Fracture permeability and seismic wave scattering—Poroelastic linear‐slip interface model for heterogeneous fractures

Nakagawa, Seiji; Myer, Larry R.

doi:10.1190/1.3255581

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…On the other hand, a recently developed model (Chapman 2003;Maultzsch 2005) explicitly describes the effects of cracks and fractures on wave propagation, since the elastic constants are derived in terms of microstructural parameters and, therefore, the model is predictive. It describes attenuation and velocity dispersion at seismic frequencies and predicts how these effects are related to the fluid type and size of the fractures.…”

Section: Introductionmentioning

confidence: 99%

Fracture-Induced Anisotropic Attenuation

2012

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The triaxial nature of the tectonic stress in the earth's crust favors the appearance of vertical fractures. The resulting rheology is usually effective anisotropy with orthorhombic and monoclinic symmetries. In addition, the presence of fluids leads to azimuthally varying attenuation of seismic waves. A dense set of fractures embedded in a background medium enhances anisotropy and rock compliance. Fractures are modeled as boundary discontinuities in the displacement u and particle velocity v as ½j Á u þ g Á v; where the brackets denote discontinuities across the fracture surface, j is a fracture stiffness, and g is a viscosity related to the energy loss. We consider a transversely isotropic background medium (e.g., thin horizontal plane layers), with sets of long vertical fractures. Schoenberg and Muir's theory combines the background medium and sets of vertical fractures to provide the 13 complex stiffnesses of the long-wavelength equivalent monoclinic and viscoelastic medium. Long-wavelength equivalent means that the dominant wavelength of the signal is much longer than the fracture spacing. The symmetry plane is the horizontal plane. The equations for orthorhombic and transversely isotropic media follow as particular cases. We compute the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts), and quality factors. The effective medium ranges from monoclinic symmetry to hexagonal (transversely isotropic) symmetry from the low-to the high-frequency limits in the case of a particle-velocity discontinuity (lossy case) and the attenuation shows typical Zener relaxation peaks as a function of frequency. The attenuation of the coupled waves may show important differences when computed versus the ray or phase angles, with triplication appearing in the Q factor of the qS wave. We have performed a full-wave simulation to compute the field corresponding to the coupled qP-qS waves in the symmetry plane of an effective monoclinic medium. The simulations agree with the predictions of the plane-wave analysis.

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Section: Introductionmentioning

confidence: 99%

Fracture-Induced Anisotropic Attenuation

2012

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“…Consider plane-wave propagation in a Cartesian coordinate system (x 1 , x 2 , x 3 ) with the 3 axis normal to the fracture plane and the 1, 3 axes defining a plane parallel to the wave propagation. Assuming small wave frequencies and a fracture that is thin compared to seismic wavelengths, the linear-slip interface boundary conditions for a poroelastic fracture can be given as (Nakagawa and Myer 2009;Nakagawa and Korneev 2014):…”

Section: Frequency Equationmentioning

confidence: 99%

“…Recently, Nakagawa and Korneev (2014) derived a Krauklis wave frequency equation for a fracture with finite fracture compliance, embedded in an infinite background. Their derivation employed the linear-slip interface model (Schoenberg 1980) extended for a poroelastic fracture, which allows wave-induced fluid flow along the fracture (Nakagawa and Schoenberg 2007;Nakagawa and Myer 2009). In this paper, we will apply this technique to a trilayer model.…”

Section: Frequency Equationmentioning

confidence: 99%

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Laboratory measurements of guided-wave propagation within a fluid-saturated fracture

Nakagawa

Nakashima

Korneev

2015

Geophysical Prospecting

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A B S T R A C TA fluid-saturated flat channel between solids, such as a fracture, is known to support guided waves-sometimes called Krauklis waves. At low frequencies, Krauklis waves can have very low velocity and large attenuation and are very dispersive. Because they propagate primarily within the fluid channel formed by a fracture, Krauklis waves can potentially be used for geological fracture characterization in the field. Using an analogue fracture consisting of a pair of flat slender plates with a mediating fluid layer-a trilayer model-we conducted laboratory measurements of the velocity and attenuation of Krauklis waves. Unlike previous experiments using ultrasonic waves, these experiments used frequencies well below 1 kHz, resulting in extremely low velocity and large attenuation of the waves. The mechanical compliance of the fracture was varied by modifying the stiffness of the fluid seal of the physical fracture model, and proppant (fracture-filling high-permeability sand) was also introduced into the fracture to examine its impact on wave propagation. A theoretical frequency equation for the trilayer model was derived using the poroelastic linear-slip interface model, and its solutions were compared to the experimental results.Key words: Scattering and waveguide, Fracture, Stoneley wave. I N T R O D U C T I O NAn open fracture containing fluid can carry highly dispersive and slow seismic waves-sometimes called Krauklis waves (Krauklis 1962;Korneev 2008;Frehner 2014). Krauklis waves are a type of guided wave resulting from mechanical interactions between fluid in a flat narrow channel and its elastic background. Although the original Krauklis waves were predicted for a fracture with an infinite background, laboratory experiments for investigating Krauklis waves must be conducted using finite-size models-typically solid-fluidsolid trilayers. Lloyd and Redwood (1965) first predicted the presence of a guided-wave mode within the fluid part of the trilayer, which is essentially the Krauklis wave in a fracture with a finite elastic background. * E-mail: SNakagawa@lbl.gov To this day, however, laboratory and field measurements of Krauklis waves are still very scarce. Ferrazzini and Aki (1987) attributed low-frequency volcanic tremors before an eruption to the resonance of slow fluid waves in magma within fractures. Tary and Van der Baan (2012) argued that resonances observed during fluid injection in an oil and gas reservoir were caused by Krauklis waves. Arguably the first conclusive experimental evidence of these highly dispersive waves was obtained by Hassan and Nagy (1997) in the laboratory. In their experiment, they examined ultrasonic waves propagating within a trilayer model consisting of a water layer trapped between thin aluminium plates. They generated waves with a wide range of frequencies (15 kHz-150 kHz) using a controlled source (piezoelectric source) and measured the resulting surface particle motions of the waves using a laser Doppler vibrometer. The results showed strongly frequency-depen...

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Reflection and transmission coefficients of a fracture in transversely isotropic media

Carcione

Picotti

2011

Stud Geophys Geod

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Fracture permeability and seismic wave scattering—Poroelastic linear‐slip interface model for heterogeneous fractures

Cited by 5 publications

References 11 publications

Fracture-Induced Anisotropic Attenuation

Fracture-Induced Anisotropic Attenuation

Laboratory measurements of guided-wave propagation within a fluid-saturated fracture

Reflection and transmission coefficients of a fracture in transversely isotropic media

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