3-D seismic modeling for cracked media: Shear‐wave splitting at zero‐offset

Abstract

Splitting of zero‐offset reflected shear‐waves is measured directly from three‐component finite‐difference synthetic seismograms for media with intersecting vertical crack systems. Splitting is simulated numerically (by finite differencing) as a function of crack density, aspect ratio, fluid content, bulk density, and the angle between the crack systems. The type of anisotropy symmetry in media containing two intersecting vertical crack systems depends on the angular relation between the cracks and their relative crack densities, and it may be horizontal transverse isotropy (HTI), tetragonal, orthorhombic, or monoclinic. The transition from one symmetry to another is visible in the splitting behavior. The polarities of the reflected quasi‐shear waves polarized perpendicular and parallel to the source particle motion distinguish between HTI and orthorhombic media. The dependence of the measured amount of splitting on crack density for HTI symmetry is consistent with that predicted theoretically by the shear‐wave splitting factor. In orthorhombic media (with two orthogonal crack systems), a linear increase is observed in splitting when the difference between crack densities of the two orthogonal crack systems increases. Splitting decreases nonlinearly with the intersection angle between the two crack systems from 0° to 90°. Surface and VSP seismograms are simulated for a model with several flat homogeneous layers, each containing vertical cracks with the same and with different orientations. When the crack orientation varies with depth, previously split shear waves are split again at each interface, leading to complicated records, even for simple models. Isotropic and anisotropic three‐component S-wave zero‐offset sections are synthesized for a zero‐offset survey line over a 2.5-D model of a carbonate reservoir with a complicated geometry and two intersecting, dipping crack sets. The polarization direction of the fast shear wave, propagating obliquely through the cracked reservoir, is predicted by theoretical approximations for effective properties of anisotropic media with two nonorthogonal intersecting crack sets.

3D Modeling of Fracture-Induced Shear-Wave Splitting in the Southern California Basin

“…Forward finite differencing is used for time stepping (Ramos-Martinez et al, 2000;Ramos-Martinez and McMechan, 2001). The use of the eighth-order central finitedifference approximation for spatial derivatives of particle velocity and stress reduces the number of grid points required per wavelength for a given accuracy and provides the capability of synthesizing high-frequency seismograms (Yoon, 1995).…”

3D, 9C seismic modeling and inversion of Weyburn Field data

“…The modeling algorithm is a particle velocity-stress formulation of the elastodynamic equations (Tessmer, 1995) implemented by eighth-order, staggered-grid, finite differencing (Ramos-Martínez et al, 2000). The size of the model is ðx; y; zÞ ¼ ð301; 251; 151Þ grid points with 10-meter spacing ð3000 × 2500 × 1500Þ m. The source wavelet is Gaussian, with a dominant frequency of 26 Hz.…”

“…To close the loop, forward modeling is performed, based on the velocity-stress relation of the elastodynamic equations for general anisotropy (Tessmer, 1995) implemented by eighth-order, staggered-grid, finite-differencing (Ramos-Martínez et al, 2000).…”

Quasi-shear wave ray tracing by wavefront construction in 3-D, anisotropic media

“…For example, shear-wave splitting measured from vertical seismic profiles can be interpreted in terms of crack-induced anisotropy (Crampin, 1985;Shearer and Chapman, 1989;Douma and Crampin, 1990;Horne et al, 1997;Crampin and Chastin, 2003;Nistala and McMechan, 2005). Such information regarding crack properties from qS-wave splitting can provide important insights for understanding reservoir performance (Ramos-Martinez et al, 2000).…”