Eigenvector Model Descriptors for the Seismic Inverse Problem

We consider the quantitative inverse problem for the recovery of subsurface Earth's properties, which relies on an iterative minimization algorithm. Due to the scale of the domains and lack of apriori information, the problem is severely ill-posed. In this work, we reduce the ill-posedness by using the ``regularization by discretization'' approach: the wave speed is described by specific bases, which limits the number of coefficients in the representation. Those bases are associated with the eigenvectors of a diffusion equation, and we investigate several choices for the PDE, that are extracted from the field of image processing. We first compare the efficiency of these model descriptors to accurately capture the variation with a minimal number of coefficients. In the context of sub-surface reconstruction, we demonstrate that the method can be employed to overcome the lack of low-frequency contents in the data. We illustrate with two and three-dimensional acoustic experiments.