Three-dimensional (3 D) magnetotelluric (MT) forward and inverse solutions are reviewed and applied in a resolution study for sub-salt imaging of an important target in marine magnetotellurics for oil prospecting. In the forward problem, finite-difference methods are used to efficiently compute predicted data and cost functional gradients. A fast preconditioner is introduced at low induction numbers to reduce the time required to solve the forward problem. We demonstrate a reduction of up to two orders of magnitude in the number of Krylov sub-space iterations and an order of magnitude reduction in time needed to solve a series of test problems. For the inverse problem, we employ a nonlinear conjugate gradient solution developed on massively parallel computing platforms. Solution stabilization is achieved with Tikhonov regularization. To further improve the image resolution of sub-salt structures, we have also incorporated two additional constraints within the inversion process. The first constraint allows for the preservation of known structural boundaries within the inverted depth sections. This type of constraint is justified for the sub-salt imaging problem because the top of salt is constrained by seismic data. The other constraint employed places variable lower bounds on the electrical conductivity above and below the top of salt. Cross-sections of the inversion results over the center of the salt structures indicate that the 3 D analysis provides somewhat more accurate images compared to faster 2 D analysis, but is computationally much more demanding. On the flanks of the structures, however, 3 D analysis is necessary as 2 D inversion shows image artifacts arising from the 3 D nature of the data. We conclude, however, that 3 D inversion may not be cost effective for the sub-salt imaging problem. Very fine data sampling along multiple profiles employed in the 3 D analysis yielded only a marginal improvement in image resolution compared to 2 D analysis along carefully selected data profiles. The study also indicates that in order to provide resolution that is required to accurately define the base of the salt, additional constraints beyond that employed here, need to be incorporated into the 3 D inversion process.
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