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（如纵波和横波速度）对于二氧化碳封存及能源勘探（例如氢能和地热）等多种地下应用至关重要。弹性全波形反演（FWI）被广泛应用于储层属性表征。本文介绍$\mathbf{\mathbb{E}^{FWI}}$，一个专门为弹性FWI设计的综合性基准数据集。$\mathbf{\mathbb{E}^{FWI}}$包含8个涵盖不同地下地质结构（如水平层状、弯曲层状、断层等）的独立数据集。我们提供了三种不同深度学习方法的基准测试结果。与我们此前发布的声波FWI数据集（称为OpenFWI，仅包含压力记录）不同，$\mathbf{\mathbb{E}^{FWI}}$中的地震数据集同时包含垂直和水平分量。此外，$\mathbf{\mathbb{E}^{FWI}}$中的速度图同时纳入了纵波和横波速度。虽然多分量数据和新增的横波速度使数据更具现实性，但也给反演的收敛性和计算成本带来了更多挑战。我们开展了全面的数值实验，以探究地震数据中纵波与横波速度之间的关系。纵波与横波速度的关系为岩性、孔隙度、流体含量等地下属性提供了关键见解。我们预期$\mathbf{\mathbb{E}^{FWI}}$将促进未来多参数反演的研究，并推动碳零排放和新能源勘探中若干关键研究课题的发展。所有数据集、代码及相关信息均可通过我们的网站https://efwi-lanl.github.io/获取。