Electrical anisotropy and conductivity distribution functions of fractal random networks and of the crust: the scale effect of connectivity

All explanations of the high-conductivity layers (HCL) found by magnetotellurics in the middle or lower crust incorporate a mixture of a low-conductivity rock matrix and a highly conductive phase, for example graphite or saline fluids. In most cases the bulk conductivity of the mixture does not depend on the conductivity of the rock matrix but rather (1) on the amount of high-conductivity material and, in particular, (2) on its geometry. The latter is quantitatively described by the parameter 'electrical connectivity'. Decomposition of the observed bulk conductivity of the mixture into these two parameters results in an ill-posed problem. Even if anisotropy occurs in the HCL, three output parameters (highly conductive phase fraction, connectivity with respect to the X direction, connectivity with respect to the Y direction) have to be estimated from the two bulk conductivities of the anisotropic HCL. The additional information required for solving this problem is provided if instead of single-site data the conductivities from many field sites are evaluated: a sample distribution of the conductivity can then be obtained. Ensembles of random networks are used to create theoretical distribution functions which match the empirical distribution functions to some extent. The use of random resistor networks is discussed in the context of other established techniques for the treatment of two-phase systems, such as percolation theory and the renormalization group approach. Models of embedded networks explain the discrepancy between 'small' anisotropy (2-3) on the laboratory scale and large anisotropy (10-100) found in electromagnetic field surveys encompassing volumes of several cubic kilometres. Strong anisotropy can indicate low electrical connectivity, and a possible explanation is that a network stays close to the percolation threshold.     

Shear-wave polarization anisotropy in the Pacific Basin

Summary. Inversion of 295. Love- and Rayleigh-wave phase travel times across the Pacific Basin has yielded a structure which has a channel that is anisotropic with respect to the polarization of shear waves. The velocity of SH waves is approximately 4.24 km/s, and the velocity of SV waves is approximately 4.10 km/s in the low-velocity channel. The lid to the channel is isotropic with respect to the polarization of S waves and the velocity is approximately 4.60 km/s. The lid to the low-velocity channel increases in thickness with lithospheric age at the expense of the channel, and its thickness is apparently still increasing at a sea-floor age of 150 Myr.
These results can be explained in terms of a model with both randomly-and preferentially-oriented, liquid-filled cracks in the channel. In the model, it is assumed that the liquid-filled cracks are due to partial melting in the channel, and that any preferred orientation is caused by a shear-flow gradient resulting from differential motion between the lid and the deeper parts of the mantle.