基于最优输运原理的陆上单分量资料弹性波全波形反演

陆上地震单分量地震数据只包含纵波信息，没有横波信号。声波全波形反演是最常用的利用纵波数据反演地下纵波速度、密度的方法，但忽略了单分量资料的弹性AVO特征和转换纵波的存在。为此，基于弹性介质假设推导了伪压力弹性波方程，该方程数值模拟结果仍为标量波信号，但具备弹性AVO特征和转换纵波信息，能够指示横波速度的变化。在此基础上构建了利用纵波数据进行弹性参数全波形反演的理论框架。由于全波形反演的高度非线性，准确的初始速度建模尤为重要，引入基于最优输运理论的二次Wasserstein距离（W₂范数），在不增加计算量的前提下优化了目标函数的凸性，克服了周期性跳跃导致的局部极值问题。在此基础上，再进行常规的基于L₂范数反演，克服了对初始模型的依赖。应用重采样的Marmousi模型验证了该方法仅用纵波数据反演纵、横波速度的有效性，以及避免周期性跳跃方面的优势。将该方法应用于中国东部M工区的实际地震资料，验证了该方法的实用性和稳定性。

Elastic full-waveform inversion of land single-component seismic data based on optimal transport theory

The single-component seismic data collected from land only contains P-wave information without S-wave. Acoustic full-waveform inversion (AFWI) is the most commonly used method to invert the P-wave velocity and density with P-wave data. However, it ignores the elastic AVO characteristics of single-component data and the existence of converted P-waves. To tackle this problem, this paper derives a new pseudo-pressure elastic wave equation based on the elastic medium assumption. The numerical simulation result of the equation is still a scalar wavefield but contains elastic AVO characteristics and converted P-wave information, which indicates the change of S-wave velocity. Then we build a theoretical framework of full-waveform inversion (FWI) to invert elastic para-meters using P-wave data. Besides, due to the high non-linearity of the FWI, modeling accurate initial velocity is crucial. In view of this, we introduce the quadratic Wasserstein distance (W₂-norm) based on the optimal transport theory to optimize the convexity of objective function and overcomes the local minima caused by periodic skipping without increasing calculations. On this basis, the conventional L₂-norm inversion (W₂ + L₂ inversion) is carried out, which eliminates the dependence on the initial model. The test using the Marmousi model after resampling verifies the effectiveness of the method in inverting P/S-wave velocities with only P-wave data, as well as its advantages in avoiding periodic skipping. Finally, this method is applied to actual seismic data of Area M in eastern China, and the inversion results illustrate the practicability and stability of the proposed method.