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.

Determination of the principal directions of azimuthal anisotropy from P-wave seismic data

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 692-706 ◽  
Author(s):  
Subhashis Mallick ◽  
Kenneth L. Craft ◽  
Laurent J. Meister ◽  
Ronald E. Chambers
Keyword(s):  
Anisotropic Medium ◽  
Seismic Data ◽  
Principal Direction ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Amplitude Variation ◽  
S Waves ◽  
Wave Data ◽  
Principal Directions ◽  
Qualitative Measure

In an azimuthally anisotropic medium, the principal directions of azimuthal anisotropy are the directions along which the quasi-P- and the quasi-S-waves propagate as pure P and S modes. When azimuthal anisotropy is induced by oriented vertical fractures imposed on an azimuthally isotropic background, two of these principal directions correspond to the directions parallel and perpendicular to the fractures. S-waves propagating through an azimuthally anisotropic medium are sensitive to the direction of their propagation with respect to the principal directions. As a result, primary or mode‐converted multicomponent S-wave data are used to obtain the principal directions. Apart from high acquisition cost, processing and interpretation of multicomponent data require a technology that the seismic industry has not fully developed. Anisotropy detection from conventional P-wave data, on the other hand, has been limited to a few qualitative studies of the amplitude variation with offset (AVO) for different azimuthal directions. To quantify the azimuthal AVO, we studied the amplitude variation with azimuth for P-wave data at fixed offsets. Our results show that such amplitude variation with azimuth is periodic in 2θ, θ being the orientation of the shooting direction with respect to one of the principal directions. For fracture‐induced anisotropy, this principal direction corresponds to the direction parallel or perpendicular to the fractures. We use this periodic azimuthal dependence of P-wave reflection amplitudes to identify two distinct cases of anisotropy detection. The first case is an exactly determined one, where we have observations from three azimuthal lines for every common‐midpoint (CMP) location. We derive equations to compute the orientation of the principal directions for such a case. The second case is an overdetermined one where we have observations from more than three azimuthal lines. Orientation of the principal direction from such an overdetermined case can be obtained from a least‐squares fit to the reflection amplitudes over all the azimuthal directions or by solving many exactly determined problems. In addition to the orientation angle, a qualitative measure of the degree of azimuthal anisotropy can also be obtained from either of the above two cases. When azimuthal anisotropy is induced by oriented vertical fractures, this qualitative measure of anisotropy is proportional to fracture density. Using synthetic seismograms, we demonstrate the robustness of our method in evaluating the principal directions from conventional P-wave seismic data. We also apply our technique to real P-wave data, collected over a wide source‐to‐receiver azimuth distribution. Computations using our method gave an orientation of the principal direction consistent with the general fracture orientation in the area as inferred from other geological and geophysical evidence.

Physical modeling of overburden effects

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. T37-T45 ◽  
Author(s):  
Mu Luo ◽  
Mamoru Takanashi ◽  
Kazuo Nakayama ◽  
Teruya Ezaka
Keyword(s):  
Seismic Data ◽  
Physical Modeling ◽  
Wave Reflection ◽  
Seismic Anisotropy ◽  
Middle Layer ◽  
P Wave ◽  
Scale Model ◽  
Reservoir Properties ◽  
P Waves ◽  
High Degree

Reservoir properties can be inferred from the amount of anisotropy estimated from seismic data. Unfortunately, irregularities in the formations above the reservoir unit can mask or overprint the true seismic anisotropy of the reservoir unit. This overburden effect subjects the measured reservoir seismic anisotropy to a high degree of uncertainty. We investigate this overburden effect on P-waves with a three-layer ultrasonic laboratory-scale model whose middle layer contains localized, gas-filled vertical fractures. We analyze the reflection amplitudes and traveltimes of a P-wave reflection event from below the overburden to understand the overburden effect on anisotropy analysis and imaging. Our study shows that steps must be taken to reduce the P-wave overburden effect when significant irregularities occur in the formations above the reservoir unit.

Weak-anisotropy moveout approximations for P-waves in homogeneous TOR layers

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. WA23-WA32 ◽  
Author(s):  
Véronique Farra ◽  
Ivan Pšenčík
Keyword(s):  
Wave Reflection ◽  
P Wave ◽  
Homogeneous Layer ◽  
Orthorhombic Symmetry ◽  
Euler Angles ◽  
Weak Anisotropy ◽  
P Waves ◽  
Anisotropy Parameters ◽  
Dip Angle

We have developed approximate P-wave reflection moveout formulas for a homogeneous layer of orthorhombic symmetry overlying a horizontal or dipping reflector. The symmetry planes of an orthorhombic medium in the layer can be arbitrarily oriented. The formulas are based on the weak-anisotropy approximation. Thus, their accuracy depends not only on the strength of anisotropy, but also on the deviations of the phase and ray velocities. Nevertheless, the performed tests indicate that for P-wave anisotropy of approximately 25%, the maximum relative traveltime errors of the formulas do not exceed 3%. The formulas are expressed in terms of six P-wave weak-anisotropy parameters and three Euler angles specifying the orientation of the symmetry planes of the orthorhombic medium. In the case of a dipping reflector, the formulas also depend on the apparent dip angle of the reflector.

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.

Feasibility study of fracture interpretation using multicomponent seismic data: SEAM II Barrett model

2021 ◽  
pp. 1-52
Author(s):  
Youfang Liu ◽  
James Simmons
Keyword(s):  
Feasibility Study ◽  
Seismic Data ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Reservoir Properties ◽  
Lateral Velocity ◽  
Converted Wave ◽  
Weak Anisotropy ◽  
Velocity Anisotropy ◽  
1D Model

Several P-wave azimuthal anisotropy studies have been conducted for the SEAM II Barrett model data. However, these analyses provide fracture property estimation that is inconsistent with the actual model properties. Therefore, we perform a feasibility study to understand the influence of the overburden and reservoir properties, and the processing and inversion steps, which together determine the success of the fracture interpretation from seismic data. 1D model properties (orthorhombic for both overburden and reservoir) are first extracted from the actual Barrett model properties at two locations. Anisotropic prestack reflectivity modeling exposes the true orthorhombic response of the 1D medium in the form of Common Offset and Common Azimuth (COCA) gathers. The true anisotropic response is obscured in the Barrett data (generated by finite element modeling) due to the mild lateral velocity variations and orthorhombic anisotropy in the overburden. We then expose the reservoir anisotropic response by using an isotropic overburden in the reflectivity modeling. This shows that the P-wave VVAZ responses generated by the reservoir itself are weak, which leads to an unstable VVAZ inversion to estimate the interval NMO velocity anisotropy. The reservoir thickness (125m or 65ms TWT) or NMO velocity anisotropy (6-7%) needs to be at least doubled to obtain a stable VVAZ inversion. Anisotropic geometrical-spreading correction improves the amplitude-versus-azimuth (AVAZ) inversion results when reflectivity modeling models orthorhombic overburden. The converted wave ( C-wave) has a stronger VVAZ response compared to the P-wave. We suggest that the C-wave data could be useful to constrain fracture interpretation in the Barrett model. We conclude that the results of previous studies are due to the combination of the residual influence of overburden after processing and imaging, and the weak anisotropy responses from the reservoir.

Reflection from a dipping plane—Transversely isotropic solid

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 851-855 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Numerical Investigation ◽  
Elastic Constants ◽  
Wave Reflection ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Isotropic Solid ◽  
Dip Angle

CMP stacking velocities for a P‐wave reflection from a dipping plane underlying a transversely isotropic solid are, after correction by the cosine of the dip angle, nearly independent of the dip angle if the symmetry axis of the solid is perpendicular to the reflector. If the symmetry axis is perpendicular to the surface, stacking velocities vary, after correction with the cosine of the dip angle, and predicting the amount and dependence on dip angle requires numerical investigation for each solid, since the stacking velocities may increase, decrease, or go through an extremum as the dip increases. The exact behavior depends on the elastic constants of the solid.

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