| In my Ph.D. study at the University of Utah, Department of Geology and Geo-physics, directed by Professor Zhdanov, I developed an approximate approach to electromagnetic inverse problem solution based on using a specific class of functions. These functions describe the arbitary geoelectrical boundaries between different conductive structures, as well as the distribution of electrical conductivity by a finite number of free parameters. This approach is called a finite function method.; The traditional approach to inversion is based on the detailed discretization of the subsurface structure into many small cells and on determination of the parameters of each of these cells. The number of the searching parameters in a general case, can reach several thousand and even more. In the case of the finite function method we solve the inverse problem with respect to the relatively small number of free parameters, characterizing the finite functions. However, due to the flexible nature of the finite functions, these few parameters make it possible to describe a very complicated conductivity distribution or geoelectrical boundary.; In my research, I applied this method to the solution of a three dimensional (3-D) electromagnetic (EM) inverse problem with 3-D continuous distribution of anomalous conductivity within geological structures and to the location of sharp geoelectrical boundaries between different conductive structures. Numerical modeling and real data inversion show that this approach produces a powerful tool for the inversion of EM data over 3-D inhomogeneous structures. |
