Determination of the mechanical properties of a solid elastic medium from a seismic wave propagation using two statistical estimators

In this paper, we study an inverse problem consisting in the determination of the mechanical properties of a layered solid elastic medium in contact with a fluid medium by measuring the variation of the pressure in the fluid while propagating a seismic/acoustic wave. The estimation of mechanical parameters of the solid is obtained from the simulation of a seismic wave propagation model governed by a system of partial differential equations. Two stochastic methods, Markov chain Monte Carlo with an accelerated version and simultaneous perturbation stochastic approximation, are implemented and compared with respect to cost and accuracy.