Parameter estimation in layered media using dispersion-constrained full waveform inversion

The need to estimate the properties of layered elastic or viscoelastic media arises commonly in various engineering applications, including geotechnical site characterization and pavement condition assessment. The layered medium is usually probed with small-amplitude waves, and the medium's response is used to drive an inverse medium problem leading to the identification of the properties. In this dissertation, we solve the property estimation problem by a new methodology that seeks to minimize the misfit between measured and computed responses, constrained by the dispersion relation of the layered medium; the latter expressed in terms of the forward eigenvalue problem and the associated orthonormality condition. The medium's properties are recovered upon satisfaction of the first-order optimality conditions of the system's Lagrangian. Next, we extend the methodology for the characterization of a finite-depth layered elastic medium to the case of a layered medium underlain by a halfspace. The layered medium is treated using a Thin Layer Method (TLM), while the halfspace is treated with the introduction of a Perfectly-Matched-Layer (PML). The PML adds complexity to the dispersion relation, including non-physical modes, which will be addressed systematically to resolve the medium's characterization. Effectively, the physical setting and the modeling choices reduce the originally three-dimensional problem to one spatial dimension along only the depth of the medium. Then, we discuss the extension of the methodology for estimating the mechanical properties and the stratification of horizontally-layered soils using surface records of soil motion induced by the passing of trains or other moving loads. At each step, we report numerical results and demonstrate the method’s capabilities and effectiveness, and discuss how the technique can be used for field applications.