Résumé
Geodetic data accurately describe interseismic deformation in seismogenic zones. A well-known approach consists in assuming that interseismic geodetic fields result from the relative slip of rigid blocks along faults. These models allow for a joint estimation of fault slip-rate, locking depth and plate rotation. We propose another approach which assumes that lateral variations of effective elastic thickness control the interseismic deformation of the lithosphere. Thus, we use an inverse method to estimate the distribution of the elastic thickness of the lithosphere on continents from geodetic measurements. The rigidity is supposed to vary continuously and is modeled by a discrete set of parameters on a regular spatial grid. By ptimizing this set of parameters, we seek for a solution which reproduces at best the interseismic GPS velocity field. Our method uses a plane-stress finite element code (CAMEF) to predict the velocity field (forward modeling). The inverse method is based on a global minimization of a cost function representing the difference between the modeled velocity field and the GPS data. The velocity boundary conditions have to be imposed for the forward modeling, but they are not precisely known (they may come from the interpolation of data close to the edges of the studied area). Here, we propose a joint minimization of both elastic parameters and velocity field on the domain boundary. In order to evaluate iteratively the best set of parameters, we use a global semi-deterministic optimization algorithm that needs to compute the gradient of the cost function with respect to these parameters. This gradient can be evaluated by the method of finite differences. In order to speed up the calculations, we evaluate it by the adjoint state method. Because the gradient computation by adjoint state method is independent from the number of parameters, this allows to perform inversions with refined grid of parameters. We present results that illustrate the behavior of our joint optimization of elastic parameters and boundary conditions in various synthetic cases. For example, we attempt to retrieve a discontinuous rigidity distribution due to a strong inclusion embedded in a low rigidity medium. Then, we apply our method to a real GPS data field in Southern California. This confronts us with an heterogeneous distribution of data and measurement errors. Our optimal solution allows for the estimation of the stress rate tensor all over the studied domain. Therefore, by including the active faults location, one can estimate the amount of stress rate that accumulates along these faults. Taking into account their seismic history and geological slip-rates, we can provide for the spatial distribution of seismic hazard simply from the inversion of the geodetic measurements. Finally, the areas where our model fails to predict the geodetic measurements are interpreted in terms of post-seismic relaxation that cannot be modeled within our current framework.