We present a multiparameter deblurring filter that approximates the Hessian inverse. This filter considers the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the same and different types of parameters. Numerical tests with elastic migration and inversion show that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude and increases the resolution of the elastic migration images, but also mitigates the crosstalk artifacts. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.


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