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We modeled permeability (k) estimation based on porosity (ϕ), electrical formation factor (F), and nuclear magnetic resonance (NMR) relaxation time (T), using periodic structures of touching and overlapping spheres. The formation factors for these systems were calculated using the theory of bounds of bulk effective conductivity for a two‐component composite. The model allowed variations in grain consolidation (degree of overlap), scaling (grain size), and NMR surface relaxivity. The correlation of the permeability (k) with the predictor a [Formula: see text] was slightly higher than [Formula: see text] (i.e., a correlation coefficient of 0.98 versus 0.95). The exponent b ranged from 1.4 for a pure grain consolidation system to 2 for a pure scaling system. Variations in surface relaxivity are shown to cause significant scatter in the correlations.

The eigenstate analysis of Lanczos, also known as singular value decomposition (SVD), is used to define eight parameters which uniquely describe the magnetotelluric impedance Z. These parameters are independent of a priori assumptions about Z and can be interpreted in terms of three‐dimensional conductivity structures. Through SVD, the impedance is represented by two characteristic states. These states consist of two pairs (E and H) of complex vectors and two corresponding, real, singular values which together describe the extremal properties of Z. The singular values are the maximum and minimum |E|/|H| ratios possible at the observation site and therefore yield the true maximum and minimum apparent resistivities. We use a variation of SVD analysis by incorporating phases in the singular values, which are then called characteristic values. These phases reflect the delay (caused by the earth’s conductivity) of the electric fields relative to their associated magnetic fields. In this analysis of Z, the characteristic values contain four parameters, two singular values and two phases. The characteristic vectors contain the remaining four parameters, two principal axis directions and two ellipticities. The principal axis directions for the E and H vectors need not be at right angles as in biorthogonal analysis. The deviation of these axes from orthogonality is called the “skew angle” S. From a model by Park, we have found S to be closely related to distortions in the telluric current system caused by current gathering due to a good conductor. From the same model, we have found the ellipticity parameters to be the largest in regions of high current distortion and at the shorter periods. Consequently, we speculate that the ellipticity parameters are associated with local induction.

Our analysis of a decade of observations from the Palmdale California telluric array is presented. The array is a system of large‐scale telluric field measurements used for the passive monitoring of electrical conductivity variations over a large region centered over the San Andreas Fault Zone northeast of Los Angeles. Since 1985, systematic changes in the relationships between the telluric field measurements around the array have been observed. These changes amounted to 1% to 2% by the time the array was closed down in 1989, with the fields measured along the fault and northeast of the fault showing signal decreases relative to the fields southwest of the fault. Because of the possible implications of these changes for conductivity variations related to tectonic activity on the San Andreas, we have attempted to sort out the geography of the zones that could cause the changes. The simplest, though nonunique, interpretation of the observed variations in the telluric relationships is a steady increase in the conductivity of the lower crustal region of the fault zone. From two‐dimensional models of the telluric response around the array, we infer that an increase of about 60 milli‐Siemens in the conductance of the lower crustal fault zone could account for the changes seen over the period 1985 to 1989. Assuming changes were in a kilometer‐wide zone and that the lower crustal fluids were very conductive, this could represent a strain of about 0.4 × 10−6. The surface strain would be much smaller and would be lost in surface strain noise. Because of the possibility that fluid pressure changes are involved, these small strains could still be significant for earthquake cycle phenomena. Alternatively the observed changes could have been produced by increases in the conductivity of the upper crust of the Mojave Desert, northeast of the fault, or by decreases in the conductivity of the upper crust in the San Gabriel Mountains southwest of the fault To produce the observed telluric changes, however, the additional conductivity and the associated strain changes would have to be much larger. The strain needed to accommodate the increased conductivity on the Mojave side would have to be of the order of 6 × 10−4, which seems unrealistically high. Smaller strains could account for conductivity changes in the San Gabriel Mountains, but these strains would have to be compressive. Water‐level changes are not considered to be a possible cause of the conductivity changes because the measurement scale is much larger than the typical scale of water level changes, and no seasonally correlated changes in the telluric fields were observed.