Anisotropy of Seismic Attenuation in Fractured Media: Theory and Ultrasonic Experiment

Abstract

This is a study on anisotropy of seismic attenuation in a transversely isotropic (TI) model, which is a long-wavelength equivalent of an isotropic medium with embedded parallel fractures. The model is based on Schoenberg's linear-slip theory. Attenuation is introduced by means of a complex-valued stiffness matrix, which includes complex-valued normal and tangential weaknesses. To study the peculiarities of seismic attenuation versus wave-propagation direction in TI media, numerical modeling was performed. The modelinput data were the complex-valued weaknesses found from the laboratory ultrasonic experiment made with a Plexiglas plate-stack model, oil-saturated (wet) and air-filled (dry). The laboratory experiment and the numerical modeling have shown that in the vicinity of the symmetry axis, in the wet model, P-wave attenuation is close to S-wave attenuation, while in the dry model, P-wave attenuation is much greater than S-wave attenuation. Moreover, the fluid fill affects the P-wave attenuation pattern. In the dry (air-saturated) model, the attenuation pattern in the vicinity of the symmetry axis exhibits steeper slope and curvature than in the wet (oil-saturated) model. To define the slope or the curvature, a QVO gradient was introduced, which was found to be proportional to the symmetry-axis Q S /Q P -ratio, which explains the differences between dry and wet models. Thus, depending on the Q S /Q P -ratio, the QVO gradient can serve as an indicator of the type of fluid in fractures, because the QVO gradient is greater in gas-saturated than in liquid-saturated rocks. The analysis of P-wave attenuation anisotropy in seismic reflection and vertical seismic profiling data can be useful in seismic exploration for distinguishing gas from water in fractures.

Seismic attenuation in glacial ice: A proxy for englacial temperature

“…Seismic anisotropy due to oriented cracks, microfractures, laminae, or crystal orientation leads to an associated attenuation anisotropy. In general, seismic attenuation is at a minimum when the seismic wave propagation is parallel to the primary axis of anisotropy [e.g., Best et al , 2007; Chinchinina et al , 2009].…”

Fracture clustering effect on amplitude variation with offset and azimuth analyses

“…We assume that fractures are vertical and parallel to each other in the simulations because subsurface natural fracture planes tend to be vertical and parallel to the maximum horizontal stress direction (Zoback, 2010). Previous numerical and experimental studies (Tadepalli et al, 1995;Fatkhan et al, 2001;Alhussain et al, 2007;Chichinina et al, 2009;Mahmoudian et al, 2012;Far et al, 2014) on models with regularly spaced fractures have demonstrated that the EMM and DFM models are equivalent when fracture spacing is sufficiently small compared with the wavelength (e.g., < λ∕10), which is the foundation for the use of EMM in fracture characterization. However, fractures are unlikely to be uniformly distributed in the earth.…”

Numerical experiments of fracture-induced velocity and attenuation anisotropy

“…If the background medium is isotropic, with elasticity components (Lamé constants) c 12 and c 55 , and the fracture set is rotationally invariant, we have Z H = Z V ≡ Z T , and the equivalent medium is TIV with a vertical symmetry axis (VTIV), whose stiffness matrix is (Schoenberg 1983; Chichinina et al 2009; Carcione et al 2012), where c 11 = c 12 + 2 c 55 , The stiffness matrix in Coates & Schoenberg (1995) is equivalent to P of eq. () considering the lossless case (= 0).…”

“…To verify that the FE implementation of the fractured medium is correct, we consider the data provided by the laboratory experiments of Chichinina et al (2009). They consider an isotropic background medium defined by c 12 = 10 GPa, c 55 = 3.9 GPa ( c 11 = 17.8 GPa) and ρ= 2300 kg m −3 .…”