Rayleigh wave synthetic seismograms from multi-dimensional simulations of underground explosions

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Abstract
A general method is presented for coupling the near-source wave fields, obtained from time-stepping numerical calculations, with analytically formulated methods for continuing the wave field to larger ranges. The source calculation may include a free surface and other material boundaries as well as arbitrary material behavior, as long as it is carried into a region where the material response is linearly elastic. The method, which is based on an elastodynamic representation theorem, is worked out in detail for the Rayleigh wave modes for an axisymmetric source in a plane-layered earth model and is demonstrated by a sample calculation for which the exact solution is known. Two realistic, axisymmetric simulations of nuclear explosions (20 and 150 kt at 1-km depth) are studied to estimate the effect of nonlinear interactions with the free surface on the far-field Rayleigh waves. The importance of these two-dimensional phenomena is quantified by comparing far-field Rayleigh waves computed from these simulations with Rayleigh waves computed from analogous one-dimensional (spherically symmetric) simulations. While the two-dimensional simulations exhibit substantial spallation associated with the free surface, the predicted effect on the Rayleigh wave peak amplitudes is negligible. Two-dimensional effects also alter the waveform very little, apart from some enhancement of very short-period components for the larger explosion.

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