The propagation of shear (S) and compression (P) waves within the Earth represents a critically important phenomenon for geologists. For many years, geologists have developed specialized computational programs to calculate wave propagation within complex geophysical regions. These programs have been instrumental in determining the location and characteristics of natural phenomena (e.g., earthquakes) and manmade activity (e.g., nuclear-blast tests).
Since these waves typically travel long distances prior to detection, these programs typically require large computational models and significant computational resources. Newer applications for this technology include border security and exploration for natural resources. The length scales of these applications are much smaller than for typical applications. Thus, the P and S waves decay less than in applications with longer length scales, and therefore cannot be ignored. As these industries apply existing technology to meet today's challenges, they are finding that new methods of solving these problems have significant advantages over traditional methods.
New methods are being developed by ACES to provide practical solutions to geophysical wave propagation problems of interest to the Department of Homeland Security, the Department of Defense, and the energy industry. These industries, as well as many others, are being served by the application of the advanced computational methods in COMSOL Multiphysics. These analyses reduce the need for large computational resources and permit geologists to conduct in-field calculations.
The example in the figure shows the velocity distribution in a half-space subjected to a dynamic excitation near the Earth's surface. The Cartesian plots show the surface and subsurface response. For the simplified case of a homogeneous half-space, engineers implemented closed-form solutions for a wide range of loadings against which to compare the computational results. The forcing functions analyzed in this work represent impact loadings with duration of 10 ms. Thus, element size and time step are important model parameters for the accurate calculation of the displacement and velocity associated with the excitation.
During these developments ACES has shown that COMSOL Multiphysics provides results that accurately represent closed-form and experimental data.
This work was performed by Dr. S.P. Yushanov, Dr. J.S. Crompton, and Dr. K.C. Koppenhoefer of ACES using COMSOL software. For more information, visit here.