Optimal Matching Full Waveform Inversion

The conventional least squares full waveform inversion (FWI) compares the seismograms point by point. It loses the inter-receiver coherency along the spatial axis and loses the inter-event coherency along the temporal axis. Optimal transport is a global comparison algorithm. However, extending it to high dimensions is challenging due to high computation costs and often irregular acquisition design. This study proposes an optimal matching function. Each receiver is represented by an extended vector attribute containing the seismic signals and their spatial coordinates. A cost matrix is calculated for each pair of receivers. An optimal path is located in the cost matrix, which indicates whether two receivers match. This algorithm avoids pointby-point comparison, and also decreases the computation by collapsing 1-D. Two modes of the optimal matching function are developed: balanced mode and unbalanced mode. The optimal matching function is extensively examined in several models. In the Marmousi-II model experiment, the performances of the L-2 norm function, the optimal transport function, and the optimal matching function are evaluated and compared. The best velocity is obtained by the optimal matching function. The second inversion experiment is conducted with the Middle East model. Both of the balanced and the unbalanced mode recovers the velocity model starting from a linear initial model. The optimal matching function is not limited to acoustic FWI. In the final inversion experiment with the elastic Society of Exploration Geophysicists (SEG)/European Association of Geoscientists and Engineers (EAGE) overthrust model, the optimal matching function interprets both of the body and surface waves, and recovers the velocity parameters.