Predicting stress‐induced velocity anisotropy in rocks

Mavko, Gary; Mukerji, Tapan; Godfrey, Nicola J.

doi:10.1190/1.1443836

Cited by 164 publications

(130 citation statements)

References 11 publications

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“…This dependence is attributed to closing of compliant parts of the pore volume with increasing mean stress [Mavko et al, 1995]. Because the effective modulus of a rock is a function of the relative proportions of pore volume and solid matrix, reducing the pore volume increases the effective modulus and thus the velocity.…”

Section: It Is Well Known That Seismic Velocities In Crustal Rocksmentioning

confidence: 99%

Source array analysis of coda waves near the 1989 Loma Prieta, California, mainshock: Implications for the mechanism of coseismic velocity changes

Dodge¹,

Beroza²

1997

J. Geophys. Res.

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Abstract. Coda waves are often considered to be generated by backscattering of primary waves from randomly distributed heterogeneifies in the crust; however, modeling and experimental work indicates that much of the coda may be due to scattering near the receiver. Knowing where the coda is generated is important for several reasons. Coda waves have been used to characterize site amplification, scattering and attenuation throughout the crust, and velocity changes associated with large earthquakes; however, a lack of knowledge of where coda waves are generated can lead to ambiguous interpretations. In this study we analyze 26 s of coda waves recorded at up to 78 stations using slowness stacking on two source arrays and find that at nearly all stations, regardless of distance from the source, nearly all the amvals are within one hemisphere, most are strongly clustered near the direct amval, and the clusters are, in general, symmetrically disposed about the array axis (fault plane). This finding suggests that the coda consists primarily of waves scattered near the stations rather than waves scattered throughout the crust. This result holds even at stations very close to the sources where the amount of coda examined is about 6 times the direct S travel time, and it suggests that much of the coseismic velocity decrease associated with the 1989 Loma Pfieta earthquake [Ellsworth et el., 1992] occurred in the shallow crust near the stations. One possible mechanism for inducing such a change is a decrease in the mean stress from the mainshock slip; however, on the basis of static stress modeling, we find that this mechanism would produce a velocity increase in the region where velocity was observed to decrease. We conclude that the velocity decrease was more likely caused by crack opening or crack coalescence due to strong shaking from the mainshock.

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Section: It Is Well Known That Seismic Velocities In Crustal Rocksmentioning

confidence: 99%

Source array analysis of coda waves near the 1989 Loma Prieta, California, mainshock: Implications for the mechanism of coseismic velocity changes

Dodge¹,

Beroza²

1997

J. Geophys. Res.

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“…The method of Mavko et al (1995) can be applied to calculate the stress-induced anisotropy in homogeneous rocks. When a borehole is drilled in a rock subjected to an applied stress, the local stress field around a borehole is changed and causes anisotropy.…”

Section: Workflow Of the Numerical Modelingmentioning

confidence: 99%

“…When a borehole is drilled in a rock subjected to an applied stress, the local stress field around a borehole is changed and causes anisotropy. Similar to the procedure proposed by Brown and Cheng (2007), in this paper, we investigate this stress-induced anisotropy around a borehole by combining the method of Mavko et al (1995) and a numerical approach illustrated in Figure 1.We first begin with a homogeneous isotropic intact rock model, on which Mavko's model is based. After experimentally obtaining the V P and V S data as a function of hydrostatic pressure, we apply equation 3 to calculate the anisotropic stiffness tensor C i jkl (σ ) of the intact rock under stress σ , which can be anisotropic.…”

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confidence: 99%

Predicting stress-induced anisotropy around a borehole

Fang

Fehler

Zhu

et al. 2012

SEG Technical Program Expanded Abstracts 2012

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SUMMARYFormation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could result in a biased estimation of formation properties but could provide a means to estimate in situ stress from sonic logging data. In order to properly account for the formation property alteration, we propose an iterative numerical approach to calculate the stress-induced anisotropy around a borehole by combining Mavko's rock physics model and a finite-element method. We show the validity and accuracy of our approach by comparing numerical results to laboratory measurements of the stress-strain relation of a sample of Berea sandstone, which contains a borehole and is subjected to uniaxial stress loading. Our iterative approach converges very fast and can be applied to calculate the spatially varying stiffness tensor of the formation around a borehole for any given stress state. et al. (1995) proposed a simple and practical method to estimate the pore space compliance of rocks using experimental data of rock velocity versus hydrostatic pressure. Their approach for calculating the stiffness tensor with stress-induced anisotropy at a stress state σ is described below: (1) Calculate the pressure-dependent isotropic elastic compliances S iso i jkl (p) from measurements of V P and V S versus hydrostatic pressure. The compliance S 0 i jkl at the largest measured pressure, under which most of the compliant parts of the pore space are closed, is chosen as a reference point. The additional compliance ∆S iso i jkl (p) due to the presence of pore space at pressure p is defined to be BRIEF REVIEW OF MAVKO'S METHOD Mavkoandwhere the repeated indices in ∆S iso j jkk and ∆S iso jk jk mean summation. (3) Calculate the stress-induced compliance ∆S i jkl (σ ) throughwhere σ is a 3×3 stress tensor, m ≡ (sinθ cosφ , sinθ sinφ , cosθ )T is the unit normal to the crack surface, θ and φ are the polar and azimuthal angles in a spherical coordinate system. Note that W N (p) and W N (p) in equations 1 and 2 have been replaced WORKFLOW OF THE NUMERICAL MODELINGThe method of Mavko et al. (1995) can be applied to calculate the stress-induced anisotropy in homogeneous rocks. When a borehole is drilled in a rock subjected to an applied stress, the local stress field around a borehole is changed and causes anisotropy. Similar to the procedure proposed by Brown and Cheng (2007), in this paper, we investigate this stress-induced anisotropy around a borehole by combining the method of Mavko et al. (1995) and a numerical approach illustrated in Figure 1.We first begin with a homogeneous isotropic intact rock model, on which Mavko's model is based. After experimentally obtaining the V P and V S data as a function of hydrostatic pressure, we apply equation 3 to calculate the anisotropic stiffness tensor C i jkl (σ ) of the intact rock under stress σ , which can be anisotropic. Next, we drill a borehole in the model and use the calculated C i jkl (σ ) as the input in our initial model containi...

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“…As an alternative, Mavko et al (1995) presented a simple recipe for estimating stress-induced velocity anisotropy directly from measured values of isotropic V P and V S versus hydrostatic pressure. This method differs from the inclusion models, because it is relatively independent of any assumed crack geometry and has no limitation to small crack densities.…”

Section: Stress-induced Velocity Anisotropymentioning

confidence: 99%

Multi-Attribute Seismic/Rock Physics Approach to Characterizing Fractured Reservoirs

Mavko¹

2000

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JUSTIFICATIONDuring Phase I, we performed our rock physics, geologic, and seismic feasibility analysis for fracture characterization. We addressed the problem of seismic fracture detection and characterization, in general, and specifically at our field site in West Texas. In this analysis, we were able to implement a number of fracture modeling procedures and to quantitatively assess the theoretical detectability of reservoir fractures. This allowed us to identify which of the several seismic attributes are most likely to be useful for fracture detection at the site. One of our results showed that Thomsen's parameters should be very useful for indicating gas-filled fractures at the site. We also outlined Monte Carlo approaches that can be applied for feasibility analysis at any site.Prior to our study, most seismic fracture detection methods have focused on qualitatively detecting seismic anisotropy. While anisotropy is critical, when used alone it has left us with interpretation ambiguities and nonuniqueness. During Phase 1 of this project, we found that by statistically integrating geologic and seismic information we can develop nontraditional methods for fracture detection. For example, we found that quantifying the correlations between fracture occurrence and depositional environment, and between fracture spacing and layer thickness, we allow us to decrease the uncertainty of fracture interpretation using seismic anisotropy. One of the reasons for this is that different depositional environments (and rock facies) give rise to differences in their seismic signatures (impedances, velocities, and Poisson's ratio.Phase II will allow us to validate and improve these methodologies by carrying out a smallscale field pilot study. Taking methods to the field, always allows us to make them more applicable. In the field, we will be able to more accurately assess the uncertainties introduced by measurement noise, source and receiver response, coupling, and near surface acoustic properties. We can then more realistically develop ways to reduce the uncertainty, as well as to identify which aspects of the geology and fracture distribution we can characterize most robustly. The small-scale field study will also help us to establish empirical fracture parameters that are needed as inputs to rock physics models. For example, ALL of the effective medium models for fracture-induced anisotropy require fracture stiffness as inputs (these are sometimes characterized as moduli or aspect ratios). There is no realistic way to assign these values DOE FINAL TECHNICAL REPORT ON PHASE 4 theoretically, so being able to calibrate them in a small pilot will give us the critical inputs we need for interpreting the full scale seismic survey in phase III. Finally, the data from the pilot will allow us to add an aspect of "data mining" to the study. In Phase I, we have exploited our best theoretical tools, but the real field data will give us the opportunity to discover other, unpredicted, signatures of fractures that might prove valuable.Our a...

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Predicting stress‐induced velocity anisotropy in rocks

Cited by 164 publications

References 11 publications

Source array analysis of coda waves near the 1989 Loma Prieta, California, mainshock: Implications for the mechanism of coseismic velocity changes

Source array analysis of coda waves near the 1989 Loma Prieta, California, mainshock: Implications for the mechanism of coseismic velocity changes

Predicting stress-induced anisotropy around a borehole

Multi-Attribute Seismic/Rock Physics Approach to Characterizing Fractured Reservoirs

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