Full-waveform inversion of borehole seismic data to delineate salt bodies: a new method using a level-set function applied to a weakly deformable mesh

SUMMARY We present a full-wave inversion algorithm (FWI) to accurately delineate the subsalt body using seismic borehole data. This ill-posed inverse problem is constrained by introducing geological a priori information through the parametrization of the salt boundary using a level set function. The implicit level set function is spanned by a set of B-spline basis functions for their ability to represent a wide range of shapes. Furthermore, the proposed FWI algorithm combines a meshed discretization with the implicit representation of shapes throughout the inversion process. A weak deformation of the mesh is applied at each iteration of the inversion to maintain the explicit discretization of the shapes when the level set boundary is updated. This method is very accurate when it comes to modelling the scattered wavefields and computing the Fréchet derivatives at interfaces. Three numerical examples using synthetic borehole seismic data illustrate the ability of the method to accurately retrieve the size, location and shape of the salt body when the density and seismic velocities are known.