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.

Multiparameter TTI tomography of P-wave reflection and VSP data

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC51-WC63 ◽  
Author(s):  
Xiaoxiang Wang ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Model Updating ◽  
Transversely Isotropic ◽  
P Wave ◽  
Ocean Bottom ◽  
Symmetry Direction ◽  
Direction Parallel ◽  
The North ◽  
Vsp Data ◽  
Anisotropy Parameters

Transversely isotropic models with a tilted symmetry axis (TTI media) are widely used in depth imaging of complex geologic structures. Here, we present a modification of a previously developed 2D P-wave tomographic algorithm for estimating heterogeneous TTI velocity fields and apply it to synthetic and field data. The symmetry-direction velocity [Formula: see text], anisotropy parameters [Formula: see text] and [Formula: see text], and symmetry-axis tilt [Formula: see text] are defined on a rectangular grid. To ensure stable reconstruction of the TTI parameters, reflection data are combined with walkaway vertical seismic profiling (VSP) traveltimes in joint tomographic inversion. To improve the convergence of the algorithm, we develop a three-stage model-updating procedure that gradually relaxes the constraints on the spatial variations of the anisotropy parameters, while the symmetry axis is kept orthogonal to the reflectors. Only at the final stage of the inversion are the parameters [Formula: see text], [Formula: see text], and [Formula: see text] updated on the same grid. We also incorporate geologic constraints into tomography by designing regularization terms that penalize parameter variations in the direction parallel to the interfaces. First, we examine the performance of the regularized joint tomography of reflection and VSP data for two sections of the BP TTI model that contain an anticline and a salt dome. All three TTI parameters in the shallow part of both sections (down to 5 km) are well resolved by the proposed model-updating process. Then, the algorithm is applied to a 2D section from 3D ocean-bottom seismic data acquired at Volve field in the North Sea. The inverted TTI model produces well-focused reflectors throughout the section and accurately positions the key horizons, which is confirmed by the available well markers.

Acoustic approximations for processing in transversely isotropic media

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 623-631 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
P Wave ◽  
Elastic Model ◽  
S Wave ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Two Parameters ◽  
Vti Media

When transversely isotropic (VTI) media with vertical symmetry axes are characterized using the zero‐dip normal moveout (NMO) velocity [[Formula: see text]] and the anisotropy parameter ηinstead of Thomsen’s parameters, time‐related processing [moveout correction, dip moveout (DMO), and time migration] become nearly independent of the vertical P- and S-wave velocities ([Formula: see text] and [Formula: see text], respectively). The independence on [Formula: see text] and [Formula: see text] is well within the limits of seismic accuracy, even for relatively strong anisotropy. The dependency on [Formula: see text] and [Formula: see text] reduces even further as the ratio [Formula: see text] decreases. In fact, for [Formula: see text], all time‐related processing depends exactly on only [Formula: see text] and η. This fortunate dependence on two parameters is demonstrated here through analytical derivations of time‐related processing equations in terms of [Formula: see text] and η. The time‐migration dispersion relation, the NMO velocity for dipping events, and the ray‐tracing equations extracted by setting [Formula: see text] (i.e., by considering VTI as acoustic) not only depend solely on [Formula: see text] and η but are much simpler than the counterpart expressions for elastic media. Errors attributed to this use of the acoustic assumption are small and may be neglected. Therefore, as in isotropic media, the acoustic model arising from setting [Formula: see text], although not exactly true for VTI media, can serve as a useful approximation to the elastic model for the kinematics of P-wave data. This approximation can boost the efficiency of imaging and DMO programs for VTI media as well as simplify their description.

scholarly journals P-Wave-Only Inversion of Challenging Walkaway VSP Data for Detailed Estimation of Local Anisotropy and Reservoir Parameters: A Case Study of Seismic Processing in Northern Poland

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2061
Author(s):  
Mateusz Zaręba ◽  
Tomasz Danek ◽  
Michał Stefaniuk
Keyword(s):  
Seismic Signal ◽  
Field Conditions ◽  
P Wave ◽  
Quality Data ◽  
Local Anisotropy ◽  
Processing Scheme ◽  
Vsp Data ◽  
Walkaway Vsp ◽  
Anisotropy Parameters ◽  
Detailed Interpretation

In this paper, we present a detailed analysis of walkaway vertical seismic profiling (VSP) data, which can be used to obtain Thomsen parameters using P-wave-only inversion. Data acquisition took place in difficult field conditions, which influenced the quality of the data. Therefore, this paper also shows a seismic data processing scheme that allows the estimation of correct polarization angles despite poor input data quality. Moreover, we showed that it is possible to obtain reliable and detailed values of Thomsen’s anisotropy parameters for data that are challenging due to extremely difficult field conditions during acquisition and the presence of an overburden of salt and anhydrite (Zechstein formation). This complex is known for its strong seismic signal-attenuating properties. We designed a special processing workflow with a signal-matching procedure that allows reliable estimation of polarization angles for low-quality data. Additionally, we showed that P-wave-only inversion for the estimation of local anisotropy parameters can be used as valuable additional input for detailed interpretation of geological media, even if anisotropy is relatively low.

Seismic anisotropy in the upper 500 m of the Southern Sydney Basin

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1901-1911 ◽  
Author(s):  
Milovan Urosević ◽  
Christopher Juhlin
Keyword(s):  
Elastic Constants ◽  
Seismic Anisotropy ◽  
Full Range ◽  
Transversely Isotropic ◽  
Real Data ◽  
Vertical Axis ◽  
P Wave ◽  
Small Range ◽  
P Waves ◽  
Vsp Data

An analysis of seismic anisotropy at a BHP mining site in the Southern Sydney Basin by combined use of crosshole and vertical seismic profiling (VSP) data is presented. The upper 250 m in this area is highly heterogeneous and has a major impact on the analysis of P-wave traveltimes. It is shown that using P-wave information solely would not, at least in this case, lead to any reasonable estimate of the elastic constants, in particular C13, even if the measurements contained a full range of incident angles. However, if the measurements of SV-waves are available, even over a small range of incident angles, then C13 is determined more accurately. P-wave velocities measured in the vertical and horizontal directions show that anisotropy is present in the area. Additional measurements, along different incident angles, indicate that the rock down to 500 m depth is predominantly transversely isotropic (TI) with a vertical axis of symmetry. The P-wave anisotropy can be approximated as elliptical. Using the elastic constants estimated from the data analyses, synthetic seismograms for heterogeneous TI media were generated. Comparison of the seismic modeling with real crosshole data shows that it is necessary to include both fault zones and gas accumulations in the model to qualitatively match the real data. By using SV-waves in the multioffset VSP data, reflectors are mapped more accurately than by using P-waves, even under the assumption of isotropy and in the presence of heterogeneity. Mapping of converted P-SV waves by a straight ray approach also produced better results than the corresponding isotropic P-wave mapping. Inclusion of elliptical anisotropy into Kirchhoff migration resulted in better P-wave images than using an isotopic migration code. We conclude that both P-wave VSP multioffset mapping and tomographic inversion methods need to account for anisotropy to be accurate in this area, while SV-waves may be handled using isotropic codes. The same is true for crosshole and surface seismic data.

scholarly journals Analysis of RTM extended images for VTI media

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. S139-S150 ◽  
Author(s):  
Vladimir Li ◽  
Ilya Tsvankin ◽  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Anisotropy Parameters ◽  
And Migration ◽  
Vti Media

Extended images obtained from reverse time migration (RTM) contain information about the accuracy of the velocity field and subsurface illumination at different incidence angles. Here, we evaluate the influence of errors in the anisotropy parameters on the shape of the residual moveout (RMO) in P-wave RTM extended images for VTI (transversely isotropic with a vertical symmetry axis) media. Using the actual spatial distribution of the zero-dip NMO velocity ([Formula: see text]), which could be approximately estimated by conventional techniques, we analyze the extended images obtained with distorted fields of the parameters [Formula: see text] and [Formula: see text]. Differential semblance optimization (DSO) and stack-power estimates are employed to study the sensitivity of focusing to the anisotropy parameters. We also build angle gathers to facilitate interpretation of the shape of RMO in the extended images. The results show that the signature of [Formula: see text] is dip-dependent, whereas errors in [Formula: see text] cause defocusing only if that parameter is laterally varying. Hence, earlier results regarding the influence of [Formula: see text] and [Formula: see text] on reflection moveout and migration velocity analysis remain generally valid in the extended image space for complex media. The dependence of RMO on errors in the anisotropy parameters provides essential insights for anisotropic wavefield tomography using extended images.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Da Shuai ◽  
Alexey Stovas ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Yang Zhao
Keyword(s):  
Standard Deviation ◽  
Elastic Wave ◽  
Significant Influence ◽  
Transversely Isotropic ◽  
Azimuth Angle ◽  
Effective Medium ◽  
P Wave ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Vertical Fractures

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures' azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the ( x2, x3) plane than that in the ( x1, x3) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium.

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.

VELOCITY ANISOTROPY MEASUREMENTS IN WELLS

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 900-916 ◽  
Author(s):  
D. M. Vander Stoep
Keyword(s):  
Seismic Waves ◽  
Layered Medium ◽  
Sedimentary Rocks ◽  
Transversely Isotropic ◽  
Anisotropy Factor ◽  
Propagation Time ◽  
Reflection Seismology ◽  
Simple Description ◽  
Velocity Anisotropy ◽  
The Difference

Sedimentary rocks are generally anisotropic to the propagation of seismic waves. Anisotropy can be defined as the difference between propagation time predicted by the simple theory of Snell’s Law and observed propagation time between two points in a layered medium that lie on a line oblique to the layers. This difference can be explained by the more complicated theory of wave propagation in transversely isotropic materials. In the zone about the vertical that is of interest in reflection seismology, the effect of anisotropy usually can be described geometrically by an anisotropy factor A. This simple description is not valid for propagation directions making large angles with the normal to the layers. The anisotropy factor as well as the vertical velocity can vary with depth. A method is given for determining the factor A as a function of depth from a continuous velocity log and a range of oblique shots into a well phone. The method is applied to two field examples. In one of the examples, it is shown by data obtained from the larger shooting distances that the simple A factor description is inadequate for higher angles of propagation direction.

Inversion of multicomponent, multiazimuth, walkaway VSP data for the stiffness tensor

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1022-1031 ◽  
Author(s):  
Pawan Dewangan ◽  
Vladimir Grechka
Keyword(s):  
Elastic Stiffness ◽  
P Wave ◽  
Vacuum Field ◽  
Stiffness Tensor ◽  
Slowness Surface ◽  
Data Set ◽  
S Waves ◽  
Stiffness Coefficients ◽  
Vsp Data ◽  
Walkaway Vsp

Vertical seismic profiling (VSP), an established technique, can be used for estimating in‐situ anisotropy that might provide valuable information for characterization of reservoir lithology, fractures, and fluids. The P‐wave slowness components, conventionally measured in multiazimuth, walkaway VSP surveys, allow one to reconstruct some portion of the corresponding slowness surface. A major limitation of this technique is that the P‐wave slowness surface alone does not constrain a number of stiffness coefficients that may be crucial for inferring certain rock properties. Those stiffnesses can be obtained only by combining the measurements of P‐waves with those of S (or PS) modes. Here, we extend the idea of Horne and Leaney, who proved the feasibility of joint inversion of the slowness and polarization vectors of P‐ and SV‐waves for parameters of transversely isotropic media with a vertical symmetry axis (VTI symmetry). We show that there is no need to assume a priori VTI symmetry or any other specific type of anisotropy. Given a sufficient polar and azimuthal coverage of the data, the polarizations and slownesses of P and two split shear (S1 and S2) waves are sufficient for estimating all 21 elastic stiffness coefficients cij that characterize the most general triclinic anisotropy. The inverted stiffnesses themselves indicate whether or not the data can be described by a higher‐symmetry model. We discuss three different scenarios of inverting noise‐contaminated data. First, we assume that the layers are horizontal and laterally homogeneous so that the horizontal slownesses measured at the surface are preserved at the receiver locations. This leads to a linear inversion scheme for the elastic stiffness tensor c. Second, if the S‐wave horizontal slowness at the receiver location is unknown, the elastic tensor c can be estimated in a nonlinear fashion simultaneously with obtaining the horizontal slowness components of S‐waves. The third scenario includes the nonlinear inversion for c using only the vertical slowness components and the polarization vectors of P‐ and S‐waves. We find the inversion to be stable and robust for the first and second scenarios. In contrast, errors in the estimated stiffnesses increase substantially when the horizontal slowness components of both P‐ and S‐waves are unknown. We apply our methodology to a multiazimuth, multicomponent VSP data set acquired in Vacuum field, New Mexico, and show that the medium at the receiver level can be approximated by an azimuthally rotated orthorhombic model.

Separating quasi-P-wave in transversely isotropic media with a vertical symmetry axis by synthesized pressure applied to ocean-bottom seismic data elastic reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C295-C307 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng ◽  
Chenlong Wang
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Wave Imaging ◽  
Obs Data

Quasi-P (qP)-wavefield separation is a crucial step for elastic P-wave imaging in anisotropic media. It is, however, notoriously challenging to quickly and accurately obtain separated qP-wavefields. Based on the concepts of the trace of the stress tensor and the pressure fields defined in isotropic media, we have developed a new method to rapidly separate the qP-wave in a transversely isotropic medium with a vertical symmetry axis (VTI) by synthesized pressure from ocean-bottom seismic (OBS) data as a preprocessing step for elastic reverse time migration (ERTM). Another key aspect of OBS data elastic wave imaging is receiver-side 4C records back extrapolation. Recent studies have revealed that receiver-side tensorial extrapolation in isotropic media with ocean-bottom 4C records can sufficiently suppress nonphysical waves produced during receiver-side reverse time wavefield extrapolation. Similarly, the receiver-side 4C records tensorial extrapolation was extended to ERTM in VTI media in our studies. Combining a separated qP-wave by synthesizing pressure and receiver-side wavefield reverse time tensorial extrapolation with the crosscorrelation imaging condition, we have developed a robust, fast, flexible, and elastic imaging quality improved method in VTI media for OBS data.

Sign in / Sign up

Export Citation Format

Share Document