EFFICIENT 3-D VISCOELASTIC MODELING WITH APPLICATION TO NEAR-SURFACE LAND SEISMIC DATA

Three-dimensional viscoelastic modeling is implemented by reparameteri zing the viscoelastic wave equation for a standard linear solid. The f ormulation uses weighting factors corresponding to relaxation frequenc ies and composite memory variables. This novel 3-D formulation require s less computer memory than the traditional relaxation time formulatio n because one set of relaxation frequencies can be used for all mechan isms for all parts of a model, and only three sets of composite memory variables are needed rather than the seven used in the standard imple mentation, giving a net reduction of 40% in the total required memory. Computational time is also reduced approximately 25% because of reduc ed input/output (I/O). The algorithm is applied to 3-D modeling of the viscoelastic response of the near-surface structure beneath a 3-D ref lection survey in the Ouachita frontal thrust zone of southeast Oklaho ma. Comparison of the 3-D field data with both viscoelastic and elasti c response clearly demonstrates the importance of inclusion of viscoel asticity when accurate amplitude fitting is desired. Observed amplitud e and traveltime variations can be explained by shallow velocity and Q distributions obtained independently by 3-D tomography.