Full Waveform Inversion (FWI) method becomes popular in recent years for estimating subsurface parameters by iteratively minimizing the difference between the modelled data and observed data. Inverting isotropic and elastic parameters using multi-parameter FWI has been studied by many researchers. While updating multiple parameters is still a challenging problem for increasing the nonlinearity of the inverse problem. One difficulty for multi-parameter FWI is known as cross-talk problem rising from the coupling effects between different physical parameters. It is known that the strong coupling effects between P-wave velocity and density make it difficult to recover density. In this research, we examine the ability of multi-parameter approximate Hessian and its parameter-type approximation in suppressing cross-talk and de-coupling the elastic parameters. We also show that they can be calculated using adjoint-state technique efficiently. Compared to the multi-parameter approximate Hessian, the parameter-type approximation can be inverted trivially and its storage requirement is reduced greatly.
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