Full waveform inversion to estimate the material properties of a layered half-space

Abstract

Estimations of material properties of layered infinite media have been considered in a variety of problems, including geophysical subsurface imaging, geotechnical site investigations, and nondestructive tests. The full waveform inversion (FWI) approach can be employed because it is versatile when used to estimate the properties of complicated systems. A rigorous formulation of the FWI approach used in conjunction with the thin-layer method, which is accurate and efficient for wave-propagation in a layered medium, is developed to estimate the material parameters of a layered half-space. We measure the vertical displacements of a layered half-space subjected to a harmonic vertical disk load on its surface. The responses are compared with those calculated using the estimated material properties of the considered medium. The estimated responses are obtained using a thin-layer model of the system. The thin-layer model is composed of mid-point integrated finite elements, the thickness of which can be complex, and perfectly matched discrete layers, which are appropriate for the representation of a layered half-space. An objective function, which is defined as the L2-norm of the difference between the measured and estimated responses, is minimized by means of gradient-based optimization. The gradient of the objective function is derived in terms of the derivatives of the eigenvectors and eigenvalues of the thin-layer representation of the considered medium. We then estimate the material properties by solving the optimization problem. The proposed approach is applied to various examples to estimate the profiles of shear-wave velocities of layered half-spaces. We demonstrate that the developed FWI strategy can estimate the material properties of layered half-spaces with satisfactory accuracy.