The statistical basis for conventional full-waveform inversion (FWI) approaches is commonly associated with Gaussian statistics. However, errors are rarely Gaussian in non-linear problems like FWI. In this work, we investigate the portability of a new objective function for FWI applications based on the graph-space optimal transport and $\kappa$-generalized Gaussian probability distribution. In particular, we demonstrate that the proposed objective function is robust in mitigating two critical problems in FWI, which are associated with cycle skipping issues and non-Gaussian errors. The results reveal that our proposal can mitigate the negative influence of cycle-skipping ambiguity and non-Gaussian noises and reduce the computational runtime for computing the transport plan associated with the optimal transport theory.

翻译：传统的全波形反演方法通常建立在高斯统计的假设基础上。然而，在全波形反演这类非线性问题中，误差极少服从高斯分布。本研究探讨了一种基于图空间最优传输与$\kappa$-广义高斯概率分布的新型目标函数在全波形反演中的适用性。我们特别证明了所提出的目标函数能有效缓解全波形反演中两个关键问题——周波跳跃现象与非高斯误差的影响。结果表明，该方法能够减轻周波跳跃模糊性与非高斯噪声的负面影响，并降低计算最优传输理论中传输方案所需的运行时间。