2-D or 3-D interpretation of conductivity anomalies: example of the Rhine-Graben conductivity anomaly

Summary. Evidence of a conductivity anomaly in the Rhine-Graben was first given about 15 years ago and consequently led to the definition of various models of induction in the region for periods ranging from a few minutes to a few hours. These models reflect two antagonistic ways of explaining the observed anomalous variations of the magnetic field: direct induction in a two-dimensional (2-D) structure or static distortion of telluric currents by the resistive crystalline Vosges (France) and Schwarzwalde (Germany) massifs. We discuss the two approaches using a simple formalism. In particular, we show that the self-induction related to the anomalous currents flowing in the Rhine-Graben is negligible for periods larger than 1000 s, and that, even though the static distortion of telluric currents does account for the observed anomaly, 2-D models can explain some of its features. We also show how the channelled currents are induced in the large sedimentary basins surrounding the area under study.
An experimental verification of this result is given.     

Guided waves in three-dimensional structures

A new formulation for the propagation of surface waves in three-dimensionally varying media is developed in terms of modal interactions. A variety of assumptions can be made about the nature of the modal field: a single set of reference modes, a set of local modes for the structure beneath a point, or a set of local modes for a laterally varying reference structure. Each modal contribution is represented locally as a spectrum of plane waves propagating in different directions in the horizontal plane. The influence of 3-D structure is included by allowing coupling between different modal branches and propagation directions. For anisotropic models, with allowance for attenuation, the treatment leads to a set of coupled 2-D partial differential equations for the weight functions for different modal orders.
The representation of the guided wavefield requires the inclusion of a full set of modes, so that, even for isotropic models, both Love and Rayleigh modes appear as different polarization states of the modal spectrum. The coupling equations describe the interaction between the different polarizations induced by the presence of the 3-D structure.
The level of lateral variation within the 3-D model is not required to be small. Horizontal refraction or reflection of the surface wavefield can be included by allowing for transfer between modes travelling in different directions. Approximate forms of the coupled equation system can be employed when the level of heterogeneity is small, for example the coupling between the fundamental mode and higher modes can often be neglected, or forward propagation can be emphasized by restricting the interaction to a limited band of plane waves covering the expected direction of propagation.     

3-D magnetotelluric inversion and model validation with gravity data for the investigation of flood basalts and associated volcanic rifted margins

20 magnetotelluric (MT) soundings were collected on the Isle of Skye, Scotland to provide a high-resolution three-dimensional (3-D) electrical resistivity model of a volcanic province within the framework of a project jointly interpreting gravity, seismic, geological and MT data. The full 3-D inversion of the MT data jointly interpreted with gravity data reveals upper crustal structure. The main features of the model are interpreted in conjunction with previous geological mapping and borehole data. Our model extends to 13 km depth, several kilometres below the top of the Lewisian basement. The top of the Lewisian basement is at approximately 7–8 km depth and the topography of its surface was controlled by Precambrian rifting, during which a 4.5 km thick sequence of Torridonian sediments was deposited. The Mesozoic sediments above, which can reach up to 2.2 km thick, have small-scale depocentres and are covered by up to 600 m of Tertiary lava flows. The interpretation of the resistivity model shows that 3-D MT inversion is an appropriate tool to image sedimentary structures beneath extrusive basalt units, where conventional seismic reflection methods may fail.