Different types of model parameters, such as the P- and S-wave velocities, can be coupled to one another in multiparameter seismic inversion. This coupling effect is not taken into account by the conventional approximation to the Hessian inverse for a single type of parameter, and so it can lead to a slow rate of convergence by an iterative inversion method. To solve this problem, we have developed a multiparameter deblurring filter that approximates the Hessian inverse. This filter takes into account the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the different types of parameters. The filters are calculated by matching the reference multiparameter migration images to their reference reflectivity models. Numerical tests with elastic migration and inversion indicate that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude, and increases the resolution of the elastic migration images, but it also mitigates the crosstalk artifacts caused by the coupling effect. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.