Simulation of Seismic Wave Propagation in Complex Media

Significant Achievements, Anticipated Outcomes and Future Work

The interaction of small-scale heterogeneities with seismic waves makes various characteristic imprints on time records associated with wave scattering. The strength of scattering depends on the scale of the heterogeneities and the level of perturbation of the media. Scattering causes attenuation of energy in the primary waves and the development of coda waves following the primary waves. The rate of attenuation due to scattering and the properties of the envelopes of coda waves can be used to investigate the physical properties of the medium. In particular, comparison of scattering attenuation ratios for P and S waves allows an independent comparison with field observations. The temporal attenuation rates of coda waves are highly dependent on the strength of the density perturbation, and thus perturbations of wavespeeds and density need to be considered in the assessment of small-scale heterogeneities in the Earth's deep interior. An alternative representation of random heterogeneities in the earth, media is provided by randomly distributed discrete heterogeneities. The scattering properties in such media are quite different from those in stochastic random media with gradual fluctuation of perturbation. Backscattered waves are more important in media with discrete obstacles due to the high impedance contrast across the boundaries of the heterogeneities, and thus the amplitudes of transmitted coda waves do not increase as much as that of the primary waves decrease. This needs to be taken into account for the investigation of heterogeneities with high impedance contrast in the earth (e.g., magma dike, plume, partial melting) should be considered in such context. Future work on scattering is intended to include comparison of field data and numerical results.

In November 2003, the program package SPECFEM3D was ported from the Department of Geology and Planetary Sciences, Caltech. This package is for the creation of synthetic seismograms, based on a 3-D velocity model, over either the full globe or a region of the globe. The package can also be used to investigate the model and manipulate the resulting seismograms. The objective is to use this program package, after sufficient testing, to provide theoretical 'data' for know models to test the efficacy of existing algorithms for analysis. In the long term we are interested in finding ways to exploit the capacity to generate seismograms for 3-D models to examine direct comparison techniques for computed and observed seismograms. So far the program port has been completed and with help from APAC National Facility staff we have got it up and running on the LC cluster for the most basic region model and parameters. Currently we are investigating transferring it to the AlphaServer SC and how changing the parameters in the program affects its running on the LC. For the basic parameters we are also beginning to build a library of synthetic seismograms for different events and test models.

Computational Techniques Used

A wavelet-based method is implemented for modelling of wave propagation in random media. The wavelet-based method considers the spatial differentiation of displacement and velocity fields of wave equations in subsequent wavelet spaces. The consideration of operators allows a computation with high accuracy since the performance of the operators is well represented by subsequent wavelet operators. Using a displacement-velocity formulation and a semigroup approach for first-order differential equation system, the wave equations can be written in a form of discrete time solution. The wavelet-based method is stable even modelling in highly perturbed media, and good for investigation of scattering of waves in random media.

The Spectral element program uses a specialized form of finite-element scheme designed explicitly to work for spherical problems. A mapping of the sphere via 6 cubes is linked to a central cube to represent the properties of the inner core and avoid singularities. Mesh doubling occurs in depth to minimise the number of elements employed. Within each element a 5 order poloynomial is used in each coordinate with sampling through a Gauss-Lobatto scheme so the resulting mass matrix in the finite element scheme is diagonal. The oceans are included by loading terms to avoid the problems of zero shear modulus in the fluid.

Publications, Awards and External Funding

External Funding and Awards

ARC grant DP0342618 supports the collection of seismic field data used in comparisons with the numerical calculations.

Publications

T.-K. Hong, B.L.N. Kennett, Scattering attenuation of 2D elastic waves: theory and numerical modeling using a wavelet-based method, Bull. Seism. Soc. Am., 93, 2003, 922-938.
T.-K. Hong, B.L.N. Kennett, Modelling of seismic waves in heterogeneous media using a wavelet-based method: application to fault and subduction zones, Geophys. J. Int., 154, 2003, 483-498.