Full-Waveform-Based Inversion for Site Characterization: Theory, Numerical Simulations, and Physical Experiments

Abstract eng:
We discuss recent progress in the full-waveform-based imaging of probed solids/soils, with geotechnical site characterization applications in mind. The primary goal is the reconstruction of the material profile of near-surface, arbitrarily heterogeneous formations using elastic waves as the probing agents. The problem requires efficient solutions of the forward wave simulation problem, robust strategies for tackling the inverse imaging problem, and designing of experimental protocols to best harness the limited field data that feed the imaging problem. To address the forward problem, the semi-infinite extent of the probed domains is truncated via the introduction of perfectly-matched-layers (PMLs) at the truncation interfaces. We discuss a new variational hybrid formulation for transient elastic wave simulations in PML-truncated domains that is computationally optimal when compared to competing schemes. We then discuss a full-waveformbased inversion framework driven by PDE-constrained optimization ideas: to address the imaging problem we seek to resolve simultaneously PML-endowed state and adjoint time-dependent BVPs, together with time-independent BV control problems that drive the material updates during inversion iterations. To address solution multiplicity and improve on the robustness of the inversion algorithms we deploy regularization schemes (Tikhonov and Total Variation), continuation schemes (frequency-, grid-, and regularization factor-continuations), and a new search-direction biasing scheme that seems to accelerate algorithmic convergence. We report satisfactory results with numerical experiments targeting inversion of both smooth and sharp profiles in two dimensions, and also provide examples attesting to the quality and efficiency of the forward wave modeling.

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