Anisotropic parameters of dry and saturated sand under stress

Abstract

Fluid substitution has wide applicability in seismic, such as in 4D and amplitude variation with offset analysis. Traditionally, the isotropic Gassmann equation has been used for this purpose; however, in many cases, anisotropic fluid substitution may be more relevant. Recent theoretical developments by Collet and Gurevich and by Thomsen based on the anisotropic Gassmann equation have pointed in particular to the fluid sensitivity of Thomsen’s anisotropy parameters. We have verified these theoretical predictions on a simple granular medium in controlled experiments in which anisotropy was induced largely by the applied stress. For this purpose, unconsolidated dry and saturated sands were loaded in uniaxial strain as well as hydrostatically, in dry and in brine-saturated conditions. Stresses were between 1 and 15 MPa. Multidirectional P- and S-wave velocities were measured by ultrasonic pulse propagation. Our experiments indicated that the P-wave anisotropy parameter [Formula: see text] and the moveout parameter [Formula: see text] decrease in magnitude upon fluid saturation. Saturated samples reveal close to elliptical anisotropy, and for the dry and the saturated case, the ellipticity remains constant during uniaxial strain experiments. These experimental observations fit the theoretical predictions within the uncertainty of the experiments. Surprisingly, the S-wave anisotropy parameter [Formula: see text] is also found to be sensitive to fluid saturation and increases upon fluid saturation. It is also seen that fluid substitution applying the isotropic Gassmann equation underestimates the saturated P-wave modulus in most cases, and that use of the anisotropic Gassmann equation does not lead to significant improvements. These observations may be explained, at least qualitatively, by correcting for anisotropic dispersion caused by Biot’s global flow mechanism.