Search

ABSTRACT A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In this paper, we focus on media containing aligned compliant pores embedded in an isotropic background matrix. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. Results are also expressed in terms of Thomsen anisotropy parameters. It turns out that the P-wave anisotropy parameter ε tends to zero in the high-frequency limit, whereas the δ parameter remains the only indicator of P-S⊥ anisotropy. The S-wave anisotropy parameter γ is not affected by the presence of fluid and remains the same for all frequency ranges. A new definition for attenuation anisotropy parameters is also proposed to quantify the attenuation anisotropy. In the most important case of liquid saturation, analytical expressions are derived for elastic properties, velocity anisotropy parameters, quality factors, and attenuation anisotropy parameters. A companion paper considers the case of cracks with an ellipsoidal distribution of orientations resulting from the application of anisotropic stress. [ABSTRACT FROM AUTHOR]

ABSTRACT A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media, however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In a companion paper, we focused on media containing aligned compliant pores embedded in an isotropic background matrix. In this paper, we investigate the case for which anisotropy results from the presence of cracks with an ellipsoidal distribution of orientations due to the application of anisotropic stress. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. In the most important case of liquid saturation, analytical expressions are derived for elastic properties and Thomsen anisotropy parameters. The main observations drawn from this model are as follows. Crack closure perpendicular to the applied stress leads to an increase in seismic velocities as a function of stress in the direction of applied stress and a decrease in squirt-flow-induced dispersion and attenuation in this direction. The anisotropy of squirt flow dispersion engenders a decrease in the degree of anisotropy with frequency. The stress-induced anisotropy remains elliptical, even in saturated media, for all frequency ranges. [ABSTRACT FROM AUTHOR]

ABSTRACT We present a generalized effective poroelastic model for periodically layered media in the mesoscopic scale range, which accounts for both Biot's global and interlayer wave-induced fluid flow, as well as for the anisotropy associated with the layering. Correspondingly, it correctly predicts the existence of the fast and slow P-waves as well as quasi and pure S-waves. The proposed analytical model is validated through comparisons of the P-wave and S-wave phase velocity dispersion and attenuation characteristics with those inferred from a one-dimensional numerical solution of Biot's poroelastic equations of motion. We also compare our model with the classical mesoscopic model of White for a range of scenarios. The results demonstrate that accounting for both wave-induced fluid flow mechanisms is essential when Biot's global flow prevails at frequencies that are comparable or smaller with respect to those governing interlayer flow. This is likely to be the case in media of high permeability, such as, for example, unconsolidated sediments, clean sandstones, karstic carbonates, or fractured rocks. Conversely, when interlayer flow occurs at smaller frequencies with respect to Biot's global flow, the predictions of this model are in agreement with White's model, which is based on quasi-static poroelasticity. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper discusses reducing computation costs for traveltime calculations in multi-layered anisotropic models. Fomel and Stovas () suggested a two-ray five-parameter approximation that they named 'generalized' because it reduces to several known three-parameter forms. Model tests, demonstrated by the authors, showed that this generalized approximation provided very high accuracy, implying it can be used in place of the exact moveout function in modelling, migration and traveltime inversion. However, detailed model studies show that for some models, with a high-velocity layer, this approximation leads to significant errors. I develop a new three-ray eight-parameter approximation that provides higher accuracy and can replace the exact traveltime function that requires numerical ray calculations for each receiver. I call it a 'two-interval approximation' because it uses two different equations for two offset intervals. Model tests show that this two-interval approximation can bring much higher accuracy compared to the generalized approximation due to the use of an additional reference ray. The two-interval new approximation can be used instead of exact traveltimes for many practical purposes. [ABSTRACT FROM AUTHOR]

ABSTRACT According to the classical approach to physical interpretation of multiple roots of the Christoffel equation in the theory of elastic wave propagation in anisotropic media, a sum of isonormal plane waves propagating in the direction of acoustic axes can have either arbitrary or circular polarization. The main question posed in this paper is as follows: can one apply conclusions drawn for plane waves to other phenomena, in particular, to waves generated by a point source? The paper proposes a new principle of physical interpretation of degeneracies stating that any assessment of the polarizations (and the group velocities) of waves propagating in anisotropic media is reasonable if there exists an experiment with a point source in which the assessment agrees with the general symmetry of the experiment. From the viewpoint of this interpretation, all degeneracies are considered on the wavefront. The inferences drawn from the performed analysis might appear surprising: in all considered cases of degeneracies (such as conic axes, tangent degeneracy on the symmetry axis of infinite order in transversely isotropic media, intersections of the slowness surfaces), ambiguity in determination of the polarization vectors either does not exist for any experiment or can be removed based on the symmetry of an experiment. A condition for convexity of the slowness surface of the fastest wave is formulated in this context. [ABSTRACT FROM AUTHOR]