No abstract

There are currently three types of algorithms in use for regularized 2-D inversion of magnetotelluric (MT) data. All seek to minimize some functional which penalizes data misfit and model structure. With the most straight‐forward approach (exemplified by OCCAM), the minimization is accomplished using some variant on a linearized Gauss‐Newton approach. A second approach is to use a descent method [e.g., nonlinear conjugate gradients (NLCG)] to avoid the expense of constructing large matrices (e.g., the sensitivity matrix). Finally, approximate methods [e.g., rapid relaxation inversion (RRI)] have been developed which use cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional. Approximate approaches can be very fast, but in practice often fail to converge without significant expert user intervention. On the other hand, the more straightforward methods can be prohibitively expensive to use for even moderate‐size data sets. Here, we present a new and much more efficient variant on the OCCAM scheme. By expressing the solution as a linear combination of rows of the sensitivity matrix smoothed by the model covariance (the “representers”), we transform the linearized inverse problem from the M-dimensional model space to the N-dimensional data space. This method is referred to as DASOCC, the data space OCCAM’s inversion. Since generally N ≪ M, this transformation by itself can result in significant computational saving. More importantly the data space formulation suggests a simple approximate method for constructing the inverse solution. Since MT data are smooth and “redundant,” a subset of the representers is typically sufficient to form the model without significant loss of detail. Computations required for constructing sensitivities and the size of matrices to be inverted can be significantly reduced by this approximation. We refer to this inversion as REBOCC, the reduced basis OCCAM’s inversion. Numerical experiments on synthetic and real data sets with REBOCC, DASOCC, NLCG, RRI, and OCCAM show that REBOCC is faster than both DASOCC and NLCG, which are comparable in speed. All of these methods are significantly faster than OCCAM, but are not competitive with RRI. However, even with a simple synthetic data set, we could not always get RRI to converge to a reasonable solution. The basic idea behind REBOCC should be more broadly applicable, in particular to 3-D MT inversion.

No abstract

Abstract.Magnetotelluric exploration has been used to image along strike variations in the electrical resistivity structure of the San Andreas Fault at Parkfield, California. A low resistivity wedge extending to a depth of sev-

Unconformity-type deposits supply a significant amount of the world's uranium and consist of uranium that is generally codeposited with graphite in a fault zone. The low resistivity of the graphite produces a significant contrast in electrical resistivity, which can be located with electromagnetic ͑EM͒ methods. The Athabasca Basin in Western Canada hosts significant uranium deposits, and exploration in deeper parts of the basin has required the application of new EM methods. This paper presents an evaluation of the audiomagnetotelluric ͑AMT͒ exploration method at the McArthur River mine in the Athabasca Basin. AMT data were collected at 132 stations on a grid, and two-dimensional ͑2D͒ and three-dimensional ͑3D͒ inversions were used to generate resistivity models. These models showed two major results: ͑1͒ a significant conductor coincident with a major basement fault ͑P2͒ and the uranium deposits ͑this conductor begins at the unconformity at a depth of 550 m and extends to a depth of at least three km͒ and ͑2͒ a resistive halo which might be caused by the silicification associated with mineralization. However, synthetic inversions showed that this halo could be an artifact of smoothing function in the inversion scheme. The 2D inversions were validated by synthetic inversions, comparison with the 3D inversion models, and correlation with well-log information. 3D AMT forward modeling showed that strong 3D effects are not present in the AMT impedance data. Induction vectors showed more evidence of complexity, but the inclusion of these data in the inversion improved subsurface resolution.

S U M M A R YTraditional methods for interpretation of magnetotelluric (MT) profile data are based on 2-D inversion, under the assumption that 3-D complications in the data can be treated as 'geological noise'. We show with synthetic models that fitting 3-D data with a 2-D inversion can result in spurious features, especially if transverse electric (TE) data are used. Inversion of a single profile of MT data with a 3-D algorithm results in significantly more realistic images of structure beneath the data profile, and also allows some resolution of nearby off-profile structure. We also consider the importance of including the on-diagonal impedance tensor terms, Z xx and Z yy , in the inversion. In synthetic test cases, fitting these diagonals improves the accuracy of images of off-profile structure, particularly near the edge of a conductive feature.

Three-dimensional inversion of Network-Magnetotelluric (MT) data has been implemented. The program is based on a conventional 3-D MT inversion code (Siripunvaraporn et al., 2004), which is a data space variant of the OCCAM approach. In addition to modifications required for computing Network-MT responses and sensitivities, the program makes use of Massage Passing Interface (MPI) software, with allowing computations for each period to be run on separate CPU nodes. Here, we consider inversion of synthetic data generated from simple models consisting of a 1 -m conductive block buried at varying depths in a 100 -m background. We focus in particular on inversion of long period (320-40,960 seconds) data, because Network-MT data usually have high coherency in these period ranges. Even with only long period data the inversion recovers shallow and deep structures, as long as these are large enough to affect the data significantly. However, resolution of the inversion depends greatly on the geometry of the dipole network, the range of periods used, and the horizontal size of the conductive anomaly.

No abstract