The relations among the resistivity, elastic-wave velocity, porosity, and permeability in Fontainebleau sandstone samples from the Ile de France region, around Paris, France were experimentally revisited. These samples followed a permeability-porosity relation given by Kozeny-Carman’s equation. For the resistivity measurements, the samples were partially saturated with brine. Archie’s equation was used to estimate resistivity at 100% water saturation, assuming a saturation exponent, [Formula: see text]. Using self-consistent (SC) approximations modeling with grain aspect ratio 1, and pore aspect ratio between 0.02 and 0.10, the experimental data fall into this theoretical range. The SC curve with the pore aspect ratio 0.05 appears to be close to the values measured in the entire porosity range. The elastic-wave velocity was mea-sured on these dry samples for confining pressure between 0 and [Formula: see text]. A loading and unloading cycle was used and did not produce any significant hysteresis in the velocity-pressure behavior. For the velocity data, using the SC model with a grain aspect ratio 1 and pore aspect ratios 0.2, 0.1, and 0.05 fit the data at [Formula: see text]; pore aspect ratios ranging between 0.1, 0.05, and 0.02 were a better fit for the data at [Formula: see text]. Both velocity and resistivity in clean sandstones can be modeled using the SC approximation. In addition, a linear fit was found between the P-wave velocity and the decimal logarithm of the normalized resistivity, with deviations that correlate with differences in permeability. Combining the stiff sand model and Archie for cementation exponents between 1.6 and 2.1, resistivity was modeled as a function of P-wave velocity for these clean sandstones.

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We analyze the sensitivity of seismic reflectivity to contrasts in density, seismic propagation velocities, Poisson’s ratio, and gas saturation using the complete Zoeppritz equations. Sensitivities of reflection coefficients to each bulk elastic parameter are computed as the partial derivatives of the seismic reflectivities, relative to each parameter. The sensitivity of reflectivity to gas saturation is then calculated as the full derivative of the reflectivities with respect to gas saturation, assuming both a homogeneous and a patchy distribution of gas in the pore fluids. We compute sensitivities for a sealing shale/gas-sand interface and a gas-sand/wet-sand (gas-water contact, GWC) interface. For the SH-SH reflectivity, the effect of density contrast is strongest in the 30°–50° range of incidence angles for the fluid-fluid interface and at nearer offsets for the shale/gas-sand interface. P-SV reflectivity forthe fluid-fluid interfaces is more sensitive to density contrast in the range of angles of incidence from 30° to 60°. The overall response of P-SV reflectivity to gas saturation throughout all offsets is dominated by the Poisson’s ratio of the gas sand. In the case of P-P reflectivity, the sensitivity to gas saturation increases with increasing incidence angles. The sensitivity of P-SV reflectivity to gas saturation tends to be greatest in the 20°–40° range of incidence angles. For SH-SH reflectivity, the sensitivity to gas saturation for most offsets is controlled mainly by the density contrast, and the sensitivity to density decreases with increasing offset. There is still not a generally accepted seismic reflection method to discriminate commercial gas concentrations from low gas saturation. From the sensitivity analysis, we conclude that the use of P-SV or SH-SH amplitude variation with offset (AVO), integrated with the P-P AVO, will be an essential element in understanding this problem fully.

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This paper describes joint effective-medium modeling of elastic and resistivity laboratory data obtained on a set of outcrop carbonate samples from the Apulia Platform in Italy. The challenge is to model both the elastic-wave velocity and resistivity using a single theoretical approach. The candidate models are (a) the differential effectivemedium (DEM) theory and (b) the self-consistent approximation (SC). DEM may accurately describe the elastic properties but fails to describe resistivity, because it explicitly assumes that the pores are inclusions in the mineral matrix and thus lack adequate connectivity. On the other hand, SC treats both the pores and the matrix as inclusions, thus implicitly providing the connectivity needed to match the measured resistivity. At the same time, SC makes it possible to match both the elastic data and the measured resistivity using one set of model parameters.We show that SC, where the rock components are assumed conceptually symmetric, is a robust approach to modeling both velocity and resistivity in our carbonate rock samples, particularly when using needle-like pores, which tend to be stiff but well connected.

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