Sinkhole Evaluation Using Full Waveform Tomography: A Comparative Numerical Study of Objective Functions

Full waveform tomography offers an effective method by which to evaluate near-surface conditions and reconstruct a subsurface model in the presence of strong heterogeneities. Because full waveform inversion (FWI) of seismic waves directly inverts both the phase and amplitude information of all recorded waveforms in a dataset, the resolution capabilities are improved relative to other seismic methods that rely on first-arrival times or dispersion-based analyses. FWI proceeds by generating a forward model that numerically simulates wave propagation within the domain. A single-objective inverse problem is subsequently formulated and solved using deterministic optimization algorithms to minimize the misfit between the observed field and simulated model waveforms. However, FWI is highly sensitive to the initial model. Poor misfit between the initial model and the true subsurface conditions can lead to inaccurate results from the inversion converging to local minima or failing to converge at all. One approach to mitigate this ill-posedness is to carefully select an appropriate objective function to characterize the misfit between field and synthetic waveforms. The misfit function often represents a tradeoff between inversion ill-posedness and resolution of the reconstructed subsurface model. The most common FWI objective function characterizes the misfit using a least-squares approach (i.e., L2 norm). However, the L2 norm misfit function tends to trap in local minima and may fail to converge for models with strong heterogeneous subsurface features, particularly when a poor initial model is selected. In this study, the recently proposed optimal transport misfit function was explored when applied to a near-surface domain. This misfit function relies on optimal transport theory, which develops a more effective measure of distance between probability distributions and exhibits reduced non-convexity relative to the least-squares misfit function. Both misfit functions were applied to invert waveform data acquired from a model with a subsurface sinkhole feature. Performance of the two misfit functions was evaluated by comparing their subsequent inversion results obtained from different starting models. The optimal transport misfit function was found to be more robust than the least-squares misfit and exhibited fewer convergence issues when a poor initial model was used for the FWI.