In 2D-multielectrode electrical surveys using the pole-pole array, the distance to 'infinite electrodes' is actually finite. As a matter of fact, the available cable length generally imposes a poor approximation of theoretical location of these electrodes at infinity. This study shows that in most of the cases, the resulting apparent resistivity pseudosection is strongly distorted. Numerical simulation validated by field test also shows that a particular finite array provides results that are as close as possible to the ones of the ideal pole-pole array. This is achieved when two conditions that are weaker than an Ž. infinite location are fulfilled: i the 'infinite electrodes' are placed symmetrically on both sides of the in-line electrodes with Ž. a spread angle of 308 and ii the length of 'infinite lines' is at least 20 times the greatest distance between in-line electrodes. The electrical 2D image obtained with this enhanced array is the least distorted one with respect to the pole-pole image. The apparent resistivities are generally underestimated, but this deviation is almost homogeneous. Though the shift cannot be determined a priori, the interpretation of such an image with direct or inverse software designed for pole-pole data provides an accurate interpretation of the ground geometry.
[1] GPR data simulations require above all an efficient forward modeling algorithm. A Finite Difference Time Domain code is presented with Simplified Unsplit Perfect Matched Layer that leads to insignificant reflections on border with few modifications of the core algorithm. In addition, the Auxiliary Differential Equation method allows GPR simulations including dispersive phenomena that could not be neglected at radar frequencies. The numerical validation is done in a classic way for amplitude/time wave propagation and SUPML, and using the nonconventional Dispersion Analysis technique for physical dispersion behavior. Full 3-D and 2-D forward modeling results are finally presented for lossy, dispersive and random media in GPR conditions.
The Céré-la-Ronde underground gas storage reservoir in the Paris Basin, a test site to study and enhance reservoir seismic monitoring, is a water-bearing sandstone reservoir in a faulted anticline structure. Seismic data acquired so far have generated a qualitative interpretation of the location of the gas bubble by studying fluid saturation (Meunier, 1998). However, between 1994 and 1997, two sonic logs showed subtle differences in V P not explained solely by saturation variations. Changes in pore pressure and stresses also influence reservoir elastic properties. Hence, we used geomechanical modeling to evaluate quantitatively how exploiting the gas reservoir impacts seismic measurements.Our method begins by computing, in a reservoir simulator, pore pressure and saturations. Pore pressure is a key input in the geomechanical modeling that produces mean effective stresses. These and the saturations are used to update seismic velocities in accordance with rock physics theory. In the final step, the introduction of a wavelet allows seismic modeling and the study of seismic attributes.Modeling. The reservoir simulation uses a 3-D finite volume code. The model covers 336 ǂ 228 km 2 . The key level of the reservoir model is split into three reservoir layers. R1 is used for gas storage. R2 and R3 are separated by shaly layers. A 2-D section was extracted from the 3-D model for the geomechanical modeling and overburden and underburden layers were added because the model has to cover the whole geologic column from the surface to a depth of 1500 m ( Figure 1).Geomechanical properties of each layer are extracted from core measurements (when available), sonic logs, or using characteristics of analogs. Initially, vertical stresses are determined by rock densities and horizontal stresses by an estimated stress ratio. The initial pore pressure is constant. The load for the geomechanical modeling is determined from cycling variations of the pore pressure in the reservoir (computed by the reservoir simulation). Our modeling has no lateral displacement at external boundaries. Figure 2 shows the results of the geomechanical modeling (i.e., pore pressure and mean total stresses variations) at well A for different production times. Mean effective stress (σeff) is defined as difference between mean total stress and pressure.Rock physics models are used to evaluate the impact of mean effective stresses on effective bulk modulus. We use contact models based on Hertz-Mindlin contact theory (Mindlin, 1949). In this technique, two identical spherical grains of radius R are deformed by normal and tangential forces. The radius of the contact area is a function of σeff, meaning effective shear and bulk moduli are also linked to mean effective stress. Using both moduli, V P and V S may be computed. Hertz-Mindlin theory assumes that velocity varies with σeff raised to the 1/6 th power. Some laboratory measurements on samples gave a smaller exponent: 0.09 for V P and 0.13 for V S . If the initial velocity (V 0 ) is known, the new velocity (V 1 )...
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