Generalized numerical techniques to absorb artificial grid boundary reflections for seismic wave modelling in arbitrary elastic, anisotropic media

In seismic wave modelling, the perfectly-matched layer (PML) technique is a popular numerical approach to absorb the artificial reflections from the edges of the modeling domain because it places no limitation on the nature of the medium. However, the time-domain PML technique requires recursive convolutional computations at each time step to obtain all the 1^st-order spatial derivatives. For the higher order spatial derivatives, it is not straightforward. In this paper, two alternatives to the PML technique are presented. One is a generalized version of the so-called 'Stiffness Reduction Method', and the other is named the 'Mass Reduction Method'. We show that both approaches simply employ complex-valued wavenumbers rather than complex-valued spatial coordinates as in the PML technique, so that seismic waves decay in the extensional zones and the artificial reflections from the computational edges are suppressed. We show that these two techniques require no additional calculations for the spatial derivatives, are applicable for both 1^st- and 2^nd-order wave equations and arbitrary elastic media, and are much easier to implement in computer coding than the PML.