Unbalanced optimal transport for full waveform inversion in visco-acoustic media

As a high-precision parameter inversion method, visco-acoustic full waveform inversion (QFWI) is widely used in the inversion of parameters such as velocity and quality factor Q in visco-acoustic media. Conventional QFWI, using the L2 norm as the objective function, is susceptible to face the cycle-skipping problem, especially with inaccurate initial models. Lately, adopting the optimal transportation (OT) distance as the objective function in QFWI (OT-QFWI) has become one of the most promising solutions. In OT-QFWI, converting oscillatory seismic data into a probability distribution that satisfies equal-mass and non-negativity conditions is essential. However, seismic data in visco-acoustic media face challenges in meeting the equal-mass assumption, primarily due to the attenuation effect (amplitude attenuation and phase distortion) associated with the quality factor Q. Unbalanced optimal transportation (UOT) has shown potential in solving equal-mass assumption. It offers the advantage of relaxing equal-mass requirements through entropy regularization. Owing to this advantage, UOT can mitigate the attenuation effect caused by inaccurate quality factor Q during the inversion. Simultaneously, the Sinkhorn algorithm can quickly solve the UOT distance through CUDA programming. Accordingly, we propose a UOT-based QFWI (UOT-QFWI) method to improve the accuracy of two-parameter inversion. The proposed method mitigates the impact of inaccurate quality factor Q by introducing the UOT distance to calculate the objective function, thereby helping to obtain more accurate inverted parameters. Experimental tests on the 1D Ricker wavelet and 2D synthetic model are used to validate the effectiveness and robustness of our proposed method.