Crosstalk suppression in multiparameter full waveform inversion through parameter decorrelation

Mariana Lume

Multiparameter full waveform inversion (FWI) is a promising technique to estimate the elastic properties of the subsurface, but it is commonly affected by crosstalk between parameters of different nature, which impacts the convergence of the local optimization algorithms and introduces artifacts and uncertainty to the results. Hence, reducing these effects is essential to increase confidence in the estimates. This thesis is focused on proposing strategies to treat these artifacts in the model space of the density (ρ), P-wave velocity (Vp), and S-wave velocity (Vs) while considering seismic surface experiments. The crosstalk effects are described and corrected by the Hessian operator, which also affects the shape of the iso-surfaces of the objective function. Therefore, two methodologies were developed based on performing constrained re-parameterizations, aiming to find an intermediate model space with decorrelated parameter classes, i.e., where the Hessian is the identity matrix, to reach convergence to an accurate minimum point, and later transform it into the original model space. The difference between both strategies lies in the type and size of the Hessian matrix used, i.e., point-wise Hessians and point-probes Hessians, as well as in the numerical approach employed to compute the transformation matrices necessary to map between model spaces. In both strategies, the estimates of Vs were relatively accurate but the results of Vp and ρ were strongly impacted by crosstalk effects in comparison to those obtained with FWI approaches that were not re-parameterized; thus, the sought intermediate model space was not properly mapped. The decorrelation ideas were successful in certain aspects, but the challenges were related to the limitations brought by the amount of crosstalk information considered through the Hessians, the selected numerical approaches, and the type of transformation matrix computed, which was able to do a good job in some locations of the model grid or for some parameter classes, but was not general enough to produce the expected transformation in a large scale.