Mark A. Hayner
J. Robert Fricke
Dept. Ocean Eng., MIT, Cambridge, MA 02139
An optimization technique is discussed which improves the numerical efficiency of the finite difference method with memory variables used to analyze wave propagation in high-loss materials [(eta)=O(1)] [Blanch et al., ``Viscoelastic finite difference modeling,'' Rice University Tech. Rep. TR93-04 (1993)]. With the conventional use of memory variables, the relaxation function of a viscoelastic material is modeled with a series of decaying exponential functions. The amplitudes and relaxation times of these exponentials are then matched, as closely as possible, to the behavior of the viscoelastic material. Using the new optimization technique, the error of the finite difference method, which is completely predictable using the von Neuman method, is accounted for during the matching process reducing the total error. For narrow-band models, the reoptimization process can reduce run times and memory requirements for 2-D models by about 8X and 4X, respectively. The usefulness and accuracy of this technique versus analytic methods are demonstrated.