Geometrical structure of shear wave surfaces near singularity directions in anisotropic media

There are three types of surfaces which are used for studying wave propagation in anisotropic media: normal surfaces, slowness surfaces and wave surfaces. Normal surfaces and slowness surfaces have been researched in detail. Wave surfaces are the most complicated and comparatively poorly known compared with the other two. Areas of complicated geometrical structure of the wave surfaces are located in the vicinity of conical acoustic axes. There is an elliptical hole on the quick shear wave surface and complicated folds and cusps on the slow shear wave surface. Decomposition of the slow shear wave surface into smooth sheets is used for the study of its geometrical structure. Complexity of shear wave surfaces can be expressed by the number of waves corresponding to a fixed ray. An original approach to the calculation of wave normals depending on ray direction is presented.     

The magnetotelluric dispersion relations over 2-D structures

The causal properties of the magnetotelluric response, first derived by Weidelt, and Fischer & Schnegg in the 1-D limit, are confirmed numerically in the 2-D limit for the particular structure consisting of two uniform quarter spaces. This finding is of interest from several points of view: (1) the dispersion relations in their 1-D form seem to retain their validity for all 2-D tensor elements, irrespective of any rotation of the coordinate system chosen at the surface; in particular, (2) they appear equally valid for the E- and B-polarization configurations. (3) Whereas the question recently debated in the literature (whether the Earth can always be considered as a linear, passive and causal system) is perhaps not yet entirely resolved, the present empirical demonstration suggests that it may in general be safe to apply the 1-D dispersion relations to structures with 2-D character.     

Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media

An algorithm for the numerical modelling of magnetotelluric fields in 2-D generally anisotropic block structures is presented. Electrical properties of the individual homogeneous blocks are described by an arbitrary symmetric and positive-definite conductivity tensor. The problem leads to a coupled system of partial differential equations for the strike-parallel components of the electromagnetic field. E _x, and H _x These equations are numerically approximated by the finite-difference (FD) method, making use of the integro-interpolation approach. As the magnetic component H _x, is constant in the non-conductive air, only equations for the electric mode are approximated within the air layer. The system of linear difference equations, resulting from the FD approximation, can be arranged in such a way that its matrix is symmetric and band-limited, and can be solved, for not too large models, by Gaussian elimination. The algorithm is applied to model situations which demonstrate some non-trivial phenomena caused by electrical anisotropy. In particular, the effect of 2-D anisotropy on the relation between magnetotelluric impedances and induction arrows is studied in detail.     

The Aegean region: deep structures and seismological properties

3-D P -wave velocity anomaly patterns, the geometry of the Hellenic Wadati-Benioff zone and of the seismically active fracture zones in the overlying continental wedge, and the depth distribution of seismogenic properties (seismic activity, energy and b value) for the Aegean region are examined in this study. The western and eastern parts of the area studied differ significantly in terms of the depth distribution of the considered seismological parameters and the velocity structures. The results indicate different physical conditions in the western and eastern parts of the region in question. Data for the surface heat flow and the evolution of the volcanism in the Aegean region since the early Eocene are employed to interpret the results of the present study. Possible geodynamic processes at the plate boundaries between Africa and Eurasia are discussed.     

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.