Image focusing and data compression in the solution of geophysical inverse problems

One of the critical problems in the inversion of geophysical data is developing a stable solution which at the same time can resolve complicated geological structures. The traditional way to obtain a stable solution is based on the criterion of maximum smoothness. This approach, however, provides smoothed "unfocused" images of real geological structures. In this dissertation we develop a new technique to solve this problem, which we call focusing of inversion images. It is based on specially selected stabilizing functionals which minimize the area where strong model parameter variations and discontinuity occur. We demonstrate that focusing inversion generates more focused and clearer images for geological structures than regularization based on conventional maximum smoothness or total variation (TV) functionals.;Numerical solution of 3-D (three-dimensional) inverse problems also requires fast computer speed and large memory resources. We present a new technique for inverse problem solution which reduces computing power requirements by orders of magnitude. This technique is based on the idea of data compression, which is widely used in the telecommunications industry to reduce the amount of transmitted data. We use compression with an interpolation pyramid in the inverse problem solution. This method produces up to 30-fold reduction in memory and execution time in the solution of a typical 3-D geophysical inverse problem.;We develop numerical algorithms and computer codes to apply image focusing and compression to interpretation of 3-D gravity and 3-D electromagnetic (EM) data. Our discussion is illustrated with comprehensive numerical examples and 3-D inversion of real gravity and EM data.