Frequency-dependent P-wave anisotropy due to scattering in rocks with aligned fractures

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. MR97-MR105 ◽  
Author(s):  
Junxin Guo ◽  
Boris Gurevich ◽  
Da Shuai
Keyword(s):  
Wave Velocity ◽  
Wave Scattering ◽  
Wave Attenuation ◽  
P Wave ◽  
Frequency Dependent ◽  
Velocity Anisotropy ◽  
P Wave Velocity ◽  
Anisotropy Parameters ◽  
Scattering Anisotropy ◽  
Attenuation Anisotropy

Frequency-dependent P-wave anisotropy due to scattering often occurs in fractured formations, whereas the corresponding theoretical study is lacking. Hence, based on a newly developed P-wave scattering model, we have studied the frequency-dependent P-wave scattering anisotropy in rocks with aligned fractures. To describe P-wave scattering anisotropy, we develop the corresponding anisotropy parameters similar to those for elastic anisotropy. Our results indicate that the P-wave velocity anisotropy parameters [Formula: see text] and [Formula: see text] do not change with frequency monotonically, which is different from that caused by wave-induced fluid flow. Fluid saturation in fractures can greatly decrease the P-wave velocity anisotropy, whose effects depend on the ratio of the fluid bulk modulus to the fracture aspect ratio. The P-wave exhibits elliptical anisotropy for the dry fracture case at low frequencies, but anelliptical anisotropy for the case with fluid-filled fractures. The P-wave attenuation anisotropy parameters [Formula: see text] and [Formula: see text] vanish in the low- and high-frequency limits but reach their maxima at the characteristic frequency when the P-wavelength is close to the fracture length. The influence of fluid on the P-wave attenuation anisotropy is similar to that on the velocity anisotropy. To further analyze frequency-dependent P-wave scattering anisotropy, theoretical predictions are compared with experimental results, which indicate reasonable agreement between them.

Plane-wave attenuation anisotropy in orthorhombic media

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. D9-D19 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin
Keyword(s):  
Attenuation Coefficient ◽  
Wave Attenuation ◽  
Fractured Reservoirs ◽  
The Body ◽  
P Wave ◽  
Attenuation Coefficients ◽  
Velocity Anisotropy ◽  
Homogeneous Wave ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy

Orthorhombic models are often used in the interpretation of azimuthally varying seismic signatures recorded over fractured reservoirs. Here, we develop an analytic framework for describing the attenuation coefficients in orthorhombic media with orthorhombic attenuation (i.e., the symmetry of both the real and imaginary parts of the stiffness tensor is identical) under the assumption of homogeneous wave propagation. The analogous form of the Christoffel equation in the symmetry planes of orthorhombic and VTI (transversely isotropic with a vertical symmetry axis) media helps to obtain the symmetry-plane attenuation coefficients by adapting the existing VTI equations. To take full advantage of this equivalence with transverse isotropy, we introduce a parameter set similar to the VTI attenuation-anisotropy parameters [Formula: see text], [Formula: see text], and [Formula: see text]. This notation, based on the same principle as Tsvankin’s velocity-anisotropy parameters for orthorhombic media, leads to concise linearized equations for thesymmetry-plane attenuation coefficients of all three modes (P, [Formula: see text], and [Formula: see text]).The attenuation-anisotropy parameters also allow us to simplify the P-wave attenuation coefficient [Formula: see text] outside the symmetry planes under the assumptions of small attenuation and weak velocity and attenuation anisotropy. The approximate coefficient [Formula: see text] has the same form as the linearized P-wave phase-velocity function, with the velocity parameters [Formula: see text] and [Formula: see text] replaced by the attenuation parameters [Formula: see text] and [Formula: see text]. The exact attenuation coefficient, however, also depends on the velocity-anisotropy parameters, while the body-wave velocities are almost unperturbed by the presence of attenuation. The reduction in the number of parameters responsible for the P-wave attenuation and the simple approximation for the coefficient [Formula: see text] provide a basis for inverting P-wave attenuation measurements from orthorhombic media. The attenuation processing must be preceded by anisotropic velocity analysis that can be performed (in the absence of pronounced velocity dispersion) using existing algorithms for nonattenuative media.

Observations of wave velocity and attenuation in two‐phase media

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2193-2199 ◽  
Author(s):  
G. W. Purnell
Keyword(s):  
Physical Model ◽  
Wave Velocity ◽  
Wave Attenuation ◽  
P Wave ◽  
Rubber Matrix ◽  
Two Phase ◽  
P Wave Velocity ◽  
Porosity And Permeability ◽  
Dispersion And Attenuation ◽  
Scattering Losses

The velocity and attenuation of a wave transmitted through a two‐phase material are functions of the material’s composition. In physical model experiments, I used suspensions of grains in a silicone rubber matrix to reduce or avoid uncertainties about framework elastic constants, porosity, and permeability that result from using fluid‐saturated grain frameworks. I varied the composition to produce materials that are useful in physical seismic modeling. In the tested suspensions, ultrasonic P-wave velocity, velocity dispersion, and attenuation all increase with grain concentration and frequency. I compared seven published mathematical models for wave propagation in two‐phase media. One given by Mehta most closely agrees with the P-wave velocities I observed. The agreement is sufficiently close to merit use of Mehta’s model in the design of physical model materials. The observed P-wave attenuation generally increases approximately linearly with frequency. This approximate linearity leads to reliable constant-Q estimates, ranging from 187 to 16 for grain concentrations from 0 to 0.49. I conclude that relative motion between the grains and the rubber matrix contributes most of the observed attenuation at lower concentrations, whereas scattering losses become much more important at higher concentrations and frequencies.

EXPERIMENTAL EVALUATION OF ULTRASONIC VELOCITIES AND ANISOTROPY IN THE TUSCALOOSA MARINE SHALE FORMATION

2020 ◽  
pp. 1-62 ◽  
Author(s):  
Jamal Ahmadov ◽  
Mehdi Mokhtari
Keyword(s):  
Wave Velocity ◽  
Mineralogical Composition ◽  
Organic Content ◽  
P Wave ◽  
S Wave ◽  
Velocity Anisotropy ◽  
Wave Velocities ◽  
Marine Shale ◽  
P Wave Velocity ◽  
Degree Of Anisotropy

Tuscaloosa Marine Shale (TMS) formation is a clay- and organic-rich emerging shale play with a considerable amount of hydrocarbon resources. Despite the substantial potential, there have been only a few wells drilled and produced in the formation over the recent years. The analyzed TMS samples contain an average of 50 wt% total clay, 27 wt% quartz and 14 wt% calcite and the mineralogy varies considerably over the small intervals. The high amount of clay leads to pronounced anisotropy and the frequent changes in mineralogy result in the heterogeneity of the formation. We studied the compressional (VP) and shear-wave (VS) velocities to evaluate the degree of anisotropy and heterogeneity, which impact hydraulic fracture growth, borehole instabilities, and subsurface imaging. The ultrasonic measurements of P- and S-wave velocities from five TMS wells are the best fit to the linear relationship with R2 = 0.84 in the least-squares criteria. We observed that TMS S-wave velocities are relatively lower when compared to the established velocity relationships. Most of the velocity data in bedding-normal direction lie outside constant VP/VS lines of 1.6–1.8, a region typical of most organic-rich shale plays. For all of the studied TMS samples, the S-wave velocity anisotropy exhibits higher values than P-wave velocity anisotropy. In the samples in which the composition is dominated by either calcite or quartz minerals, mineralogy controls the velocities and VP/VS ratios to a great extent. Additionally, the organic content and maturity account for the velocity behavior in the samples in which the mineralogical composition fails to do so. The results provide further insights into TMS Formation evaluation and contribute to a better understanding of the heterogeneity and anisotropy of the play.

Pyrolysis-induced P-wave velocity anisotropy in organic-rich shales

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. D41-D53 ◽  
Author(s):  
Adam M. Allan ◽  
Tiziana Vanorio ◽  
Jeremy E. P. Dahl
Keyword(s):  
Wave Velocity ◽  
Elastic Anisotropy ◽  
Rock Physics ◽  
Confining Pressure ◽  
Source Rocks ◽  
Acoustic Properties ◽  
P Wave ◽  
Velocity Anisotropy ◽  
Geochemical Parameters ◽  
P Wave Velocity

The sources of elastic anisotropy in organic-rich shale and their relative contribution therein remain poorly understood in the rock-physics literature. Given the importance of organic-rich shale as source rocks and unconventional reservoirs, it is imperative that a thorough understanding of shale rock physics is developed. We made a first attempt at establishing cause-and-effect relationships between geochemical parameters and microstructure/rock physics as organic-rich shales thermally mature. To minimize auxiliary effects, e.g., mineralogical variations among samples, we studied the induced evolution of three pairs of vertical and horizontal shale plugs through dry pyrolysis experiments in lieu of traditional samples from a range of in situ thermal maturities. The sensitivity of P-wave velocity to pressure showed a significant increase post-pyrolysis indicating the development of considerable soft porosity, e.g., microcracks. Time-lapse, high-resolution backscattered electron-scanning electron microscope images complemented this analysis through the identification of extensive microcracking within and proximally to kerogen bodies. As a result of the extensive microcracking, the P-wave velocity anisotropy, as defined by the Thomsen parameter epsilon, increased by up to 0.60 at low confining pressures. Additionally, the degree of microcracking was shown to increase as a function of the hydrocarbon generative potential of each shale. At 50 MPa confining pressure, P-wave anisotropy values increased by 0.29–0.35 over those measured at the baseline — i.e., the immature window. The increase in anisotropy at high confining pressure may indicate a source of anisotropy in addition to microcracking — potentially clay mineralogical transformation or the development of intrinsic anisotropy in the organic matter through aromatization. Furthermore, the evolution of acoustic properties and microstructure upon further pyrolysis to the dry-gas window was shown to be negligible.

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