Attenuation equations for seismic peak ground acceleration, ground velocity or seismic response spectra, in terms of distance to the source and magnitude of the causative event are typically based on results of the theory of linearly elastic wave propagation in homogenous solids. The latter also furnishes the fundaments for both the study of vibrations induced by surface loadings on the ground and for the design of isolation systems. In engineering applications, the propagation of seismic waves through inhomogeneous materials acquires unquestionable relevance. At the same time, analytical solutions impose increasing difficulties, requiring resort to numerical approaches. In the paper, a version of the Discrete Element Method, herein designated as Lattice Element Method (LDEM), is employed to study propagation of body waves in linearly elastic homogeneous and inhomogeneous media, with or without viscous linear material damping, with the objective of assessing bounds for solutions based on the assumption of linear elastic material models.

地震峰值地面加速度、地面速度或地震响应谱的衰减方程，就到源的距离和起因事件的大小而言，通常基于均质固体中线性弹性波传播理论的结果。后者还为研究由地面表面载荷引起的振动和设计隔离系统提供了基础。在工程应用中，地震波在非均质材料中的传播具有无可置疑的相关性。同时，解析解带来了越来越多的困难，需要求助于数值方法。在论文中，离散元方法的一个版本，在此称为格元方法（LDEM），