Frequency‐Dependent P Wave Anisotropy Due to Wave‐Induced Fluid Flow and Elastic Scattering in a Fluid‐Saturated Porous Medium With Aligned Fractures

Abstract

Seismic anisotropy is an important attribute for fracture detection and characterization. If fracture size is comparable to the wavelength or fluid diffusion length, the P wave anisotropy is frequency dependent. By solving the Biot's equations of dynamic poroelasticity and using the Foldy approximation, we investigate the frequency‐dependent P wave anisotropy in a fluid‐saturated porous rock with a set of aligned penny‐shaped fractures. This approach includes the effects of both wave‐induced fluid flow (WIFF) and elastic scattering on P wave anisotropy. The results show that the velocity and attenuation anisotropy in the WIFF and elastic scattering regimes have quite different features and are affected by various factors. In particular, the background permeability and fluid viscosity primarily affect the frequency‐dependent anisotropy caused by WIFF. The fracture geometry (radius and thickness) and fracture density have significant effects on both WIFF and elastic scattering‐induced frequency‐dependent anisotropy. The fluid bulk modulus also affects the frequency‐dependent anisotropy. With the vanishing fluid bulk modulus, the frequency dependency vanishes in the WIFF regime but is the largest in the elastic scattering regime. Predictions of the model agree with previous models in all known limiting cases. Comparison with experimental data shows that WIFF and elastic scattering are important causes for frequency‐dependent P wave anisotropy, and our model is capable to account for these effects.

Experimental Study on Petrophysical Properties as a Tool to Identify Pore Fluids in Tight-Rock Reservoirs

“…Seismic wave velocity dispersion and attenuation are considered to be caused by the wave-induced fluid flow mechanism (Mavko and Nur, 1979;Murphy, 1982;Winkler and Nur, 1982;Müller et al, 2010). Different poroelastic models have been developed to predict the velocity and attenuation observed in the laboratory and in the field data (Biot, 1956;White, 1975;Pride et al, 2004;Gurevich et al, 2010;Ba et al, 2017;Guo and Gurevich, 2020). Based on these models, rock-physics templates (RPTs) can be used to estimate porosity and saturation (Liu et al, 2015;Pang et al, 2019Pang et al, , 2020.…”

Dynamic SV‐Wave Signatures of Fluid‐Saturated Porous Rocks Containing Intersecting Fractures

“…The derivations for the SV‐wave incidence are similar except that the incident SV‐wave induces different shear stresses compared to the P‐wave. Therefore, we also follow a derivation procedure similar to that in Guo and Gurevich (2020) but replace the incident shear stresses by the P‐wave with those by the SV‐wave. The resulting dual integral equation for the coefficient $${A}_{3}^{m}(k)$$ for Fracture 1 is: $$$\left\{\begin{array}{l}{\int }_{0}^{\infty }\left({d}_{31}-{d}_{32}\right){A}_{3}^{m}(k)k{J}_{m}(kr)dk={F}_{3}(r),\quad 0\le r\le a\hfill \\ {\int }_{0}^{\infty }\frac{{A}_{3}^{m}(k)}{k}{J}_{m}(kr)dk=0,\quad a< r< \infty \hfill \end{array}\right.,$$$ where the expressions for the coefficients d 31 and d 32 are as follows: $$${d}_{31}=2{q}_{1}-\frac{2{k}^{2}-{k}_{3}^{2}}{{q}_{3}}+\frac{\left(H+C{\chi }_{1}\right){k}_{1}^{2}\left(2{k}^{2}-{k}_{3}^{2}\right)}{2\mu {k}^{2}{q}_{3}},$$$ …”

“…Hence, they should be similar to the aligned fracture case. This has been studied by Guo and Gurevich (2020) for the P‐wave incidence. The boundary conditions for the SV‐wave incidence are similar except that the incident shear stresses are different: $$${\sigma }_{zz1(2)}=0,\ (0\le r< \infty ,z=0),$$$ $$${u}_{\theta 1(2)}={u}_{r1(2)}=0,\ (a< r< \infty ,z=0),$$$ $$${\sigma }_{z\theta 1(2)}+{\sigma }_{z\theta 1(2)}^{in}=0,\ (0\le r\le a,z=0),$$$ $$${\sigma }_{zr1(2)}+{\sigma }_{zr1(2)}^{in}=0,\ (0\le r\le a,z=0),$$$ $$${p}_{1(2)}=0,\ (0\le r< \infty ,z=0),$$$ where u θ 1(2) and u r 1(2) denote the solid displacements in the θ ‐ and r ‐ directions respectively for Fracture 1 (or 2); σ zθ 1(2) and σ zr 1(2) are ...…”

“…The motions of fracture surface induced by incident waves can be decomposed into the normal and shear oscillations (Guo & Gurevich, 2020), which generate the corresponding sub‐scattered wavefields. To obtain the total scattered wavefields, we can sum up the two sub‐scattered wavefields.…”

Acoustothermoelasticity for Joint Effects of Stress and Thermal Fields on Wave Dispersion and Attenuation

“…The information of wave dispersion and attenuation plays a crucial role in interpreting the properties of subsurface rock and fluid, conducting rock-physical experiments and compensating the seismic signal, which has become one of the research focuses of geophysics (Gurevich et al, 2010;Mavko & Jizba, 1990). The effects of heterogeneity of background medium (Zheng et al, 2009), wave-induced fluid flow (Borgomano et al, 2017) and formation scattering (Guo & Gurevich, 2020) on wave dispersion and attenuation have been comprehensively studied. To better understand the effect of thermal field on the wave dispersion and attenuation, Rudgers (1990) and Carcione et al (2020) investigated the wave propagation velocities and attenuation coefficients of P wave, S wave and T wave in thermoelastic media.…”