Ambiguous reflection coefficients for anelastic media

Ruud, Bent Ole

doi:10.1007/s11200-006-0030-z

Cited by 37 publications

(22 citation statements)

References 24 publications

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“…In viscoelastic anisotropic media, such selection algorithms are not straightforward, and are not treated here. For a detailed discussion of the selection criteria see Ruud (2006) and Krebes and Daley (2007), where many other references can be found.…”

Section: Discussionmentioning

confidence: 99%

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Červený

2007

Stud Geophys Geod

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The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves are complex-valued, p = P + iA p = P + iA, where P P is the propagation vector, and A A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0 A = 0), homogeneous plane waves (A 6 = 0 A 6 = 0, P P and A A parallel), and inhomogeneous plane waves (A 6 = 0 A 6 = 0, P P and A A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace. The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail.

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Section: Discussionmentioning

confidence: 99%

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Červený

2007

Stud Geophys Geod

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“…1 shows an example of the above‐mentioned errors for the medium parameters in Table 1. See also Ruud (2005), Ruud (2006) for a similar example involving the PP reflection coefficient, and also Richards (1984).…”

Section: Sh Wavesmentioning

confidence: 99%

“…A 180° phase change in turn would produce a physically implausible polarity reversal between the elastic and anelastic reflected waveforms, computed by geometrical ray theory, for wide‐angle reflections for some offsets. For examples of these effects in the PP case, see for example, Hearn & Krebes (1990, figs 10 and 12) and Ruud (2005), Ruud (2006).…”

Section: Sh Wavesmentioning

confidence: 99%

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Difficulties with computing anelastic plane-wave reflection and transmission coefficients

Krebes¹,

Daley²

2007

Geophysical Journal International

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S U M M A R YConsider a plane homogeneous wave incident upon an interface between two anelastic halfspaces. Computing the plane-wave displacement reflection and transmission coefficients requires determining the proper signs of the vertical slownesses of all the reflected and transmitted waves. In certain cases, this is not straightforward. Previous work has shown that choosing the signs by applying the elastic radiation condition results in certain vertical slownesses, and hence coefficients, varying discontinuously and unphysically with the angle of incidence, and that choosing the signs so that the vertical slownesses vary continuously can also produce errors. We suggest three approaches for treating these cases. In the first approach, the signs are chosen so that the vertical slownesses vary continuously up to a certain angle of incidence (close to the elastic critical angle), with the elastic radiation condition being applied beyond that. We show that this is actually just an extension of the elastic radiation condition to complex-valued squared slownesses. In the spherical wave case in which a point source lies in the upper half-space, the approach also agrees with the results obtained by applying the saddle point method to approximate the integral for the reflected wavefield. This approximation is just geometrical ray theory. The first approach also produces coefficients with unphysical aspects, but these are confined to the critical zone, where geometrical ray theory is not valid anyway. Outside of this zone, the coefficients compare quite well with the elastic ones. In the second approach, real values of the horizontal slowness are used to compute the coefficients. This results in coefficients which are continuous and have no unphysical aspects, but do not compare as well with the elastic ones. The third approach involves using other paths in the complex plane (of horizontal slowness) to evaluate the coefficients. We show two examples. The first example is an approximation which involves replacing certain vertical slownesses with their complex conjugates before the coefficients are computed. This is equivalent to evaluating the horizontal slowness along a curve just above the real axis. The second example involves using a path which yields coefficients that are almost identical to the elastic ones. The third approach also results in continuous coefficients with no unphysical aspects, which compare well with the elastic ones.The errors mentioned above suggest to us that the problem of how to correctly compute plane-wave anelastic reflection and transmission coefficients, even in the apparently simple case of a homogeneous incident plane wave, still requires further study.

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“…This method may be used also for visco-elastic media if the necessary precautions, as discussed by Ruud (2006), are taken into account. The reflection coefficients of the fractured reservoir (Fig.…”

Section: Reflection Coefficientsmentioning

confidence: 99%

Effects of pore fluid pressure on the seismic response of a fractured carbonate reservoir

et al. 2007

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An effective medium model for the stress-dependent seismic properties of fractured reservoirs is developed here on the basis of a combination of a general theory of viscoelastic waves in rock-like composites with recently published formulae for deformation of communicating and interacting cavities (interconnected pores/cracks and fractures at finite concentration) under drained loading. The inclusion-based model operates withspheroidal cavities at two different length scales; namely, the microscopic scale of the pores and (grain-boundary) cracks, and the mesoscopic scale of the fractures (controlling the flow of fluid). The different cavity types can in principle have any orientation and aspect ratio, but the microscopic pores/cracks and mesoscopic fractures were here assumed to be randomly and vertically oriented, respectively. By using three different aspect ratios for the relatively round pores (representing the stiff part of the pore space) and a distribution of aspect ratios for the relatively flat cracks (representing the compliant part of the pore space), we obtained a good fit between theoretical predictions and ultrasonic laboratory measurements on an unfractured rock sample under dry conditions. By using a single aspect ratio for the mesoscopic fractures, we arrived at a higher-order microstructural model of fractured porous media which represents a generalization of the first-order model developed by Chapman et al. (2002Chapman et al. ( ,2003. The effect of cavity size was here modelled under the assumption that the characteristic time for wave-induced (squirt) flow at the scale of a particular cavity (pore/crack vs. fracture) is proportional with the relevant scale-size. In the modelling, we investigate the effect of a decreasing pore pressure with constant confining pressure (fixed depth), and hence, increasing effective pressure. The analysis shows that the attenuation-peak due to the mesoscopic fractures in the reservoir will move downward in frequency as the effective pressure increases. In the range of seismic frequencies, our modelling indicates that the P-wave velocities may change by more than 20% perpendicular to the fractures and close to 10% parallel to the fractures. In comparison, the vertical S-wave velocities change by only about 5% for both polarization directions (perpendicular and parallel to the fractures) when the effective pressure increases from 0 to 15 MPa. This change is mainly due to the overall change in porosity with pressure. The weak pressure dependence is a consequence of the fact that the S waves will only sense if the fractures are open or not, R. Agersborg et al. 90 Stud. Geophys. Geod., 51 (2007) and since all the fractures have the same aspect ratio, they will close at the same effective pressure (which is outside the analysed interval).Approximate reflection coefficients were computed for a model consisting of the fractured reservoir embedded as a layer in an isotropic shale and analysed with respect to variations in Amplitude Versus Offset and aZimuth (AVOZ) ...

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Ambiguous reflection coefficients for anelastic media

Cited by 37 publications

References 24 publications

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Difficulties with computing anelastic plane-wave reflection and transmission coefficients

Effects of pore fluid pressure on the seismic response of a fractured carbonate reservoir

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