EFFICIENT SIMULATION OF CONSTANT-Q USING COARSE-GRAINED MEMORY VARIABLES

Improvements in computing speed have progressively increased the usabl e bandwidth of seismic wave-field simulations computed with time-stepp ed numerical schemes (e.g., finite difference, finite element, pseudos pectral). As computational bandwidth increases, anelastic losses becom e increasingly significant for some important applications such as ear thquake ground-motion modeling, whole earth seismogram simulation, and exploration seismic profile modeling, and these losses need to be inc luded in the simulations. As bandwidth increases, however, the memory variables necessary to incorporate realistic anelastic losses account for an increasing proportion of total computational storage requiremen ts, a consequence of the broad relaxation spectrum of typical earth ma terials. To reduce these storage requirements, we introduce a new meth od in which the memory variables are coarse grained, that is, redistri buted in such a way that only a single relaxation time is represented at each node point (and therefore a single memory variable per stress component is required). Guided by a perturbation analysis, we effect t his redistribution in such a way that spatial variability of this sing le relaxation time simulates the full relaxation spectrum. Such coarse graining reduces memory-variable storage requirements by a factor of 8 for 3D problems or a factor of 4 for 2D problems. In fourth-order fi nite-difference computations for the 3D acoustic-wave equation, the me thod simulates frequency-independent Q within a 3% tolerance over 2 de cades in frequency, and it is highly accurate and free of artifacts ov er the entire usable bandwidth of the underlying finite-difference sch eme. These results should also hold for the elastodynamic equations. T he method is readily generalized to approximate specific frequency-dep endent Q models such as power laws or to further reduce memory require ments. In its present implementation, the main limitation of the metho d is that it generates artifacts at wavelengths equal to 4 grid cell d imensions and shorter, which may, in some limited circumstances, overl ap the usable bandwidth of very high-order finite-difference and/or ps eudospectral schemes.