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Memory-Efficient Displacement-Based Internal Friction for Wave Propagation Simulation

Jacobo Bielak, Haydar Karaoglu, & Ricardo Taborda

Published 2011, SCEC Contribution #1468

This paper presents a new internal friction model with the quality factor, Q, as the defining parameter in a formulation entirely based on displacements. We initially describe the model for a fiber, and then extend it to three-dimensional elastodynamics. For a fiber, the model consists of a set of parallel Maxwell elements with a Kelvin-Voigt element, also in parallel. We implemented this model in Hercules---the parallel octree-based finite element wave propagation simulator developed by the Quake Group at Carnegie Mellon University. We also tested the model and our implementation for two 3D idealized problems. The first is an infinite-space problem, whose results are compared with the corresponding exact analytical solution. The second is a half-space problem, previously used for a coarse-grain memory variable approach. Our model, with only two Maxwell elements, exhibits an almost constant quality factor with a tolerance of five percent with respect to the target Q value; it also provides a close approximation to the variation of the phase velocity with frequency.

Bielak, J., Karaoglu, H., & Taborda, R. (2011). Memory-Efficient Displacement-Based Internal Friction for Wave Propagation Simulation. Geophysics, 76(6), T131-T145. doi: 10.1190/geo2011-0019.1.