scholarly journals Estimation of weak anisotropy parameters and fracture density of asymmetric fractures in monoclinic medium

2020 ◽  
Vol 17 (6) ◽  
pp. 1049-1064
Author(s):  
Zijian Ge ◽  
Shulin Pan ◽  
Jingye Li ◽  
Dongjun Zhang ◽  
Haoran Luo
Keyword(s):  
Wave Reflection ◽  
In Situ Stress ◽  
P Wave ◽  
Reflection Coefficients ◽  
Calculation Error ◽  
High Porosity ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Compliance Matrix ◽  
Amplitude Inversion

Abstract One of the typical anisotropic media is the monoclinic anisotropy (MA) medium, which is formed by embedding two sets of non-orthogonal fracture sets into an isotropic or vertical transverse isotropic (VTI) background medium. Weak anisotropy (WA) parameters and fracture density provide important in situ stress and high-porosity zone information. Estimation of WA parameters and fracture density of MA medium by prestack seismic amplitude inversion is important for shale reservoir characterisation. We derive the expression of generalised WA parameters in a basic reflection coefficients formula of MA medium by incorporating a stiffness matrix of VTI background and disturbance compliance matrix of asymmetric fracture. We then re-express the P-wave reflection coefficients in terms of WA parameters and fracture compliance tensors. To achieve the direct inversion of fracture density, we rewrite the linearised expression of P-wave reflection coefficients related to WA parameters and fracture density. Finally, under the Bayesian framework, the WA parameters and fracture density are estimated by using the amplitude versus offset and azimuth (AVOA) inversion parameters. We use a Monte Carlo simulation to test the effect of uncertainties in the priori information about fracture property parameters. The application of synthetic seismic gathers show that the proposed inversion strategy is reliable within moderate noise. Compared with the results obtained by using inversion based on a rotationally invariant fracture, the test indicates that a fracture model with a simplified shape or wrong assumption will increase calculation error and reduce the inversion accuracy.

scholarly journals Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium

2020 ◽  
Vol 10 (15) ◽  
pp. 5136 ◽  
Author(s):  
Zijian Ge ◽  
Shulin Pan ◽  
Jingye Li
Keyword(s):  
Fractured Rock ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Wave ◽  
Inversion Method ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Amplitude Versus Offset ◽  
Porosity And Permeability ◽  
Transverse Isotropic

In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.

scholarly journals Analysis of fluid substitution in a porous and fractured medium

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA157-WA166 ◽  
Author(s):  
Samik Sil ◽  
Mrinal K. Sen ◽  
Boris Gurevich
Keyword(s):  
Water Saturation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Reflection Coefficients ◽  
Fluid Substitution ◽  
Fracture Density ◽  
Maximum Increase ◽  
Amplitude Variation With Offset ◽  
Fractured Medium ◽  
Medium Change

To improve quantitative interpretation of seismic data, we analyze the effect of fluid substitution in a porous and fractured medium on elastic properties and reflection coefficients. This analysis uses closed-form expressions suitable for fluid substitution in transversely isotropic media with a horizontal symmetry axis (HTI). For the HTI medium, the effect of changing porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients are examined. The effects of fracture density on these four parameters are also studied. For the model used in this study, a 35% increase in porosity lowers the value of P-wave moduli by maximum of 45%. Consistent with the reduction in P-wave moduli, P-wave velocities also decrease by maximum of 17% with a similar increment in porosity. The reduction is always larger for the horizontal P-wave modulus than for the vertical one and is nearly independent of fracture density. The magnitude of the anisotropic parameters of the fractured medium also changes with increased porosity depending on the changes in the value of P-wave moduli. The reflection coefficients at an interface of the fractured medium with an isotropic medium change in accordance with the above observations and lead to an increase in anisotropic amplitude variation with offset (AVO) gradient with porosity. Additionally, we observe a maximum increase in P-wave modulus and velocity by 30% and 8%, respectively, with a 100% increase in water saturation. Water saturation also changes the anisotropic parameters and reflection coefficients. Increase in water saturation considerably increases the magnitude of the anisotropic AVO gradient irrespective of fracture density. From this study, we conclude that porosity and water saturation have a significant impact on the four studied parameters and the impacts are seismically detectable.

Reflection coefficients in attenuative anisotropic media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB193-WB202 ◽  
Author(s):  
Jyoti Behura ◽  
Ilya Tsvankin
Keyword(s):  
Plane Wave ◽  
Wave Reflection ◽  
Symmetry Plane ◽  
Anisotropic Media ◽  
P Wave ◽  
Substantial Contribution ◽  
Reflection Coefficients ◽  
Slowness Vector ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy

Such reservoir rocks as tar sands are characterized by significant attenuation and, in some cases, attenuation anisotropy. Most existing attenuation studies are focused on plane-wave attenuation coefficients, which determine the amplitude decay along the raypath of seismic waves. Here we study the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on transversely isotropic models with a vertical symmetry axis (VTI). Concise analytic solutions obtained by linearizing the exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation must be strong, with the quality factor [Formula: see text] not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-styleattenuation-anisotropy parameters is relatively large. In general, the linearized reflection coefficients in attenuative media include velocity-anisotropy parameters but have almost “isotropic” dependence on attenuation. Our formalism also helps evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP- and PS-wave reflection coefficients, which makes conventional amplitude-variation-with-offset (AVO) analysis inadequate for strongly attenuative media. For instance, an incident P-wave with a nonzero inhomogeneity angle generates a mode-converted PS-wave at normal incidence, even if both half-spaces have a horizontal symmetry plane. The developed linearized solutions can be used in AVO inversion for highly attenuative (e.g., gas-sand and heavy-oil) reservoirs.

Quartic reflection moveout in a weakly anisotropic dipping layer

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. D1-D13 ◽  
Author(s):  
Vladimir Grechka ◽  
Andrés Pech
Keyword(s):  
General Formula ◽  
Anisotropic Medium ◽  
Seismic Data ◽  
Wave Reflection ◽  
P Wave ◽  
Weak Anisotropy ◽  
Effective Anisotropy ◽  
Isotropic Solid ◽  
Strike Direction

Deviations of P-wave reflection traveltimes from a hyperbola, called the nonhyperbolic or quartic moveout, need to be handled properly while processing long-spread seismic data. As observed nonhyperbolic moveout is usually attributed to the presence of anisotropy, we devote our paper to deriving and analyzing a general formula that describes an azimuthally varying quartic moveout coefficient in a homogeneous, weakly anisotropic medium above a dipping, mildly curved reflector. To obtain the desired expression, we consistently linearize all quantities in small stiffness perturbations from a given isotropic solid. Our result incorporates all known weak-anisotropy approximations of the quartic moveout coefficient and extends them further to triclinic media. By comparing our approximation with nonhyperbolic moveout obtained from the ray-traced reflection traveltimes, we find that the former predicts azimuthal variations of the quartic moveout when its magnitude is less than 20% of the corresponding hyperbolic moveout term. We also study the influence of reflector curvature on nonhyperbolic moveout. It turns out that the curvature produces no quartic moveout in the reflector strike direction, where the anisotropy-induced moveout nonhyperbolicity is usually nonnegligible. Thus, the presence of nonhyperbolic moveout along the reflector strike might indicate effective anisotropy.

Quartic moveout coefficient for a dipping azimuthally anisotropic layer

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 699-707 ◽  
Author(s):  
Andrés Pech ◽  
Ilya Tsvankin
Keyword(s):  
Reservoir Characterization ◽  
Fractured Reservoirs ◽  
Symmetry Plane ◽  
Exact Expression ◽  
Naturally Fractured Reservoirs ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Velocity Anisotropy

Interpretation and inversion of azimuthally varying nonhyperbolic reflection moveout requires accounting for both velocity anisotropy and subsurface structure. Here, our previously derived exact expression for the quartic moveout coefficient A4 is applied to P‐wave reflections from a dipping interface overlaid by a medium of orthorhombic symmetry. The weak‐anisotropy approximaton for the coefficient A4 in a homogeneous orthorhombic layer is controlled by the anellipticity parameters η(1), η(2), and η(3), which are responsible for time processing of P‐wave data. If the dip plane of the reflector coincides with the vertical symmetry plane [x1, x3], A4 on the dip line is proportional to the in‐plane anellipticity parameter η(2) and always changes sign for a dip of 30○. The quartic coefficient on the strike line is a function of all three η–parameters, but for mild dips it is mostly governed by η(1)—the parameter defined in the incidence plane [x2, x3]. Whereas the magnitude of the dip line A4 typically becomes small for dips exceeding 45○, the nonhyperbolic moveout on the strike line may remain significant even for subvertical reflectors. The character of the azimuthal variation of A4 depends on reflector dip and is quite sensitive to the signs and relative magnitudes of η(1), η(2), and η(3). The analytic results and numerical modeling show that the azimuthal pattern of the quartic coefficient can contain multiple lobes, with one or two azimuths of vanishing A4 between the dip and strike directions. The strong influence of the anellipticity parameters on the azimuthally varying coefficient A4 suggests that nonhyperbolic moveout recorded in wide‐azimuth surveys can help to constrain the anisotropic velocity field. Since for typical orthorhombic models that describe naturally fractured reservoirs the parameters η(1,2,3) are closely related to the fracture density and infill, the results of azimuthal nonhyperbolic moveout analysis can also be used in reservoir characterization.

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