The movement and deformation of the Earth’s crust and upper mantle provide critical insights into the evolution of earthquake processes and future earthquake potentials. Crustal deformation can be modeled by dislocation models that represent earthquake faults in the crust as defects in a continuum medium. In this study, we propose a physics-informed deep learning approach to model crustal deformation due to earthquakes. Neural networks can represent continuous displacement fields in arbitrary geometrical structures and mechanical properties of rocks by incorporating governing equations and boundary conditions into a loss function. The polar coordinate system is introduced to accurately model the displacement discontinuity on a fault as a boundary condition. We illustrate the validity and usefulness of this approach through example problems with strike-slip faults. This approach has a potential advantage over conventional approaches in that it could be straightforwardly extended to high dimensional, anelastic, nonlinear, and inverse problems.

地壳和上地幔的运动和变形为地震过程的演化和未来的地震潜力提供了重要的见解。地壳变形可以通过位错模型来模拟，位错模型将地壳中的地震断层表示为连续介质中的缺陷。在这项研究中，我们提出了一种基于物理学的深度学习方法来模拟地震引起的地壳变形。神经网络可以通过将控制方程和边界条件纳入损失函数来表示任意几何结构和岩石力学特性中的连续位移场。引入极坐标系以准确模拟断层上的位移不连续性作为边界条件。我们通过走滑断层的示例问题来说明这种方法的有效性和实用性。这种方法与传统方法相比具有潜在优势，因为它可以直接扩展到高维、滞弹性、非线性和反问题。