Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem with two sets of constraints: Partial-differential equation (PDE) constraints governing elastic wave propagation and physical model constraints implementing prior information. The alternating direction method of multipliers is used to solve the problem, resulting in an iterative algorithm with well-conditioned subproblems. Although wavefield reconstruction is the most challenging part of the iteration, sparse linear algebra techniques can be used for moderate-sized problems and frequency domain formulations. The Hessian matrix is blocky with diagonal blocks, making model updates fast. Gradient ascent is used to update Lagrange multipliers by summing PDE violations. Various numerical examples are used to investigate algorithmic components, including model parameterizations, physical model constraints, the role of the Hessian matrix in suppressing interparameter cross-talk, computational efficiency with the source sketching method, and the effect of noise and near-surface effects.

翻译：弹性全波形反演是一种通过拟合地震数据同时满足波动传播物理规律来估计地下属性的过程。该问题被表述为具有两类约束的最小二乘数据拟合最小化问题：控制弹性波传播的偏微分方程约束和实现先验信息的物理模型约束。采用交替方向乘子法求解该问题，生成具有良态子问题的迭代算法。尽管波场重构是迭代中最具挑战性的部分，但对于中等规模问题和频域公式可采用稀疏线性代数技术。Hessian矩阵呈分块对角结构，使得模型更新速度较快。通过累加偏微分方程违例量，采用梯度上升法更新拉格朗日乘子。通过多种数值算例研究了算法组件，包括模型参数化、物理模型约束、Hessian矩阵在抑制参数间串扰中的作用、源草图方法的计算效率，以及噪声和近地表效应的影响。