density and shear modulus in a scatterer embedded in a half-space. The well-to-well source-receiver scheme commonly used in geophysical exploration is considered in the model in which two incident frequencies are used to uncouple the parameters in frequency domain. The weighted residual method, along with bilinear interpolating functions, are used in the discretization procedure. Computer simulations have been conducted on several examples with different density and shear modulus configurations. The numerical results show that the approach proposed has a uniformly convergence for the given objects and has a feature of treating the limited-source well-to-well scheme that causes a more ill-conditioned equation in the inversion procedure.