Reflection waveform inversion based on Wasserstein-2 distance

Abstract

The background velocity model is essential for accurate imaging, particularly in complicated geological features, as it serves as the foundation for high-precision velocity inversion. Reflection waveform inversion (RWI) plays an important role in reconstructing this model by efficiently tracing reflection wave paths, combining reflection energy with the demigration operator to enable precise velocity updates. However, the conventional least-squares norm objective function, sensitive to amplitude and phase variations in reflections, often leads to local minima, compromising inversion accuracy. To address this issue, this paper introduces an optimized inversion method based on optimal transport theory, specially using Wasserstein-2 distance. This approach reduces the dependence on reflection amplitudes and enhances the convexity of the objective function, mitigating the risk of local minima. Additionally, this paper incorporates the Poynting vector for wavefield decomposition, which enables more accurate tracing of reflection wave paths. Numerical tests demonstrate that this method significantly improves both the accuracy and stability of the inversion, providing a more accurate background velocity for FWI.