There are many occasions on which the magnetotelluric impedance tensor is affected by local galvanic distortion (channelling) of electric currents arising from induction in a conductive structure which is approximately two‐dimensional (2‐D) on a regional scale. Even though the inductive behavior is 2‐D, the resulting impedance tensor can be shown to have three‐dimensional (3‐D) behavior. Conventional procedures for rotating the impedance tensor such as minimizing the mean square modulus of the diagonal elements do not in general recover the principal axes of induction and thus do not recover the correct principal impedances but rather linear combinations of them. This paper presents a decomposition of the impedance tensor which separates the effects of 3‐D channeling from those of 2‐D induction. Where the impedance tensor is actually the result of regional 1‐D or 2‐D induction coupled with local frequency independent telluric distortion, the method correctly recovers the principal axes of induction and, except for a static shift (multiplication by a frequency independent real constant), the two principal impedances. Also obtained are two parameters (twist and shear), which partially describe the effects of telluric distortion. It is shown that the tensor operator which describes the telluric distortions can always be factored into the product of three tensor sub‐operators (twist, shear, local anisotropy) and a scalar. This product factorization allows assimilation of local anisotropy, if present, into the regional anisotropy. The method of decomposition is given in the paper along with a discussion of the improvements obtained over the conventional method and an example with real data.

An outcropping hemispherical inhomogeneity embedded in a two‐dimensional (2-D) earth is used to model the effects of three‐dimensional (3-D) near‐surface electromagnetic (EM) “static” distortion. Analytical solutions are first derived for the galvanic electric and magnetic scattering operators of the heterogeneity. To represent the local distortion by 3-D structures of fields which were produced by a large‐scale 2-D structure, these 3-D scattering operators are applied to 2-D electric and magnetic fields derived by numerical modeling to synthesize an MT data set. Synthetic noise is also included in the data. These synthetic data are used to study the parameters recovered by several published methods for decomposing or parameterizing the measured MT impedance tensor. The stability of these parameters in the presence of noise is also examined. The parameterizations studied include the conventional 2-D parameterization (Swift, 1967), Eggers’s (1982) and Spitz’s (1985) eigenstate formulations, LaTorraca et al.’s (1986) SVD decomposition, and the Groom and Bailey (1989) method designed specifically for 3-D galvanic electric scattering. The relationships between the impedance or eigenvalue estimates of each method and the true regional impedances are examined, as are the azimuthal (e.g., regional 2-D strike, eigenvector orientation and local strike) and ellipticity parameters. The 3-D structure causes the conventional 2-D estimates of impedances to be site‐dependent mixtures of the regional impedance responses, with the strike estimate being strongly determined by the orientation of the local current. For strong 3-D electric scattering, the local current polarization azimuth is mainly determined by the local 3-D scattering rather than the regional currents. There are strong similarities among the 2-D rotation estimates of impedance and the eigenvalue estimates of impedance both by Eggers’s and Spitz’s first parameterization as well as the characteristic values of LaTorraca et al. There are striking similarities among the conventional estimate of strike, the orientations given by the Eggers’s, Spitz’s (Q), and LaTorraca et al.’s decompositions, as well as the estimate of local current polarization azimuth given by Groom and Bailey. It was found that one of the ellipticities of Eggers, LaTorraca et al., and Spitz is identically zero for all sites and all periods, indicating that one eigenvalue or characteristic value is linearly polarized. There is strong evidence that this eigenvalue is related to the local current. For these three methods, the other ellipticity differs from zero only when there are significant differences in the phases of the regional 2-D impedances (i.e., strong 2-D inductive effects), implying the second ellipticity indicates a multidimensional inductive response. Spitz’s second parameterization (U), and the Groom and Bailey decomposition, were able to recover information regarding the actual regional 2-D strike and the separate character of the 2-D regional impedances. Unconstrained, both methods can suffer from noise in their ability to resolve structural information especially when the current distortion causes the impedance tensor to be approximately singular. The method of Groom and Bailey, designed specifically for quantifying the fit of the measured tensors to the physics of the parameterization, constraining a model, and resolving parameters, can recover much of the information in the two regional impedances and some information about the local structure.

[1] GRACE satellite gravity data is used to estimate terrestrial (surface plus ground) water storage within the Congo Basin in Africa for the period of April, 2002 -May, 2006. These estimates exhibit significant seasonal (30 ± 6 mm of equivalent water thickness) and long-term trends, the latter yielding a total loss of $280 km 3 of water over the 50-month span of data. We also combine GRACE and precipitation data sets (CMAP, TRMM) to explore the relative contributions of the source term to the seasonal hydrological balance within the Congo Basin. We find that the seasonal water storage tends to saturate for anomalies greater than 30-40 mm of equivalent water thickness. Furthermore, precipitation contributed roughly three times the peak water storage after anomalously rainy seasons, in early 2003 and 2005, implying a $60-70% loss from runoff and evapotranspiration. Finally, a comparison of residual land water storage (monthly estimates minus best-fitting trends) in the Congo and Amazon Basins shows an anticorrelation, in agreement with the ''see-saw'' variability inferred by others from runoff data.

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Many tomographic interpretations of crosshole seismic traveltimes have approximated the raypaths with straight lines connecting the source and receiver. This approximation is valid where the velocity does not vary greatly, but in many regions of interest velocity variations of 10–20 percent or more are observed, causing significant ray curvature. Other work has taken this nonlinear effect into account, but there do not appear to be many cases of demonstrated success in its application to the crosshole seismic problem. We present here an iterative inversion scheme based on two‐dimensional ray tracing and its successful application to field data. The interpretation method iteratively ray traces and then updates the velocity model. Within each iteration, the differences between the data and the current model traveltimes obtained by ray tracing are related to the unknown velocity perturbations through a system of linear equations. A damped least‐squares method solves for the velocity perturbations which update the model. The iterations continue until the synthetic traveltimes fit the data to within the data error or until no improvement in the fit of the traveltimes is observed. The method is demonstrated on a small synthetic data set, where convergence to the correct solution is achieved in a few iterations. The method is then applied to field data from a crosshole experiment in crystalline rock. The frequency range of the seismograms is 1 to 6.6 kHz, allowing resolution of velocity structure on a scale of several meters. The resulting velocity image shows good agreement with other geologic and geophysical data. Synthetic Maslov seismograms calculated for the derived velocity model agree well with the waveform data, providing an independent test of the validity of the inversion method.