Small‐angle AVO response of PS‐waves in tilted TI media

Abstract

Field records for small source-receiver offsets often contain intensive converted PS-waves that cannot be generated in laterally homogeneous isotropic models. Among the most likely physical reasons for this converted energy is the presence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted PS 1-and PS 2-waves (R P S1 and R P S2) for a horizontal interface separating two transversely isotropic media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients R P S1 (0) and R P S2 (0) vanish when both halfspaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values close to 0.1, even if the strength of anisotropy is moderate. To study the influence of the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropy approximations for the reflection coefficients and compare them with exact numerical results. In particular, the analytic solutions show that the contributions of the Thomsen parameters and δ to the coefficients R P S1 (0) and R P S2 (0) are governed by simple functions of the symmetry-axis tilt ν, which have the same form for both halfspaces. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are mostly influenced by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the PS 1 and PS 2 modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion based on the exact reflection coefficients.

Weak‐anisotropy approximation for P‐wave reflection coefficient at the boundary between two tilted transversely isotropic media

“…In this approximation, authors obtain polarisation vectors of shear waves by perturbing polarisation vectors of SV‐ and SH‐waves in isotropic background. This perturbation is the simple rotation at an angle Φ, called the polarisation angle, which is defined uniquely away from the singular direction (Jech and Psencik ; Behura and Tsvankin ). The rotation is performed in the plane perpendicular to the background (isotropic) slowness vector and can be expressed as: where Here, , and α is the phase angle with the vertical in isotropic background.…”

“…In this approximation, authors obtain polarisation vectors of shear waves by perturbing polarisation vectors of SV-and SH-waves in isotropic background. This perturbation is the simple rotation at an angle , called the polarisation angle, which is defined uniquely away from the singular direction (Jech and Psencik 1989;Behura and Tsvankin 2005). The rotation is performed in the plane perpendicular to the background (isotropic) slowness vector and can be expressed as:…”

“…The P‐wave slowness surface approximation in is used to calculate the P‐wave polarisation vector; however, polarisation vectors for SV‐ and SH‐ waves are not easy to obtain explicitly since there exists an on‐axis singularity where slowness vectors of SV‐ and SH‐waves are coincident. In order to overcome this issue, an approximation derived by Behura and Tsvankin () was used. In this approximation, authors obtain polarisation vectors of shear waves by perturbing polarisation vectors of SV‐ and SH‐waves in isotropic background.…”

“…Shaw, Shen and Chatterjee () attempted to estimate the dip of fractures based on the amplitude versus offset and azimuth approximation derived by Shaw and Sen () using the Born formalism. Behura and Tsvankin () developed an approximation for a small‐angle PS ‐reflection coefficient in TTI media. In this paper, we propose a 3D Shuey‐type (Shuey ) approximation of the plane‐wave PP ‐reflection coefficient at the boundary between TTI half‐spaces and discussed its validity and accuracy.…”