Efficient 3-D viscoelastic modeling with application to near-surface land seismic data

Three-dimensional viscoelastic modeling is implemented by reparameterizing the viscoelastic wave equation for a standard linear solid. The formulation uses weighting factors corresponding to relaxation frequencies and composite memory variables. This novel 3-D formulation requires less computer memory than the traditional relaxation time formulation because one set of relaxation frequencies can be used for all mechanisms for all parts of a model, and only three sets of composite memory variables are needed rather than the seven used in the standard implementation, giving a net reduction of 40% in the total required memory. Computational time is also reduced approximately 25% because of reduced 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 reflection survey in the Ouachita frontal thrust zone of southeast Oklahoma. Comparison of the 3-D field data with both viscoelastic and elastic response clearly demonstrates the importance of inclusion of viscoelasticity when accurate amplitude fitting is desired. Observed amplitude and traveltime variations can be explained by shallow velocity and Q distributions obtained independently by 3-D tomography.