COMPOSITE MEMORY VARIABLE VELOCITY-STRESS VISCOELASTIC MODELLING

Abstract

The full 3-D viscoelastic wave equations have been reformulated,using the velocity-stress formulation for a curved grid, to include a set of memory variables for each particle velocity component. The earlier standard formulation includes a set of memory variables for each stress component. In 3-D this reduces the number of memory variables by three for each extra relaxation parameter above 1. This reformulation requires transforming the usual first order differential equation for velocity-stress modelling to a second order differential equation which again requires storage of two consecutive time step values of the particle velocities. No memory saving therefore is achieved using just one relaxation mechanism. However, the memory saved by the new formulation increases with increasing number of included relaxation mechanisms, and is around 30 per cent for 5-7 relaxation mechanisms, which is often required for accurate Q modelling. Incidentally, for media of heterogeneous Q, the new formulation is two to three times slower in simulations than the old formulation, so the new formulation should be used in memory critical applications and/or for heterogeneous media with layers/blocks of homogeneous Q, for which also CPU will be saved.