HR: 0800h
AN: GP41B-0872    [Abstracts]
TI: Adaptive Finite Element Modeling Using Unstructured Grids: the 2D Magnetotelluric Example
AU: * Key, K W
EM: kkey@ucsd.edu
AF: Scripps Institution of Oceanography, University of California San Diego 9500 Gilman Drive, La Jolla, CA 92093-0225 United States
AU: Weiss, C J
EM: cjweiss@snadia.gov
AF: Sandia National Laboratories, PO Box 5800 MS-0750, Albuquerque, NM 87185 United States
AB: Existing numerical modeling techniques commonly employed for electromagnetic exploration are bound by the inherent limitations of approximating complex structures using a rectangular grid. A more flexible tool is the adaptive finite element method using unstructured grids. Composed of irregular triangular finite elements, an unstructured grid can readily conform to complicated structural boundaries. In order to ensure the numerical accuracy of the unstructured grid, adaptive refinement using an an posteriori error estimator is used to iteratively refine the grid in regions where solution accuracy is insufficient. Two recently developed asymptotically exact a posteriori error estimators are based on a superconvergent gradient recovery operator. The first relies solely on the normed difference between the recovered gradients and the piecewise constant finite element gradients, and is effective for lowering the global error in the finite element solution. However, it is often the case that an accurate solution is required at only a few discrete regions within the model. Under such circumstances, a more efficient refinement scheme considers the local influence of errors from coarse elements elsewhere in the grid. The second error estimator accomplishes this by using weights determined from the solution to an appropriate dual problem to modify the first error indicator. Application of these methods for two-dimensional magnetotelluric (MT) modeling reveal, as expected, that the dual weighted error indicator is far more efficient in achieving accurate MT responses. Refining about 15% of elements per iteration gives the fastest convergence rate. For a given refined grid, the solution error at higher frequencies varies in proportion to the skin depth, requiring refinement about every two decades of frequency. The transverse electric and transverse magnetic modes exhibit different field behavior and refinement should consider the effects of both. An example resistivity model of seafloor bathymetry underlain by complex salt intrusions and dipping and faulted sedimentary layers illustrates the benefits of this new technique.
DE: 0545 Modeling (4255)
DE: 0925 Magnetic and electrical methods (5109)
DE: 3914 Electrical properties
SC: Geomagnetism and Paleomagnetism [GP]
MN: Fall Meeting 2005