Linearized elastic inversion in the $k - \omega$ domain

Giancarlo Bernasconi, Giuseppe Drufuca, Fabio Rocca

ABSTRACT

We present an algorithm for elastic linearized inversion in the wavenumber-frequency domain. The medium is considered to be composed of a known constant background plus an unknown small variation of P-impedance, S-impedance and density. The linearized approach enables us to use the tools of linear algebra to analyze the ill-conditioning of the inversion. Operating in the wavenumber-frequency domain, we gain the advantage of the simplicity of the theory, as the scattering process becomes the interaction of monochromatic plane waves with sinusoidal variations of the elastic parameters. Inversion and analysis of the information give a smoothed but reliable image of the original model. We test the algorithm on synthetic data. Because of the ill-conditioning of the inverse problem, we find that even small numerical errors cause deterioration of the quality of inversion: P-P reflections allow an accurate estimation of P-impedance perturbation only. Multicomponent data are necessary to recover S-impedance perturbation with this approach.