Abstract

We present a method for determining the elastic parameters of a horizontally stratified medium from its plane-wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least-squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency-wave slowness domain and can be readily adapted to various source-receiver configurations.The behavior of the algorithm conforms to the predictions of generalized least-squares inverse the-ory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P-wave velocity (or P-wave impedance) by considering plane waves in the low slowness region (near-normal angles of incidence), then in optimizing for the S-wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise-free synthetic data prove that the proposed inversion method satisfactorally reconstructs the elastic properties of a stratified medium from a limited set of plane-wave components, at a reasonable computing cost.

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