Continuum model of fractured media in direct and inverse seismic problems

A numerical modeling of a seismic survey is an important part of modern geological exploration process. Novel algorithms for seismic inverse problems are capable of handling heterogeneous geological media but require high quality results of direct problem modeling. The most difficult object in the forward modeling of the geological media is the fractured inclusion. Different approaches exist to describe its dynamic behavior, mostly limited to the linear contact conditions on crack boundaries. This work presents the nonlinear continuum model of the layered medium with visco-plastic interlayers and adopts it to the dynamic problem of wave propagation. The model relies on the linear isotropic theory and the theory of periodic media. The slip velocity vector and the delamination velocity vector are treated as continuous functions of time and coordinates. The formulated system in partial derivatives is semi-linear and contains small parameter in the denominator of the free term. To prevent the oscillation occurrence on the explicit finite-difference schemes, a novel explicit-implicit method is proposed in this paper. The method splits the problem into the elastic part and the correction procedure at each time step. The method is used to generate synthetic day surface data for the Marmousi II model containing the fractured inclusion. Deep convolutional neural networks are used to provide a fast solution for inverse problem of restoring the spatial position of the fractured inclusion based on the surface measurements.