Representation of Matched-layer Kernels with Viscoelastic Mechanical Models

The Kosloff & Kosloff (KK) absorbing-boundary method is shown to be a particular case of the split-PML method introduced by Bérenger. In its original form, the PML technique has been implemented for Maxwell’s electromagnetic equations. On the other hand, the KK method was applied to the Schrödinger and acoustic wave equations. Both techniques have subsequently widely been used in dynamic elasticity, involving different rheological equations, including poroelasticity, and electromagnetism. The coordinate stretching used in the PML method is equivalent to the damping kernel in the KK method, which is based on the Maxwell viscoelastic model. Inside the absorbing strips, the result is a traveling wave which gradually attenuates without changing shape or undergoing dispersion. Moreover, we also show that the recently developed unsplit CPML method is based on the memory-variable formalism to describe anelasticity introduced by Carcione and co-workers, and that the damping kernel is based on the Zener viscoelastic model. The theoretical reflection coefficients, i.e., before discretization, are obtained and re-interpreted using the theory of viscoelasticity through the acoustic/electromagnetic analogy.