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

The incorporation of intrinsic attenuation into time domain simulations of seismic wave fields is a key ingredient for the realistic modeling of transient wave propagation in soil and rock materials. The general subject of intrinsic wave attenuation is vast and has applications in many fields. In recent years, most of the proposed rheological models for anelasticity have been based on first-order mixed velocity-stress formulations of the equations of elastodynamics. While this formulation is extensively used in finite difference and occasionally in finite element approximations, most finite element wave propagation formulations use displacements as the only dependent variables. We present here a new internal friction model with Q as the defining parameter, based on a displacement-only formulation. We describe the model initially for a fiber, and then extend it to three-dimensional elastodynamics. We implemented this method into Hercules---the parallel octree-based finite element simulator developed by the Quake Group at Carnegie Mellon University. We test the method and our implementation for two 3D idealized problems. This model exhibits an almost constant quality factor with a maximum error of five percent with respect to the target Q.