Coupling of the elastic isotropic medium parameters in the context of iterative linearized inversion

Elastic isotropic medium is described with the three parameters. In seismic migration a perturbation of one elastic parameter contributes to the images of all three, which means that these parameters are coupled. In fact, the migration provides only qualitative description of elastic characteristics. For a quantitative reconstruction of the real elastic medium reflectivity one can apply an iterative linearized migration/inversion, where minimization of the misfit functional is done by the conjugate gradient method. The final result of an iterative approach can be obtained directly by means of Newton's method by using a pseudo-inverse of Hessian matrix. The calculation of this matrix for a realistic model is an extremely resource-intensive problem, but for the simple model of a scatterer in a homogeneous medium problem is quite feasible. Numerical results of the elastic linearized inversion are presented in the paper, both with iterative approach and full Hessian matrix. Experiments show that in both cases the elastic parameters are coupled weaker than in the case of migration. Therefore, the iterative approach allows to achieve acceptable inversion results, but requires a large number of iterations. For faster convergence it is necessary to use preconditioned conjugate gradient method. Optimal preconditioning will improve convergence of the method and quality of the inversion.