HR: 16:00h
AN: S42J-01    [PDF]
TI: Waves on a Spherical Membrane
AU: * Tape, C H
EM: carl.tape@earth.ox.ac.uk
AF: Oxford University, Dept. of Earth Sciences Parks Road, Oxford, OX1 3PR United Kingdom
AU: Woodhouse, J H
EM: john@earth.ox.ac.uk
AF: Oxford University, Dept. of Earth Sciences Parks Road, Oxford, OX1 3PR United Kingdom
AB: The purpose of this study is to develop a numerical model for wave propagation on a spherical membrane and to compare the results with predictions made from ray theory. Such membrane waves are an analogue for seismic surface waves. The two-dimensional wave equation on a sphere is solved using a finite-difference method on a spherical grid of several thousand hexagonal faces. The spherical grid is first tested using a homogeneous phase velocity field with an initial Gaussian source. The resulting numerical solutions, $u(\theta, \phi, t)$, agree with analytical solutions for the homogeneous case. Next a heterogeneous phase velocity field, $c(\theta, \phi)$, is used; the solutions reveal the variation in amplitude and phase due to the lateral heterogeneity. Surface wave ray-tracing equations are then used to calculate the amplitude and phase anomalies for a set of source-receiver pairs. Exact ray theory calculates these values along the actual ray path, which may deviate considerably from the great-circle path between the source and receiver, which is the basis for the linearized ray theory calculations. We find that multipathing --- multiple ray paths between a source and receiver --- is quite common for the current resolution of long-period surface wave phase velocity maps, and it gives an indication of the divergence of linearized ray theory from exact ray theory. Using the results from the numerical model, we are able to examine the regimes under which ray theory predictions are invalid, and we discuss the results in terms of the ray theory validity condition, $\lambda \ll \Lambda$, where $\lambda$ is the wavelength of the waves in the numerical model and $\Lambda$ is the minimum scalelength of heterogeneity in the phase velocity map. We show that exact ray theory is better than linearized ray theory at predicting both phase and amplitude anomalies. We find that ray theory predictions of phase are quite stable. Predictions of amplitude, however, are valid only when the validity condition is well-satisfied.
DE: 7218 Lithosphere and upper mantle
DE: 7255 Surface waves and free oscillations
DE: 7260 Theory and modeling
SC: Seismology [S]
MN: 2003 Fall Meeting