Search

Several studies have shown that global 3D models of the compression wave speed in the Earth's mantle can provide superior first P travel time predictions at both regional and teleseismic distances. However, given the variable data quality and uneven data sampling associated with this type of model, it is essential that there be a means to calculate high-quality estimates of the path-dependent variance and covariance associated with the predicted travel times of ray paths through the model. In this paper, we show a methodology for accomplishing this by exploiting the full model covariance matrix. Typical global 3D models have on the order of 1/2 million nodes, so the challenge in calculating the covariance matrix is formidable: 0.9 TB storage for 1/2 of a symmetric matrix, necessitating an Out-Of-Core (OOC) blocked matrix solution technique. With our approach the tomography matrix (G which includes Tikhonov regularization terms) is multiplied by its transpose (GTG) and written in a blocked sub-matrix fashion. We employ a distributed parallel solution paradigm that solves for (GTG)-1 by assigning blocks to individual processing nodes for matrix decomposition update and scaling operations. We first find the Cholesky decomposition of GTG which is subsequently inverted. Next, we employ OOC matrix multiplication methods to calculate the model covariance matrix from (GTG)-1 and an assumed data covariance matrix. Given the model covariance matrix we solve for the travel-time covariance associated with arbitrary ray-paths by integrating the model covariance along both ray paths. Setting the paths equal yields the variance for that path., Published in the Proceedings of the 2011 Monitoring Research Review - Ground-Based Nuclear Explosion Monitoring Technologies, 13-15 September 2011, Tucson, AZ. Volume I. Sponsored by the Air Force Research Laboratory (AFRL) and the National Nuclear Security Administration (NNSA). U.S. Government or Federal Rights License

MAGI, a three-dimensional shock and material response code which is based on Smoothed Particle Hydrodynamics is described. Calculations are presented and compared with experimental results. The SPH method is unique in that it employs no spatial mesh. The absence of a grid leads to some nice features such as the ability to handle large distortions in a pure Lagrangian frame and a natural treatment of voids. Both of these features are important in the tracking of debris clouds produced by hypervelocity impact, a difficult problem for which Smoothed Particle Hydrodynamics seems ideally suited. It is believed this is the first application of SPH to the dynamics of elastic-plastic solid., Prepared in collaboration with New Mexico Institute of Mining and Technology, Center for Explosives Technology Research, Socorro, NM and Advanced Sciences, Inc, Albuquerque, NM.