Point Cloud-Based High-Dimensional Optimal Transport for Full Waveform Inversion

In full waveform inversion (FWI), the synthetic seismic events could deviate from the observed events along the time and receiver axes. Conventional FWI compares seismograms point by point. Coherency between seismic events and between neighboring receivers is not exploited. Consequently, the initial model should be accurate enough to ensure that the seismic deviation is within half a period, which is the well-known cycle skipping problem. This motivates us to develop a high-dimensional convex objective function with an optimal transport (OT) algorithm based on point cloud distribution. A point cloud distribution is a collection of unstructured and arbitrarily positioned scattered points. Taking seismograms as point cloud distribution naturally satisfies the OT requirement of positiveness and mass conservation. Because the OT function matches patterns, each seismic event is potentially compared to all other events along the time and space axes, and at the end, an optimal matching is computed. We demonstrate how our high-dimensional OT algorithm correctly captures the mass deviation in 2-D and 3-D spaces. In FWI, we apply it to both land and marine seismic datasets. The land seismic experiment is conducted in the SEG/EAGE overthrust complex onshore model. The experiment shows the superiority over the least-squares (L2) inversion and that the high-dimensional OT function recovers cleaner models than its 1-D version. Finally, we invert the synthetic dataset provided by Chevron in 2014. In all these experiments, we start from crude initial models and achieve high-resolution subsurface structures. This is not possible for conventional FWI.