From Seismic Wave Simulation to Mechanics Computation: A New Numerical Method for Infinite-Domain Stress Modeling

The stress modeling of equilibrium states has been an important issue both in mechanics computations and geophysical investigations. In infinite-domain static problems, if the far-field boundaries are not properly set, truncation errors will be carried to the computational domain, thereby leading to incorrect stress modeling results. Based on a finite-difference (FD) seismic wave simulation scheme, we proposed a new stress modeling method that solves the far-field boundary problem accurately and efficiently. The static stress states are acquired through a forward modeling approach instead of solving the equilibrium equation system. The far-field boundaries are implemented as wave-absorbing layers by the perfectly matched layers (PMLs), whose stress and displacement states are not required but fulfilled dynamically in the computation process. Several benchmarks and numerical applications are presented to demonstrate its validation and advantages. We also illustrate that the commonly used implementations for the undetermined boundaries based on the assumption of “far” or “rigid” are less accurate enough for specific cases. As an alternative, the proposed method is well adapted for the unbounded static stress problems, without any mapping transformations or hybrid numerical schemes.