Reflection and transmission coefficients of a fracture in transversely isotropic media

Carcione, José M.; Picotti, Stefano

doi:10.1007/s11200-011-9034-4

Cited by 26 publications

(8 citation statements)

References 19 publications

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“…There is energy loss at the interface and corresponds to the damped oscillator as we shall see later. This model was used by Carcione (, , ) and Carcione and Picotti () to obtain the reflection and transmission coefficients of fractures and cracks.…”

Section: Modelmentioning

confidence: 99%

Geophone‐ground coupling with flat bases

Carcione

Almalki

Qadrouh

2015

Geophysical Prospecting

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A B S T R A C TSeismic acquisition can be costly and inefficient when using spiked geophones. In most cases, such as the desert, the most practical solution is the use of flat bases, where geophone-ground coupling is based on an optimal choice of the mass and area of contact between the receiver and the ground. This optimization is necessary since areas covered by sand are loose sediments and poor coupling occurs. Other cases include ground coupling in stiff pavements, for instance urban areas and ocean-bottom nodes. We consider three different approaches to analyse coupling and model the geophone with a flat base (plate) resting on an elastic half-space. Two existing models, based on the full-wave theory, which we refer to as the Wolf and Hoover-O'Brien models, predict a different behaviour with respect to the novel method introduced in this work. This method is based on the transmission coefficient of upgoing waves impinging in the geophone-ground contact, where the ground is described as an anelastic halfspace. The boundary conditions at the contact have already been used to model fractures and are shown here to provide the equation of the damped oscillator. This fracture-contact model depends on the stiffness characteristic of the contact between the geophone base plate and the ground. The transmission coefficient from the ground to the plate increases for increasing weight and decreasing base plate area. The new model predicts that the resonant frequency is independent of the geophone weight and plate radius, while the recorded energy increases with increasing weight and decreasing base plate area (as shown from our own experiments and measurements by Krohn) which is contrary to the theories developed by Wolf and Hoover-O'Brien. The transient response is obtained by an inverse Fourier transform. Optimal geophoneground coupling and energy transmission are required, the first concept meaning that the geophone is following the motion of the ground and the second one that the signal is detectable. As a final example, we simulate seismic acquisition based on the novel theory, showing the differences between optimal and poor ground-to-geophone energy transmission.

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Section: Modelmentioning

confidence: 99%

Geophone‐ground coupling with flat bases

Carcione

Almalki

Qadrouh

2015

Geophysical Prospecting

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“…Once the P-wave reflection coefficient for a fractured TI medium is obtained, the mode number, m, can be calculated numerically for the reflection angle, u, from 08 to 908 . The reflection coefficient is derived for a Pwave incident upon a fracture in a TI medium based on the work of Carcione & Picotti (2012). A fracture is represented by a set of boundary conditions that is often referred to as the displacement discontinuity theory or the linear-slip theory (Murty 1975;Schoenberg 1980;Kitsunezaki 1983;Pyrak-Nolte et al 1990a, b).…”

Section: Fractured Media With Sub-wavelength Layer Thicknessmentioning

confidence: 99%

“…Carcione & Picotti (2012) derived the matrix equation for the reflection and transmission coefficients for a fracture in a TI medium:…”

Section: Fractured Media With Sub-wavelength Layer Thicknessmentioning

confidence: 99%

Wave guiding in fractured layered media

Shao

Petrovitch

Pyrak‐Nolte

2014

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Many carbonate rocks are composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties to be anisotropic. Co-located fractures and layers in carbonate rock lead to competing wave-scattering mechanisms: both layers and parallel fractures generate compressional-wave (P-wave) guided modes. The guided modes generated by the fractures may obscure the presence of the layers. In this study, we examine compressional-wave guided modes for two cases: wave guiding by fractures in a layered medium with sub-wavelength layer thickness; and wave guiding in media with competing scattering mechanisms, namely layering (where the thickness is greater than a wavelength) and parallel sets of fractures. In both cases, the fracture spacing is greater than a wavelength. When the layer thickness is smaller than a wavelength, P-wave guiding is controlled by the spacing of the fractures, fracture specific stiffness, the frequency of the signal and the orientation of the layering relative to the fracture set. The orientation of the layering determines the directionally dependent P-wave velocity in the anisotropic matrix. When the layer thickness is greater than a wavelength and an explosive point source of a signal is located in the layer containing a fracture, the fracture either enhanced or suppressed compressional-mode wave guiding caused by the layering in the matrix.Carbonate reservoirs pose a scientific and engineering challenge to geophysical prediction and monitoring of fluid flow in the subsurface. This is particularly true for carbonate rocks, many of which form in spatially and temporally variable depositional environments, and are modified further by diagenesis and deformation during the subsequent rock history. Variations in primary depositional geometries (metre to kilometre scale), as influenced by factors such as their depositional environments, sealevel fluctuations and climate, are reflected by distinct stacking patterns of rock layers or bodies, and variations in their thickness and lateral continuity. Depositional and/or construction processes influence finer-scale (micron to centimetre scale) textural variations and the formation of sedimentary structures. The resulting pore systems in the rock matrix comprise pores that vary in scale from submicron to centimetres. Fossil and primary mineral content, as well as spatial and compositional variations in cements, introduce further heterogeneities to the rock texture. Both cements and pore structure can be modified multiple times by temporal variations in the compositions, temperatures and flow rates of fluids migrating through the rocks. Carbonate rocks that have been subjected to deformation in response to burial, tectonic and induced (e.g. during hydrocarbon production) stresses commonly develop arrays of fractures as well as stylolites. While the orientations of these features vary with the burial and deformation history, fracture arrays are commonly steeply dipping, while stylolites tend to be oriented parallel to bedding.Diffi...

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“…The literature is vast in the case of a single interface. The authors attacked the problem for welded and non-welded interfaces (cracks and fractures), in some cases considering wave anisotropy and attenuation (Carcione, 1996(Carcione, , 1997(Carcione, , 1998Carcione and Picotti, 2012), and in the poroelastic case using Biot's theory (Santos et al, 1992), and a three-phase extension of this theory (Carcione et al, 2003;Rubino et al, 2006;Santos et al, 2004). There are relatively many works for a layer described by a single-phase (solid) case, e.g., Widess (1973) and Bakke and Ursin (1998) consider the normal incidence case for a thin layer, Juhlin and Young (1993) studied AVO effects of a thin layer, while the effect of the thickness of a sedimentary layer has been investigated by Chung and Lawton (1995a,b).…”

Section: Introductionmentioning

confidence: 99%

Reflection and transmission coefficients of a single layer in poroelastic media

Corredor

Santos

Gauzellino

et al. 2014

The Journal of the Acoustical Society of America

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Wave propagation in poroelastic media is a subject that finds applications in many fields of research, from geophysics of the solid Earth to material science. In geophysics, seismic methods are based on the reflection and transmission of waves at interfaces or layers. It is a relevant canonical problem, which has not been solved in explicit form, i.e., the wave response of a single layer, involving three dissimilar media, where the properties of the media are described by Biot's theory. The displacement fields are recast in terms of potentials and the boundary conditions at the two interfaces impose continuity of the solid and fluid displacements, normal and shear stresses, and fluid pressure. The existence of critical angles is discussed. The results are verified by taking proper limits-zero and 100% porosity-by comparison to the canonical solutions corresponding to single-phase solid (elastic) media and fluid media, respectively, and the case where the layer thickness is zero, representing an interface separating two poroelastic half-spaces. As examples, it was calculated the reflection and transmission coefficients for plane wave incident at a highly permeable and compliant fluid-saturated porous layer, and the case where the media are saturated with the same fluid.

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Reflection and transmission coefficients of a fracture in transversely isotropic media

Cited by 26 publications

References 19 publications

Geophone‐ground coupling with flat bases

Geophone‐ground coupling with flat bases

Wave guiding in fractured layered media

Reflection and transmission coefficients of a single layer in poroelastic media

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