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ABSTRACT The dependence of fluid-saturated rocks' elastic properties to the measuring frequency is related to fluid-flow phenomena at different scales. In the frequency range of [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 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]

2.5D modelling approximates 3D wave propagation in the dip-direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful. We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in-plane and out-of-plane geometrical spreading. We also derive some new inversion/migration results. An AVA-compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common-image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy-flux-normalized plane-wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation. Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in-plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out-of-plane geometrical spreading, necessary for amplitude-preserving computations, for the TI medium is dependent on the same parameters that govern in-plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in-plane kinematics and the scattering coefficients. Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude-preserving migration followed by AVA analysis. SYMBOLS AND NOTATION A list of symbols and notation is given in . [ABSTRACT FROM AUTHOR]