Tilted Orthorhombic Model Building with Geomechanics: Theory and Observations

Thanoon, David; Bachrach, Ran; Zdraveva, Olga; Chen, S.

doi:10.3997/2214-4609.201412947

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…Several authors used the model of aligned cracks with a stress‐dependent crack density to model the effect of stress on elastic properties (e.g., Brajanovski, Gurevich, and Schoenberg ; Thanoon et al . ). The anisotropy resulting from the application of a uniaxial stress on an initially isotropic medium was found to be elliptical (e.g., Rasolofosaon ; Sun and Prioul ), which is characterized in terms of Thomsen () anisotropy parameters by:

ε = δ

.…”

Section: Discussionmentioning

confidence: 99%

Frequency dependence of anisotropy in fluid saturated rocks – Part I: aligned cracks case

Collet

Gurevich

2016

Geophysical Prospecting

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A major cause of attenuation in fluid‐saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media however, most of the existing squirt flow models only provide the low‐ and high‐frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In this paper, we focus on media containing aligned compliant pores embedded in an isotropic background matrix. The low‐ and high‐frequency limits of the predicted fluid‐saturated elastic properties are respectively consistent with Gassmann theory and Mukerji–Mavko squirt flow model. Results are also expressed in terms of Thomsen anisotropy parameters. It turns out that the P‐wave anisotropy parameter ε tends to zero in the high‐frequency limit, whereas the δ parameter remains the only indicator of P‐S⊥ anisotropy. The S‐wave anisotropy parameter γ is not affected by the presence of fluid and remains the same for all frequency ranges. A new definition for attenuation anisotropy parameters is also proposed to quantify the attenuation anisotropy. In the most important case of liquid saturation, analytical expressions are derived for elastic properties, velocity anisotropy parameters, quality factors, and attenuation anisotropy parameters. A companion paper considers the case of cracks with an ellipsoidal distribution of orientations resulting from the application of anisotropic stress.

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ε = δ

.…”

Section: Discussionmentioning

confidence: 99%

Frequency dependence of anisotropy in fluid saturated rocks – Part I: aligned cracks case

Collet

Gurevich

2016

Geophysical Prospecting

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“…() and Thanoon et al . ()) leads to different attenuation and anisotropy patterns than the ones obtained by evaluating the crack orientation distribution resulting from preferential crack closure caused by the application of anisotropic stress.…”

Section: Discussionmentioning

confidence: 95%

“…Another noteworthy feature is the fact that, in the case of aligned fractures, the S-wave anisotropy parameter γ remains the same for all frequency ranges, whereas it decreases with frequency in the stress-induced anisotropy case. Hence, modelling stress-induced anisotropy using aligned cracks oriented in the direction of the maximum stress (e.g., Brajanovski et al (2005) and Thanoon et al (2015)) leads to different attenuation and anisotropy patterns than the ones obtained by evaluating the crack orientation distribution resulting from preferential crack closure caused by the application of anisotropic stress.…”

Section: Discussionmentioning

confidence: 99%

“…The application of stress on an initially isotropic medium and the subsequent preferential closure of cracks leads to a particular crack orientation distribution, which results in anisotropy. In order to minimize the number of parameters required to characterize the medium under stress, some authors simplistically assume the cracks to be oriented in the plane normal to the minimum stress direction (e.g., Brajanovski, Gurevich, and Schoenberg (2005) and Thanoon et al (2015)). This case was studied in the first paper, later referred as Paper I, dealing with squirt flow attenuation and dispersion in isotropic media permeated by aligned cracks.…”

Section: Introductionmentioning

confidence: 99%

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Frequency dependence of anisotropy in fluid saturated rocks – Part II: Stress‐induced anisotropy case

Collet

Gurevich

2016

Geophysical Prospecting

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A B S T R A C TA major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media, however, most of the existing squirt flow models only provide the low-and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In a companion paper, we focused on media containing aligned compliant pores embedded in an isotropic background matrix. In this paper, we investigate the case for which anisotropy results from the presence of cracks with an ellipsoidal distribution of orientations due to the application of anisotropic stress. The low-and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. In the most important case of liquid saturation, analytical expressions are derived for elastic properties and Thomsen anisotropy parameters. The main observations drawn from this model are as follows. Crack closure perpendicular to the applied stress leads to an increase in seismic velocities as a function of stress in the direction of applied stress and a decrease in squirt-flow-induced dispersion and attenuation in this direction. The anisotropy of squirt flow dispersion engenders a decrease in the degree of anisotropy with frequency. The stress-induced anisotropy remains elliptical, even in saturated media, for all frequency ranges.

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3D mapping of kinematic attributes in anisotropic media

Ivanov

Stovas

2019

GEOPHYSICS

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Based on the rotation of a slowness surface in anisotropic media, we have derived a set of mapping operators that establishes a point-to-point correspondence for the traveltime and relative-geometric-spreading surfaces between these calculated in nonrotated and rotated media. The mapping approach allows one to efficiently obtain the aforementioned surfaces in a rotated anisotropic medium from precomputed surfaces in the nonrotated medium. The process consists of two steps: calculation of a necessary kinematic attribute in a nonrotated, e.g., orthorhombic (ORT), medium, and subsequent mapping of the obtained values to a transformed, e.g., rotated ORT, medium. The operators we obtained are applicable to anisotropic media of any type; they are 3D and are expressed through a general form of the transformation matrix. The mapping equations can be used to develop moveout and relative-geometric-spreading approximations in rotated anisotropic media from existing approximations in nonrotated media. Although our operators are derived in case of a homogeneous medium and for a one-way propagation only, we discuss their extension to vertically heterogeneous media and to reflected (and converted) waves.

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Tilted Orthorhombic Model Building with Geomechanics: Theory and Observations

Cited by 5 publications

References 8 publications

Frequency dependence of anisotropy in fluid saturated rocks – Part I: aligned cracks case

Frequency dependence of anisotropy in fluid saturated rocks – Part I: aligned cracks case

Frequency dependence of anisotropy in fluid saturated rocks – Part II: Stress‐induced anisotropy case

3D mapping of kinematic attributes in anisotropic media

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