High-resolution seismic imaging applied to the characterization of very shallow highly contrasted structures

High resolution seismic imaging could be achieved through the so-called full waveform inversion (FWI) which attempts to extract the information from the whole seismogram. This technique has been applied successfully in the characterization of deep structures for oil and gas industry. Near surface applications are less numerous as various seismic phases coming from the free surface interaction and the weathered layer zone introduce an increasing complexity in the signal, leading to optimization difficulties for the FWI. Both surface and body waves should be considered in the optimization procedure as independent or collaborative contributions. We present a numerical investigation of FWI performances for imaging very shallow and highly contrasted structures with velocity contrasts up to ten for P wave velocity and to twenty for S wave velocity as often met for very superficial investigation to a depth of few meters and at frequencies of few hundreds of hertz. Seismic wave modeling is performed by a discontinuous Galerkin (DG) finite element method in the frequency domain for 2D visco-elastic geometries: technique suitable for high contrasts of material properties. The related discretization of the medium is performed through a unstructured triangular mesh.The optimization approach is based on the estimation of a misfit function between observed data and synthetic data in the frequency domain. We shall update velocity quantities independently at each node of the meshing which acts as a diffractor. Because the forward modeling is time-consuming, we proceed through a local Quasi-Newton approach: the gradient is estimated through the adjoint formulation while an estimation of an approximate Hessian is obtained through the LBFGS method. In order to mitigate non-linear effects of the optimization procedure which can be trapped into secondary minima, we perform a two-levels strategy: we invert sequentially from low to high frequencies where the reconstructed medium at a given frequency band is used as the initial model for the next frequency band and, for each frequency band, we adjust a decreasing damping factor of the frequency data corresponding to short to large time-windowing around the first arrival of the signal. We test this strategy on realistic synthetic data on unstructured meshes with P0 (constant) or P1 (linear) interpolation functions inside each cell. We have encouraging results that show that the interaction between diffractors, the acquisition system, and the free surface is critical for the convergence of the inverse problem. The influence of surface waves which carry large amplitudes in the gradient estimation is of great importance while scattered body waves bring the main contribution of the heterogeneity structure. We show that a carefully tuned strategy is needed to mitigate the influence of the surface waves when reconstructing structures with high impedance contrasts. This numerical strategy is applied to concrete structures in soft materials as an extreme configuration we could expect near the free surface.