Seismic critical-angle anisotropy analysis in the τ -p domain

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. A53-A57 ◽  
Author(s):  
Samik Sil ◽  
Mrinal K. Sen
Keyword(s):  
Critical Angle ◽  
Seismic Anisotropy ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Seismic Line ◽  
Full Wave ◽  
Current Implementation ◽  
Approximation Errors ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry

Seismic critical-angle reflectometry is a relatively new field for estimating seismic anisotropy parameters. The theory relates changes in the critical angle with azimuth of the seismic line to the principal axis and anisotropy parameters. Current implementation of the critical-angle reflectometry process has certain shortcomings in that the critical angle is determined from critical offset and the process is vulnerable to different approximation errors. Seismic critical-angle analysis in the plane-wave [Formula: see text] domain can handle these issues and has the potential to become an independent tool for estimating anisotropy parameters. The theory of seismic critical-angle reflectometry is modified to make it suitable for [Formula: see text] domain analysis. Then using full-wave synthetic seismograms at three different azimuths for a transversely isotropic medium with a horizontal axis of symmetry (HTI), the effectiveness of anisotropy parameter estimation is demonstrated.

Relationships between the anisotropy parameters for transversely isotropic mudrocks

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR195-MR203
Author(s):  
Fuyong Yan ◽  
Lev Vernik ◽  
De-Hua Han
Keyword(s):  
Elastic Properties ◽  
Seismic Anisotropy ◽  
Measurement Data ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
The Other ◽  
Quality Analysis ◽  
Directional Bias ◽  
Empirical Relations ◽  
Anisotropy Parameters

Studying the empirical relations between seismic anisotropy parameters is important for the simplification and practical applications of seismic anisotropy. The elastic properties of mudrocks are often described by transverse isotropy. Knowing the elastic properties in the vertical and horizontal directions, a sole oblique anisotropy parameter determines the pattern of variation of the elastic properties of a transversely isotropic (TI) medium in all of the other directions. The oblique seismic anisotropy parameter [Formula: see text], which determines seismic reflection moveout behavior, is important in anisotropic seismic data processing and interpretation. Compared to the other anisotropy parameters, the oblique anisotropy parameter is more sensitive to the measurement error. Although, theoretically, only one oblique velocity is needed to determine the oblique anisotropy parameter, the uncertainty can be greatly reduced if multiple oblique velocities in different directions are measured. If a mudrock is not a perfect TI medium but it is expediently treated as one, then multiple oblique velocity measurements in different directions should lead to a more representative approximation of [Formula: see text] or [Formula: see text] because the directional bias can be reduced. Based on a data quality analysis of the laboratory seismic anisotropy measurement data from the literature, we found that there are strong correlations between the oblique anisotropy parameter and the principal anisotropy parameters when data points of more uncertainty are excluded. Examples of potential applications of these empirical relations are discussed.

scholarly journals Scanning anisotropy parameters in complex media

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. U13-U22 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Anisotropic Medium ◽  
Homogeneous Medium ◽  
Transversely Isotropic ◽  
Transient Behavior ◽  
Complex Media ◽  
Linear Partial Differential Equations ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry ◽  
Ti Media ◽  
Taylor’S Series

Parameter estimation in an inhomogeneous anisotropic medium offers many challenges; chief among them is the trade-off between inhomogeneity and anisotropy. It is especially hard to estimate the anisotropy anellipticity parameter η in complex media. Using perturbation theory and Taylor’s series, I have expanded the solutions of the anisotropic eikonal equation for transversely isotropic (TI) media with a vertical symmetry axis (VTI) in terms of the independent parameter η from a generally inhomogeneous elliptically anisotropic medium background. This new VTI traveltime solution is based on a set of precomputed perturbations extracted from solving linear partial differential equations. The traveltimes obtained from these equations serve as the coefficients of a Taylor-type expansion of the total traveltime in terms of η. Shanks transform is used to predict the transient behavior of the expansion and improve its accuracy using fewer terms. A homogeneous medium simplification of the expansion provides classical nonhyperbolic moveout descriptions of the traveltime that are more accurate than other recently derived approximations. In addition, this formulation provides a tool to scan for anisotropic parameters in a generally inhomogeneous medium background. A Marmousi test demonstrates the accuracy of this approximation. For a tilted axis of symmetry, the equations are still applicable with a slightly more complicated framework because the vertical velocity and δ are not readily available from the data.

Analysis of seismic anisotropy parameters for sedimentary strata

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D495-D502 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Samik Sil ◽  
Xue-Lian Chen
Keyword(s):  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Measurement Data ◽  
Transversely Isotropic ◽  
Theoretical Expression ◽  
Strong Correlations ◽  
Backus Averaging ◽  
Anisotropy Parameters ◽  
Intrinsic Anisotropy ◽  
Gas Bearing

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.

The measurement of weak anisotropy with the generalized reciprocal method

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1583-1591 ◽  
Author(s):  
Derecke Palmer
Keyword(s):  
Phase Velocity ◽  
Critical Angle ◽  
Seismic Velocity ◽  
Anisotropy Parameter ◽  
Anisotropy Factor ◽  
Weak Anisotropy ◽  
Refraction Tomography ◽  
Anisotropy Parameters ◽  
Reciprocal Method ◽  
Refraction Data

Anisotropy parameters can be determined from seismic refraction data using the generalized reciprocal method (GRM) for a layer in which the velocity can be described with the Crampin approximation for transverse isotropy. The parameters are the standard anisotropy factor, which is the horizontal velocity divided by the vertical velocity, and a second poorly determined parameter which, for weak anisotropy, is approximated by a linear relationship with the anisotropy factor. Although only one anisotropy parameter is effectively determined, the second parameter is essential to ensure that the anisotropy does not degenerate to the elliptical condition which is indeterminate using the approach described in this paper. The anisotropy factor is taken as the value for which the phase velocity at the critical angle given by the Crampin equation is equal to the average velocity computed with the optimum XY value obtained from a GRM analysis of the refraction data. The anisotropy parameters can be used to improve the estimate of the refractor velocity, which can exhibit marked dip effects when the overlying layer is anisotropic. In a model study, depths computed with the phase velocity at the critical angle are within 3% of the true values, whereas those calculated with the horizontal phase velocity (which assumes isotropy) are greater than the true depths by about 25%. Anisotropy illustrates the pitfalls of model‐based inversion strategies, which seek agreement between the travetime data and the computed response of the model. With anisotropic layers, the traveltime data provide the seismic velocity in the overlying layer in the horizontal direction, whereas the seismic velocity near the critical angle is required for depth computations. If anisotropy is applicable, then the GRM using the methods described in this paper is able to provide a good starting model for other approaches, such as refraction tomography.

P‐wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 713-722 ◽  
Author(s):  
Andreas Rüger
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Numerical Solutions ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Horizontal Axis ◽  
P Wave ◽  
Reflection Coefficients ◽  
Gradient Term ◽  
Axis Of Symmetry

The study of P‐wave reflection coefficients in anisotropic media is important for amplitude variation with offset (AVO) analysis. While numerical evaluation of the reflection coefficient is straightforward, numerical solutions do not provide analytic insight into the influence of anisotropy on the AVO signature. To overcome this difficulty, I present an improved approximation for P‐wave reflection coefficients at a horizontal boundary in transversely isotropic media with vertical axis of symmetry (VTI media). This solution has the same AVO‐gradient term describing the low‐order angular variation of the reflection coefficient as the equations published previously, but is more accurate for large incidence angles. The refined approximation is then extended to transverse isotropy with a horizontal axis of symmetry (HTI), which is caused typically by a system of vertical cracks. Comparison of the approximate reflection coefficients for P‐waves incident in the two vertical symmetry planes of HTI media indicates that the azimuthal variation of the AVO gradient is a function of the shear‐wave splitting parameter γ, and the anisotropy parameter describing P‐wave anisotropy for nearvertical propagation in the vertical plane containing the symmetry axis.

scholarly journals An analysis of AVO inversion for postcritical offsets in HTI media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. N11-N20 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Tariq Alkhalifah
Keyword(s):  
Critical Angle ◽  
Azimuthal Angle ◽  
Spherical Wave ◽  
Transversely Isotropic ◽  
Resolving Power ◽  
Reflection Coefficients ◽  
Avo Analysis ◽  
Avo Inversion ◽  
Hti Media ◽  
Anisotropy Parameters

Azimuthal variations of wavefield characteristics, such as traveltime or reflection amplitude, play an important role in the identification of fractured media. A transversely isotropic medium with a horizontal symmetry axis (HTI medium) is the simplest azimuthally anisotropic model typically used to describe one set of vertical fractures. There exist many techniques in industry to recover anisotropic parameters based on moveout equations and linearized reflection coefficients using such a model. However, most of the methods have limitations in defining properties of the fractures due to linearizations and physical approximations used in their development. Thus, azimuthal analysis of traveltimes based on normal moveout ellipses recovers a maximum of three medium parameters instead of the required five. Linearizations made in plane-wave reflection coefficients (PWRCs) limit the amplitude-versus-offset (AVO) analysis to small incident angles and weak-contrast interfaces. Inversion based on azimuthal AVO for small offsets encounters nonuniqueness in the resolving power of the anisotropy parameters. Extending the AVO analysis and inversion to and beyond the critical reflection angle increases the amount of information recovered from the medium. However, well-accepted PWRCs are not valid in the vicinity of the critical angle and beyond it, due to frequency and spherical wave effects. Recently derived spherical and effective reflection coefficient (ERC) methods overcome this problem. We extended the ERCs approach to HTI media to analyze the potential of near- and postcritical reflections in azimuthal AVO analysis. From the sensitivity analysis, we found that ERCs are sensitive to different sets of parameters prior to and beyond the critical angle, which is useful in enhancing our resolution of the anisotropy parameters. Additionally, the resolution of the parameters depends on a sufficient azimuthal coverage in the acquisition setup. The most stable AVO results for the azimuthal acquisition setup with minimum number of lines (three) are achieved when the azimuthal angle between lines is greater than 45°.

Diffraction traveltime approximation for TI media with an inhomogeneous background

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC103-WC111 ◽  
Author(s):  
Umair bin Waheed ◽  
Tariq Alkhalifah ◽  
Alexey Stovas
Keyword(s):  
Seismic Data ◽  
Eikonal Equation ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
Best Fitting ◽  
Axis Of Symmetry ◽  
Ti Media

Diffractions in seismic data contain valuable information that can help improve our modeling capability for better imaging of the subsurface. They are especially useful for anisotropic media because they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. We develop a scheme for diffraction traveltime computations based on perturbation of the anellipticity anisotropy parameter for transversely isotropic media with tilted axis of symmetry (TTI). The expansion, therefore, uses an elliptically anisotropic medium with tilt as the background model. This formulation has advantages on two fronts: first, it alleviates the computational complexity associated with solving the TTI eikonal equation, and second, it provides a mechanism to scan for the best-fitting anellipticity parameter [Formula: see text] without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameter [Formula: see text]. The accuracy of such an expansion is further enhanced by the use of Shanks transform. We established the effectiveness of the proposed formulation with tests on a homogeneous TTI model and complex media such as the Marmousi and BP models.

Simplified anisotropy parameters for transversely isotropic sedimentary rocks

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1933-1935 ◽  
Author(s):  
Colin M. Sayers
Keyword(s):  
Elastic Constants ◽  
Sedimentary Rocks ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
P Wave ◽  
Time Migration ◽  
Vsp Data ◽  
Walkaway Vsp ◽  
Anisotropy Parameters ◽  
The Difference

Sedimentary rocks frequently possess an anisotropic structure resulting, for example, from fine scale layering, the presence of oriented microcracks or fractures, or the preferred orientation of nonspherical grains or anisotropic minerals. For many rocks the anisotropy may be described, to a good approximation, as being transversely isotropic. The purpose of this note is to present simplified anisotropy parameters for these rocks that are valid when the P‐wave normal moveout (NMO) and vertical velocities differ by less than 25%. This condition appears reasonable since depths calculated from P‐wave stacking velocities are often within 10% of actual depths (Winterstein, 1986). It is found that when this condition is satisfied the elastic constants [Formula: see text] and [Formula: see text] affect the P‐wave NMO velocity and anellipticity only through the combination [Formula: see text], a combination of elastic constants that can be determined using walkaway VSP data (Miller et al., 1993). The anellipticity quantifies the deviation of the P‐phase slowness from an ellipse and also determines the difference between the vertical and NMO velocities for SV‐waves. Helbig (1983) has shown that a time‐migrated section for which elliptical anisotropy has been taken into account is identical to one that has been determined under the assumption of isotropy. The anellipticity is therefore the important anisotropy parameter for anisotropic time migration. The results given are of interest for anisotropic velocity analysis, time migration, and time‐to‐depth conversion.

Layer-induced seismic anisotropy from full-wave sonic logs: Theory, application, and validation

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. D183-D190 ◽  
Author(s):  
Christopher L. Liner ◽  
Tong W. Fei
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Seismic Anisotropy ◽  
Seismic Data Processing ◽  
Dominant Wavelength ◽  
Depth Migration ◽  
Full Wave ◽  
Theory Application ◽  
Anisotropy Parameters ◽  
Intrinsic Anisotropy

Thin isotropic elastic layering in the earth is one cause of seismic VTI anisotropy, along with intrinsic anisotropy and fractures. An important issue related to the routine use of VTI seismic data processing is the estimation of the necessary parameters. The full set of layer-induced VTI anisotropy parameters can be computed from full-wave sonic and density log data using Backus averaging. Intrinsic anisotropy can be incorporated if it is known from laboratory analysis. The isotropic layering method is applied to six wells in eastern Saudi Arabia, and the estimated anisotropy parameters are persistent across distances of many kilometers. This leads to the possibility of parameter estimation at sparse well locations for use in seismic data processing. Validation is demonstrated by direct numerical simulation of elastic wavefields in original and Backus-averaged earth models with various window lengths. We observe precise equivalence of the full wavefield when the averaging length is less than or equal to one-third of the minimum dominant wavelength. First arrival information, used in depth migration, is preserved with much longer averaging windows, up to twice the minimum dominant wavelength.

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