Inversion des formes d'onde élastique dans le domaine espace-fréquence en deux dimensions.
Application à la caractérisation de la subsurface dans le cadre de la détection de cavités souterraines.

摘要

Imaging the soil physical parameters with surface seismic recordings is a non linear inverse problem. The elastic full waveform inversion is a quantitative multiparameters imaging method of diffractors that requires beforehand the knowledge of an initial velocity model. The corresponding forward problem, the elastic waves propagation, is solved in the frequency domain, allowing to efficiently take into account multisources and multireceivers acquisitions, with a finite difference method that modelizes the propagation of all wave types (body waves, surface waves, diffrated waves, refracted waves ...). The chosen finite difference stencil precisely simulates the free surface and surface waves propagation. This linearized inversion is based on a gradient method that minimizes a misfit function containing the difference between observed and calculated data. Two seismic parameters are reconstructed from vertical and horizontal seismograms. The inversion is performed from low to high frequencies, allowing to progressively introduce higher wavelengths in the parameters images. The latter are sensitive to the choice of the physical approximations chosen to calculate the misfit function gradient (Born or Rytov approximation), to the acquisition geometry, to the data preconditionning and to the inverted parameters choice. This method is then applicated to media containing a free surface. The free surface is a very contrasted interface that generates very energetic surface waves in seismograms. Near-surface media are complex, propagating waves are reflected or diffrated several times. When the medium contains two anomalies whose velocity contrast is equal to $20 %$, the inversion correctly localize them in a known backgound model. Images are improved and anomalies amplitudes are very well recovered when the number of inverted frequencies increases and the data are selected from low to high offset. With a strongly contrasted anomaly like an empty cavity, the inversion correctly recovers the object position, shape and size but its amplitude is underestimated.The application to subsurface real vertical data recorded in a complex medium containing a cavity shows that the inversion constructs a heterogeneous medium allowing to better fit data and allows to reproduce inverted waves. Nevertheless the cavity is not imaged.