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In order to handle the distortion of large-scale induced electric currents by local conductivity anomalies, the problem of electromagnetic induction in non-uniform thin sheets has been reformulated in terms of an integral equation over the anomalous domain. This formulation considers in the layered substratum in addition to toroidal currents also the poloidal current mode (vertical current loops), at the expense that two scalar functions have to be determined. Simple formulas for the required kernels are derived.The algorithm is applied to model the gross features of the northern Pyrenean induction anomaly. It is suggested that this pronounced anomaly results from a conductive channel between the Atlantic Ocean and the Mediterranean Sea.

S U M M A R YEstimates of thermal conductivity of the main non-clay and clay sedimentary minerals are presented, especially for the case of argillaceous ones. These estimates are averaged estimates based on the interpretation of laboratory conductivity, porosity and mineralogy measurements performed on small volumes (of the order of 100cm3) of water-saturated, moist and air-saturated samples. The sampling is representative of the main sedimentary rocks (sandstones, carbonates, evaporites and shales), and it is composed of samples considered as structurally isotropic material.First, we experimentally verify the first-order control of mineralogy, porosity and fluid content on bulk conductivity, and we demonstrate that such influences may be predicted accurately using a geometric mean model, as long as isotropic samples are used. Then we interpret the data using an inverse method, in order to estimate the average mineral conductivities of the main non-clay and clay minerals which give the best fit to the individual laboratory measurements through the geometric mean model.The analysis is based on measurements on 82 non-clay samples and 29 clay samples taken on oil-well cores or cuttings, on outcrops and on artificially recompacted samples. Estimates of average mineral conductivities returned by the inversion process, for the main non-clay minerals, are similar to generally admitted values: 7.7 W m-' K-' for quartz, 3.3 W m-I K-' for calcite, 5.3 W m-l K-' for dolomite and 6.3 W m-' K-' for anhydrite. Values obtained for the clay minerals are systematically lower than those obtained for non-clay ones, they are of the order of 1.9 W m-' K-' for illite and smectite, 2.6 W m-' K-' for kaolinite and 3.3 W m-l K-' for chlorite.These estimates, combined with porosity and mineralogy data, are used with the geometric mean model in order to verify its first-order validity for predicting thermal conductivity of small volumes of porous isotropic sedimentary rocks. The bulk conductivity is predicted with an accuracy of the order of f 1 0 per cent for moist or water-saturated samples, and of the order of f 2 0 per cent for air-saturated samples.