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Stability and Accuracy Analysis of Coarse-Grain Viscoelastic Simulations

We analyze the stability and accuracy of the coarse-grain memory variable technique used for viscoelastic wave-field simulations. Our analysis shows that the general behavior of the coarse-grain system is well described by effective parameters ( M E and Q E ) that are derived from the harmonic average of the moduli over the volume of the coarse-grain cell. The use of these effective parameters proves essential for analyzing the performance and accuracy of the coarse-grain system for Q values less than about 20. A necessary stability condition for the coarse-grain system requires that the weighting coefficients be bounded between 0 and 1. Specifying the weights using the approach of Day and Bradley (2001) satisfies this condition for Q values of about 3 and larger; however, using unconstrained optimization techniques will often produce weights that violate this condition at much higher Q values. We also derive a variation of the original coarse-grain methodology called the element-specific modulus (ESM) formulation in which each element of the coarse-grain cell uses a different unrelaxed modulus. We demonstrate that the accuracy of the coarse-grain system for Q values lower than about 20 is significantly improved with the ESM formulation without increasing the computational cost. Finally, we present a technique for optimizing the accuracy of the coarse-grain system for very low Q based on the use of the effective quality factor ( Q E ). We demonstrate that using conventional optimization techniques that do not employ the effective parameter Q E will actually degrade the accuracy of the coarse-grain system.

Manuscript received 21 March 2002.