Résumé
ABSTRACT Electrical logs are sensitive to conductive anisotropic structures present in rock formations both at macroscopic scale (such as bedding, faulting and fracturing) and microscopic scale (such as pervasive microcracking) as a consequence of depositional processes and tectonic stresses. Such structures are modelled in this paper by a set of equally spaced conductive features of volume ?f, conductivity contrast to the host rock ? and dip?. The conductivity of the modeled media C(?) is represented in tensor notation and the dip direction ignored due to the cylindrical nature of axi-symetric measurements. The deep lateral resistivity devices CLLd) measure the horizontal resistivity Rh, and shallow sensors (RLLs) the mean resistivity (RhRv)-2. A forward model of lateral device readings in fractured or thinly-bedded rocks is constructed from C(?), then expressed as a function of dip ? and anisotropy coefficient ?. This anisotropy coefficient is a simple function of ?f and ? and thus quantifies the fact that thick-resistive events cannot be discriminated from thin-conductive layers solely from electrical measurements. In active and paleo-compressive environments where subhorizontal conductive structures dominate, RLLs >= RLLd. In the presence of subvertical conductive structures, either due to extension or to a strike-slip regime, RLLs <= RLLd . These results are proven to be valid for any theoretical model, that is any values of (?f. ?), providing that ?f remains small (?f_<=0. 10). In the two extreme cases (0-30 and 60-90ø dips), the conductivity of the host rock is computed directly from in situ data. If the conductivity of the fractures Cf is known from laboratory measurements, the fracture porosity ?f can be computed. In the intermediate domain (from 30ø to 60ø), such derivations are not possible. A series of examples from crystalline and sedimentary environments are used to illustrate this analytical approach which provides results similar to those of previous finite elements models (Sibbit and Faivre, 1985). This approach can be applied to the study of fractured carbonate reservoirs.