Optimal Transport Time Difference Objective Function and Energy Correction Inversion Method
摘要
Full Waveform Inversion (FWI) is a high-precision velocity modeling technique widely used in seismic exploration. However, traditional objective functions based on the L2 norm are prone to the cycle-skipping problem, which leads to the inversion falling into local minima and failing to converge to the global optimum. Although optimal transport distance-based objective functions can improve the convexity of the inversion problem and alleviate cycle-skipping to a certain extent, they still suffer from defects such as uneven energy matching between observed and synthetic data and insufficient convergence efficiency in practical applications. To address these issues, this paper proposes a novel FWI method that integrates an optimal transport time-difference objective function with an energy correction preprocessing strategy. First, an energy correction preprocessing method is designed to balance the energy distribution of seismic data in shallow, middle, and deep layers, suppress the dynamic range difference of seismic records, and convert the data into a probability distribution that meets the requirements of optimal transport. Second, a rigorous optimal transport time-difference objective function is constructed to focus on travel time information and weaken the interference of amplitude differences. The proposed method is verified on typical geophysical models. The results show that it can effectively expand the convergence domain of FWI, improve inversion accuracy and efficiency, and enhance robustness to noise and incomplete data. The method provides a new technical approach for high-precision velocity modeling of complex structures in oil and gas exploration.