A Perfectly Matched Layer Technique Applied to Lattice Spring Model in Seismic Wavefield Forward Modeling for Poisson’s Solids

ABSTRACT As a complementary way to traditional wave-equation-based forward modeling methods, lattice spring model (LSM) is introduced into seismology for wavefield modeling owing to its remarkable stability, high-calculation accuracy, and flexibility in choosing simulation meshes, and so forth. The LSM simulates seismic-wave propagation from a micromechanics perspective, thus enjoying comprehensive characterization of elastic dynamics in complex media. Incorporating an absorbing boundary condition (ABC) is necessary for wavefield modeling to avoid the artificial reflections caused by truncated boundaries. To the best of our knowledge, the perfectly matched layer (PML) method has been a routine ABC in the wave-equation-based numerical modeling of wave physics. However, it has not been used in the nonwave-equation-based LSM simulations. In this work, we want to apply PML to LSM to attenuate the boundary reflections. We divide the whole simulation region into PML region and inner region, PML region surrounds the inner region. To incorporate PML to LSM, we establish elastic-wave equations corresponding to LSM. The simulation in the PML region is conducted using the established wave equations and the simulation in the inner region is conducted using LSM. Three simulation examples show that the PML scheme is effective and outperforms Gaussian ABC.

An Efficient Mixed Finite Element Perfectly Matched Layer with Optimal Parameters Selection for Two-Dimensional Time Domain Soil-Structure Interaction Analysis

Perfectly matched layer (PML) is known as one of the best methods to simulate infinite domains in many fields such as soil-structure interaction (SSI). The performance of PML is significantly affected by PML parameters selection. However, the way to select PML parameters still remains unclear. This study proposes a method for PML parameters determination for elastic wave propagation in two-dimensional (2D) media. The scaling and attenuation functions are developed in order to increase the accuracy and effectiveness of the PML. The proposed scheme is applied for a mixed PML in time domain. The finite element method (FEM) formulations of the PML are presented so that it can be easily applied to the existing codes. ABAQUS, a popular FEM code, is used for numerical applications in this study. The proposed PML is imported into ABAQUS by using a user-defined element (UEL) written in Fortran language. Six numerical analyses of SSI are implemented to prove the efficiency of the proposed PML. The numerical analyses cover many realistic problems, including free field, surface structure, and embedded structure problems. The results demonstrate the efficiency of the proposed PML in terms of the accuracy and computational cost.

An isogeometric formulation of locally-conformal perfectly matched layer for acoustic scattering problems

This paper presents an isogeometric formulation of the locally-conformal perfectly matched layer (PML) for time-harmonic acoustic scattering problems. The new formulation is a generalization of the conventional locally-conformal PML, in which the NURBS patch supporting the PML domain is transformed from real space to complex space. This is achieved by complex coordinate stretching, based on a stretching vector field indicating the directions in which incident sound waves are absorbed. The performance of the isogeometric PML formulation is discussed through several acoustic scattering problems, spanning from one to three dimensions. It is found that the proposed method presents superior computational accuracy, high geometric adaptivity, and good robustness against challenging geometric features. The geometry-preserving ability inherent in the isogeometric framework could bring extra benefits by eliminating geometric errors that are unavoidable in the conventional PML. Meanwhile, these properties are not sensitive to the location of the sound source or the depth of the PML domain.