Wave Propagation from Complex 3d Sources Using the Representation Theorem

In spite of extensive prior research on generation of seismic waves by underground nuclear explosions, it is still not possible to provide a complete explanation for the observed wavefields, particularly at regional distances. Spherically symmetric explosion models embedded in layered elastic media effectively model the P phases generated by explosions, and the major characteristics of some reflected and transmitted phases. Nonlinear Saxisymmetric finite difference calculations of explosions including gravity and the effect of the free surface can n model a more realistic explosion source that directly generates shear waves. These models explain more (~\ characteristics of explosion-generated seismic waves, including some aspects of regional shear phases. However, it f •» is clear that linear and nonlinear near-source 3D effects are important in many cases. SH waves are commonly observed within a few km of explosions, too close to have been generated by (simple) conversion of vertical and (_} radial components, and often larger than those components. Furthermore, it has not been established what impact 3D effects have on discriminants and on explosion yield estimates. It is important, therefore, to be able to model and understand how 3D source and source region heterogeneity affect the seismic wavefield, and what impact this has on parameters used for nuclear monitoring. We are in the second year of a project to develop and test a three-dimensional nonlinear finite element code CRAM3D, which will be used to calculate nonlinear explosion sources that have both 3D source geometry and may occur in a 3D heterogeneous medium. The code includes the same well-tested material models that have been used in earlier axisymmetric calculations. In addition, we are developing algorithms based on the representation theorem to propagate the motion from these source region calculations to any desired distance. We have implemented a technique that allows us to propagate the results of near source 3D finite element calculations to regional and teleseismic distances. The Green's function and its derivatives are used in conjunction with the numerical solutions on a monitoring surface enclosing the complex source region. Full-waveform solutions at distance, due to complex explosion sources, are computed with the full-waveform Green's function using wavenumber integration; surface wave solutions are computed with the surface wave Green's functions using mode summation; and far field body wave solutions are computed with the outgoing waves from the source region. The excellent agreement in the surface wave portion between the full-wave solutions and surface-wave solutions demonstrates the accuracy of the implementation of the representation theorem and the respective Green's functions and their derivatives. To test the code, we have performed calculations using cavities of three shapes: spherical, rectangular and elliptical, each with the same volume. An explosion with the same yield was detonated inside each cavity. We compare the solutions from these three cavity explosions in the near field and at distance. Gravity is included in the calculations, and we start with an equilibrium solution obtained by running the finite-element CRAM3D with overburden pressure only, prior to the start of the explosion calculation. Nonlinear deformation is seen around the cavity. The results show very good agreement between 2D and 3D solutions at distance for the spherical cavity explosion. Nonspherical wave components from nonspherical rectangular and elliptical cavities are clearly seen in the near field. The rectangular cavity shows more pronounced tangential motion than the elliptical cavity away from axes of symmetry. Q