Memory-efficient simulation of anelastic wave propagation

Realistic anelastic attenuation can be incorporated rigorously into finite difference and other numerical wave propagation methods using internal or m emory variables. The main impediment to the realistic treatment of anelasti c attenuation in 3D is the very large computational storage requirement imp osed by the additional variables. We previously proposed an alternative to the conventional memory-variable formulation, the method of coarse-grain me mory variables, and demonstrated its effectiveness in acoustic problems. We generalize this memory-efficient formulation to 3D anelasticity and descri be a fourth-order, staggered-grid finite-different implementation. The anel astic coarse-grain method applied to plane wave propagation successfully si mulates frequency-independent Q(P), and Q(S), Apparent Q values are constan t to within 4% tolerance over approximately two decades in frequency and bi ased less than 4% from specified target values, This performance is compara ble to that achieved previously for acoustic-wave propagation, and accuracy could be further improved by optimizing the memory-variable relaxation tim es and weights. For a given assignment of relaxation times and weights, the coarse-grain method provides an eight-fold reduction in the storage requir ement for memory variables, relative to the conventional approach. The meth od closely approximates the wavenumber-integration solution for the respons e of an anelastic half-space to a shallow dislocation source, accurately ca lculating all phases including the surface-diffracted SP phase and the Rayl eigh wave. The half-space test demonstrates that the wave field-averaging c oncept underlying the coarse-grain method is effective near boundaries and in the presence of evanescent waves. We anticipate that this method will al so be applicable to unstructured grid methods, such as the finite-element m ethod and the spectral-element method, although additional numerical testin g will be required to establish accuracy in the presence of grid irregulari ty. The method is not effective at wavelengths equal to and shorter than 4 grid cell dimensions, where it produces anomalous scattering effects. This limitation could be significant for very high-order numerical schemes under some circumstances (i.e., whenever wavelengths as short as 4 grids are oth erwise within the usable bandwidth of the scheme), but it is of no practica l importance in our fourth-order finite-difference implementation.