Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO$_2$ sequestration and energy exploration (e.g., hydrogen and geothermal). Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties. In this paper, we introduce $\mathbf{\mathbb{E}^{FWI}}$, a comprehensive benchmark dataset that is specifically designed for elastic FWI. $\mathbf{\mathbb{E}^{FWI}}$ encompasses 8 distinct datasets that cover diverse subsurface geologic structures (flat, curve, faults, etc). The benchmark results produced by three different deep learning methods are provided. In contrast to our previously presented dataset (pressure recordings) for acoustic FWI (referred to as OpenFWI), the seismic dataset in $\mathbf{\mathbb{E}^{FWI}}$ has both vertical and horizontal components. Moreover, the velocity maps in $\mathbf{\mathbb{E}^{FWI}}$ incorporate both P- and S-wave velocities. While the multicomponent data and the added S-wave velocity make the data more realistic, more challenges are introduced regarding the convergence and computational cost of the inversion. We conduct comprehensive numerical experiments to explore the relationship between P-wave and S-wave velocities in seismic data. The relation between P- and S-wave velocities provides crucial insights into the subsurface properties such as lithology, porosity, fluid content, etc. We anticipate that $\mathbf{\mathbb{E}^{FWI}}$ will facilitate future research on multiparameter inversions and stimulate endeavors in several critical research topics of carbon-zero and new energy exploration. All datasets, codes and relevant information can be accessed through our website at https://efwi-lanl.github.io/

翻译：弹性地球物理属性（如纵波速度和横波速度）对于二氧化碳封存和能源勘探（例如氢能和地热）等地下应用至关重要。弹性全波形反演（FWI）广泛用于储层属性表征。本文介绍$\mathbf{\mathbb{E}^{FWI}}$，一个专门为弹性FWI设计的全面基准数据集。$\mathbf{\mathbb{E}^{FWI}}$包含8个不同数据集，覆盖多种地下地质结构（平坦、弯曲、断层等）。我们提供了三种不同深度学习方法生成的基准结果。与我们此前为声学FWI提出的数据集（压力记录，称为OpenFWI）相比，$\mathbf{\mathbb{E}^{FWI}}$的地震数据集同时包含垂直和水平分量。此外，$\mathbf{\mathbb{E}^{FWI}}$中的速度图整合了纵波和横波速度。虽然多分量数据和新增的横波速度使数据更加真实，但也引入了反演收敛性和计算成本方面的更多挑战。我们开展全面的数值实验，以探究地震数据中纵波速度和横波速度之间的关系。纵波与横波速度的关系为地下属性（如岩性、孔隙度、流体含量等）提供关键见解。我们预计$\mathbf{\mathbb{E}^{FWI}}$将促进未来多参数反演研究，并推动碳净零与新能源勘探中若干关键研究课题的进展。所有数据集、代码及相关信息可通过我们的网站https://efwi-lanl.github.io/ 获取。