Elastic Wave Simulation in Heterogeneous Viscoelastic Media with a Curved Traction-Free Surface

摘要

Numerical modelling of elastic wave propagation in heterogeneous viscoelastic media with free-surfaces has been studied by using various schemes in the past. The principal methods are finite-element, finite-difference, pseudo-spectral and spectral-element methods. Finite-element methods are very flexible in handling perfectly elastic models with free surfaces. Spectral-element methods are special higher-order finite-element formulations. The latter is one of the best methods to tackle free surface problems as they balance the requirements of complexity, accuracy, and computation time. However the implementation is complicated compared with finite difference methods. Pseudo-spectral methods are accurate but time-consuming, and have difficulty in handling strongly curved or rugged stress-release surfaces although they handle smooth free surfaces reasonably well. Finite-difference methods use fine grids to treat irregular stress-release surfaces and are easily implemented. This work focuses attention on using a staggered finite-difference method. The finite-difference method was chosen because it is simple and the codes are portable. Moreover, this method provides a convenient environment to implement complicated boundary conditions. Based on the variable-order algorithms in finite-difference methods, we extended the existing imaging and variable-order finite-difference algorithms to heterogeneous viscoelastic media with rugged free-surfaces. The implementation of finite-difference algorithms incorporated with curved stress-release boundaries are studied. Under stable conditions with constraints, the proposed method works effectively for modelling wave propagation for 2-D viscoelastic models. With the use of gradually variable orders in space, the unstable problem associated with spatial derivative calculations has not been seen. Results obtained by our algorithms are compared with those using vacuum schemes for representing free surfaces. We also test the viscoelastic model against a perfectly elastic model for high values of quality factor. Our numerical investigations demonstrate that the algorithm is efficient and effective. It can also be extended to 3-D viscoelastic heterogeneous media without problems.