Reflection moveout inversion for horizontal transverse isotropy: Accuracy, limitation, and acquisition

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 222-231 ◽  
Author(s):  
Abdulfattah Al‐Dajani ◽  
Tariq Alkhalifah
Keyword(s):  
Parameter Estimation ◽  
Vertical Velocity ◽  
Transverse Isotropy ◽  
Angular Separation ◽  
P Wave ◽  
Velocity Anisotropy ◽  
Hti Media ◽  
Inversion Procedure ◽  
Anisotropy Strength

Horizontal transverse isotropy (HTI) is the simplest azimuthally anisotropic model used to describe vertical fracturing in an isotropic matrix. Assuming that the subsurface is laterally homogeneous, and using the elliptical variation of P-wave NMO velocity with azimuth measured in at least three different source‐to‐receiver orientations, we can estimate three key parameters of HTI media: the vertical velocity, anisotropy, and the azimuth of the symmetry axis. Such parameter estimation is sensitive to the angular separation between the survey lines in 2-D acquisition or, equivalently, to source‐to‐receiver azimuths in 3-D acquisition and the set of azimuths used in the inversion procedure. The accuracy in estimating the azimuth, in particular, is also sensitive to the strength of anisotropy, while the accuracy in resolving vertical velocity and anisotropy is about the same for any strength of anisotropy. To maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the source‐to‐receiver directions 60° apart when only three directions are used. This requirement is feasible in land seismic data acquisition where wide azimuthal coverage can be designed. In marine streamer acquisition, however, the azimuthal data coverage is limited. Multiple survey directions are necessary to achieve such wide azimuthal coverage in streamer surveys. To perform the inversion using three azimuth directions, 60° apart, an HTI layer overlain by an azimuthally isotropic overburden should have a time thickness, relative to the total time, of at least the ratio of the error in the NMO (stacking) velocity to the interval anisotropy strength of the HTI layer. Having more than three source‐to‐receiver azimuths (e.g., full azimuthal coverage), however, provides a useful data redundancy that enhances the quality of the estimates, thus allowing acceptable parameter estimation at smaller relative thicknesses.

Moveout inversion of P-wave data for horizontal transverse isotropy

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1219-1229 ◽  
Author(s):  
Pedro Contreras ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Anisotropic Parameter ◽  
Data Set ◽  
Velocity Models ◽  
Wave Data ◽  
Hti Media

The transversely isotropic model with a horizontal symmetry axis (HTI media) has been extensively used in seismological studies of fractured reservoirs. In this paper, a parameter‐estimation technique originally developed by Grechka and Tsvankin for the more general orthorhombic media is applied to horizontal transverse isotropy. Our methodology is based on the inversion of azimuthally‐dependent P-wave normal‐moveout (NMO) velocities from horizontal and dipping reflectors. If the NMO velocity of a given reflection event is plotted in each azimuthal direction, it forms an ellipse determined by three combinations of medium parameters. The NMO ellipse from a horizontal reflector in HTI media can be inverted for the azimuth β of the symmetry axis, the vertical velocity [Formula: see text], and the Thomsen‐type anisotropic parameter δ(V). We describe a technique for obtaining the remaining (for P-waves) anisotropic parameter η(V) (or ε(V)) from the NMO ellipse corresponding to a dipping reflector of arbitrary azimuth. The interval parameters of vertically inhomogeneous HTI media are recovered using the generalized Dix equation that operates with NMO ellipses for horizontal and dipping events. High accuracy of our method is confirmed by inverting a synthetic multiazimuth P-wave data set generated by ray tracing for a layered HTI medium with depth‐varying orientation of the symmetry axis. Although estimation of η(V) can be carried out by the algorithm developed for orthorhombic media, for more stable results the HTI model has to be used from the outset of the inversion procedure. It should be emphasized that P-wave conventional‐spread moveout data provide enough information to distinguish between HTI and lower‐symmetry models. We show that if the medium has the orthorhombic symmetry and is sufficiently different from HTI, the best‐fit HTI model cannot match the NMO ellipses for both a horizontal and a dipping event. The anisotropic coefficients responsible for P-wave moveout can be combined to estimate the crack density and predict whether the cracks are fluid‐filled or dry. A unique feature of the HTI model that distinguishes it from both vertical transverse isotropy and orthorhombic media is that moveout inversion provides not just zero‐dip NMO velocities and anisotropic coefficients, but also the true vertical velocity. As a result, reflection P-wave data acquired over HTI formations can be used to build velocity models in depth and perform anisotropic depth processing.

VTI anisotropic corrections and effective parameter estimation after isotropic prestack depth migration

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. D35-D43 ◽  
Author(s):  
Moshe Reshef ◽  
Murray Roth
Keyword(s):  
Parameter Estimation ◽  
Vertical Velocity ◽  
Transverse Isotropy ◽  
Real Data ◽  
P Wave ◽  
Prestack Depth Migration ◽  
Anisotropic Parameter ◽  
Depth Migration ◽  
Residual Correction ◽  
Dip Angle

In the method for applying anisotropic corrections after isotropic prestack depth migration (PSDM), the correction, which is calculated and implemented in the depth domain, is defined as a time difference between isotropic and anisotropic traveltimes, under the assumption that the vertical velocity is known. The definition of this correction uses a special postmigration common-image-gather (CIG) ordering, which collects the migrated data according to the input-trace’s source and receiver distance from the surface CIG location. In this postmigration domain, the dip of the events can be directly related to their horizontal position in the CIG, called the imaging offset, and the separation of flat and dipping reflectors becomes easy to perform. The dependency of the seismic anisotropic effect on the subsurface dip angle is well pronounced in these CIGs. After application of an isotropic PSDM, effective anisotropic-parameter estimation is performed at selected CIG locations by using a simple two-parameter scan procedure. The optimal anisotropic parameters can be used to perform a final anisotropic PSDM or to apply a residual correction to the isotropically migrated data. We demonstrate the method for P-wave data in 2D media with vertical transverse isotropy (VTI) symmetry by using both synthetic and real data. We also present a strategy for handling the ambiguity between the vertical velocity and the anisotropic parameters.

Feasibility of nonhyperbolic moveout inversion in transversely isotropic media

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 957-969 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Transverse Isotropy ◽  
Horizontal Velocity ◽  
P Wave ◽  
Vacuum Field ◽  
Percentage Error ◽  
Correlated Errors ◽  
Data Set ◽  
Time Migration ◽  
Quartic Term

Inversion of reflection traveltimes in anisotropic media can provide estimates of anisotropic coefficients required for seismic processing and lithology discrimination. Nonhyperbolic P-wave moveout for transverse isotropy with a vertical symmetry axis (VTI media) is controlled by the parameter η (or, alternatively, by the horizontal velocity Vhor), which is also responsible for the influence of anisotropy on all time‐processing steps, including dip‐moveout (DMO) correction and time migration. Here, we recast the nonhyperbolic moveout equation, originally developed by Tsvankin and Thomsen, as a function of Vhor and normal‐moveout (NMO) velocity Vnmo and introduce a correction factor in the denominator that increases the accuracy at intermediate offsets. Then we apply this equation to obtain Vhor and η from nonhyperbolic semblance analysis on long common midpoint (CMP) spreads and study the accuracy and stability of the inversion procedure. Our error analysis shows that the horizontal velocity becomes relatively well‐constrained by reflection traveltimes if the spreadlength exceeds twice the reflector depth. There is, however, a certain degree of tradeoff between Vhor and Vnmo caused by the interplay between the quadratic and quartic term of the moveout series. Since the errors in Vhor and Vnmo have opposite signs, the absolute error in the parameter η (which depends on the ratio Vhor/Vnmo) turns out to be at least two times bigger than the percentage error in Vhor. Therefore, the inverted value of η is highly sensitive to small correlated errors in reflection traveltimes, with moveout distortions on the order of 3–4 ms leading to errors in η up to ±0.1—even in the simplest model of a single VTI layer. Similar conclusions apply to vertically inhomogeneous media, in which the interval horizontal velocity can be obtained with an accuracy often comparable to that of the NMO velocity, while the interval values of η are distorted by the tradeoff between Vhor and Vnmo that gets amplified by the Dix‐type differentiation procedure. We applied nonhyperbolic semblance analysis to a walkaway VSP data set acquired at Vacuum field, New Mexico, and obtained a significant value of η = 0.19 indicative of nonnegligible anisotropy in this area. Then we combined moveout inversion results with the known vertical velocity to resolve the anisotropic coefficients ε and δ. However, in agreement with our modeling results, η estimation was significantly compounded by the scatter in the measured traveltimes. Certain instability in η inversion has no influence on the results of anisotropic poststack time migration because all kinematically equivalent models obtained from nonhyperbolic moveout give an adequate description of long‐spread reflection traveltimes. Also, inversion of nonhyperbolic moveout provides a relatively accurate horizontal‐velocity function that can be combined with the vertical velocity (if it is available) to estimate the anisotropic coefficient ε. However, η represents a valuable lithology indicator that can be obtained from surface P-wave data. Therefore, for purposes of lithology discrimination, it is preferable to find η by means of the more stable DMO method of Alkhalifah and Tsvankin.

Inversion of azimuthally dependent NMO velocity in transversely isotropic media with a tilted axis of symmetry

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 232-246 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Wave Velocity ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Model Parameters ◽  
Symmetry Direction ◽  
Time Migration ◽  
Inversion Procedure ◽  
Tti Media

Just as the transversely isotropic model with a vertical symmetry axis (VTI media) is typical for describing horizontally layered sediments, transverse isotropy with a tilted symmetry axis (TTI) describes dipping TI layers (such as tilted shale beds near salt domes) or crack systems. P-wave kinematic signatures in TTI media are controlled by the velocity [Formula: see text] in the symmetry direction, Thomsen’s anisotropic coefficients ε and δ, and the orientation (tilt ν and azimuth β) of the symmetry axis. Here, we show that all five parameters can be obtained from azimuthally varying P-wave NMO velocities measured for two reflectors with different dips and/or azimuths (one of the reflectors can be horizontal). The shear‐wave velocity [Formula: see text] in the symmetry direction, which has negligible influence on P-wave kinematic signatures, can be found only from the moveout of shear waves. Using the exact NMO equation, we examine the propagation of errors in observed moveout velocities into estimated values of the anisotropic parameters and establish the necessary conditions for a stable inversion procedure. Since the azimuthal variation of the NMO velocity is elliptical, each reflection event provides us with up to three constraints on the model parameters. Generally, the five parameters responsible for P-wave velocity can be obtained from two P-wave NMO ellipses, but the feasibility of the moveout inversion strongly depends on the tilt ν. If the symmetry axis is close to vertical (small ν), the P-wave NMO ellipse is largely governed by the NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η. Although for mild tilts the medium parameters cannot be determined separately, the NMO-velocity inversion provides enough information for building TTI models suitable for time processing (NMO, DMO, time migration). If the tilt of the symmetry axis exceeds 30°–40° (e.g., the symmetry axis can be horizontal), it is possible to find all P-wave kinematic parameters and construct the anisotropic model in depth. Another condition required for a stable parameter estimate is that the medium be sufficiently different from elliptical (i.e., ε cannot be close to δ). This limitation, however, can be overcome by including the SV-wave NMO ellipse from a horizontal reflector in the inversion procedure. While most of the analysis is carried out for a single layer, we also extend the inversion algorithm to vertically heterogeneous TTI media above a dipping reflector using the generalized Dix equation. A synthetic example for a strongly anisotropic, stratified TTI medium demonstrates a high accuracy of the inversion (subject to the above limitations).

Inversion of reflection traveltimes for transverse isotropy

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1095-1107 ◽  
Author(s):  
Ilya Tsvankin ◽  
Leon Thomsen
Keyword(s):  
Wave Velocity ◽  
Vertical Velocity ◽  
Joint Inversion ◽  
Transverse Isotropy ◽  
Taylor Series Expansion ◽  
High Sensitivity ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Quartic Term

In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector depth) if only P‐wave data are included. A general analysis of the P‐wave inverse problem proves the existence of a broad set of models with different vertical velocities, all of which provide a satisfactory fit to the exact traveltimes. This strong ambiguity is explained by a trade‐off between vertical velocity and the parameters of anisotropy on gathers with a limited angle coverage. The accuracy of the inversion procedure may be significantly increased by combining both long‐spread P and SV moveouts. The high sensitivity of the long‐spread SV moveout to the reflector depth permits a less ambiguous inversion. In some cases, the SV moveout alone may be used to recover the vertical S‐wave velocity, and hence the depth. Success of this inversion depends on the spreadlength and degree of SV‐wave velocity anisotropy, as well as on the constraints on the P‐wave vertical velocity.

Nonhyperbolic reflection moveout for horizontal transverse isotropy

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1738-1753 ◽  
Author(s):  
AbdulFattah Al‐Dajani ◽  
Ilya Tsvankin
Keyword(s):  
Transverse Isotropy ◽  
Single Layer ◽  
Azimuthal Velocity ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Analytic Description ◽  
Pure Mode ◽  
Quartic Term ◽  
Hti Media ◽  
Vertical Transverse Isotropy

The transversely isotropic model with a horizontal axis of symmetry (HTI) has been used extensively in studies of shear‐wave splitting to describe fractured formations with a single system of parallel vertical penny‐shaped cracks. Here, we present an analytic description of longspread reflection moveout in horizontally layered HTI media with arbitrary strength of anisotropy. The hyperbolic moveout equation parameterized by the exact normal‐moveout (NMO) velocity is sufficiently accurate for P-waves on conventional‐length spreads (close to the reflector depth), although the NMO velocity is not, in general, usable for converting time to depth. However, the influence of anisotropy leads to the deviation of the moveout curve from a hyperbola with increasing spread length, even in a single‐layer model. To account for nonhyperbolic moveout, we have derived an exact expression for the azimuthally dependent quartic term of the Taylor series traveltime expansion [t2(x2)] valid for any pure mode in an HTI layer. The quartic moveout coefficient and the NMO velocity are then substituted into the nonhyperbolic moveout equation of Tsvankin and Thomsen, originally designed for vertical transverse isotropy (VTI). Numerical examples for media with both moderate and uncommonly strong nonhyperbolic moveout show that this equation accurately describes azimuthally dependent P-wave reflection traveltimes in an HTI layer, even for spread lengths twice as large as the reflector depth. In multilayered HTI media, the NMO velocity and the quartic moveout coefficient reflect the influence of layering as well as azimuthal anisotropy. We show that the conventional Dix equation for NMO velocity remains entirely valid for any azimuth in HTI media if the group‐velocity vectors (rays) for data in a common‐midpoint (CMP) gather do not deviate from the vertical incidence plane. Although this condition is not exactly satisfied in the presence of azimuthal velocity variations, rms averaging of the interval NMO velocities represents a good approximation for models with moderate azimuthal anisotropy. Furthermore, the quartic moveout coefficient for multilayered HTI media can also be calculated with acceptable accuracy using the known averaging equations for vertical transverse isotropy. This allows us to extend the nonhyperbolic moveout equation to horizontally stratified media composed of any combination of isotropic, VTI, and HTI layers. In addition to providing analytic insight into the behavior of nonhyperbolic moveout, these results can be used in modeling and inversion of reflection traveltimes in azimuthally anisotropic media.

Effects of transverse isotropy on P‐wave AVO for gas sands

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 883-888 ◽  
Author(s):  
Ki Young Kim ◽  
Keith H. Wrolstad ◽  
Fred Aminzadeh
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Velocity Anisotropy ◽  
Special Cases ◽  
Class 1 ◽  
Zero Offset ◽  
Ti Media

Velocity anisotropy should be taken into account when analyzing the amplitude variation with offset (AVO) response of gas sands encased in shales. The anisotropic effects on the AVO of gas sands in transversely isotropic (TI) media are reviewed. Reflection coefficients in TI media are computed using a planewave formula based on ray theory. We present results of modeling special cases of exploration interest having positive reflectivity, near‐zero reflectivity, and negative reflectivity. The AVO reflectivity in anisotropic media can be decomposed into two parts; one for isotropy and the other for anisotropy. Zero‐offset reflectivity and Poisson’s ratio contrast are the most significant parameters for the isotropic component while the δ difference (Δδ) between shale and gas sand is the most important factor for the anisotropic component. For typical values of Tl anisotropy in shale (positive δ and ε), both δ difference (Δδ) and ε difference (Δε) amplify AVO effects. For small angles of incidence, Δδ plays an important role in AVO while Δε dominates for large angles of incidence. For typical values of δ and ε, the effects of anisotropy in shale are: (1) a more rapid increase in AVO for Class 3 and Class 2 gas sands, (2) a more rapid decrease in AVO for Class 1 gas sands, and (3) a shift in the offset of polarity reversal for some Class 1 and Class 2 gas sands.

Anisotropic velocity analysis for lithology discrimination

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1564-1574 ◽  
Author(s):  
B. S. Byun ◽  
D. Corrigan ◽  
J. E. Gaiser
Keyword(s):  
Vertical Velocity ◽  
Transversely Isotropic ◽  
Wave Model ◽  
P Wave ◽  
Velocity Analysis ◽  
Velocity Anisotropy ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
Vsp Data

A new velocity analysis technique is presented for analyzing moveout of signals on multichannel surface seismic or VSP data. An approximate, skewed hyperbolic moveout formula is derived for horizontally layered, transversely isotropic media. This formula involves three measurement parameters: the average vertical velocity and horizontal and skew moveout velocities. By extending Dix‐type hyperbolic moveout analysis, we obtain improved coherence over large source‐geophone offsets for more accurate moveout correction. Compared with the stacking velocity obtained by simple hyperbolic analysis methods, the three velocity parameters estimated by this technique contain more physically meaningful geologic information regarding the anisotropy and/or velocity heterogeneity of the subsurface. Synthetic P‐wave model experiments demonstrate that the skewed hyperbolic moveout formula yields an excellent fit to time‐distance curves over a wide range of ray angles. Consequently, the measurement parameters are shown to reflect adequately the characteristics of velocity dependence on ray angle, i.e., velocity anisotropy. The technique is then applied to two field offset VSP data sets to measure and analyze the velocity parameters. The results show that the apparent anisotropy, defined as the ratio between the horizontal moveout velocity and average vertical velocity, correlates reasonably well with lithology. Highly anisotropic shale and chalk exhibit higher horizontal‐to‐vertical velocity ratios and sandstones show lower ratios.

Reflection moveout and parameter estimation for horizontal transverse isotropy

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 614-629 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Shear Wave ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Symmetry Direction ◽  
Wave Splitting ◽  
Hti Media ◽  
Splitting Parameter

Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. Here, I present an exact equation for normal‐moveout (NMO) velocities from horizontal reflectors valid for pure modes in HTI media with any strength of anisotropy. The azimuthally dependent P‐wave NMO velocity, which can be obtained from 3-D surveys, is controlled by the principal direction of the anisotropy (crack orientation), the P‐wave vertical velocity, and an effective anisotropic parameter equivalent to Thomsen's coefficient δ. An important parameter of fracture systems that can be constrained by seismic data is the crack density, which is usually estimated through the shear‐wave splitting coefficient γ. The formalism developed here makes it possible to obtain the shear‐wave splitting parameter using the NMO velocities of P and shear waves from horizontal reflectors. Furthermore, γ can be estimated just from the P‐wave NMO velocity in the special case of the vanishing parameter ε, corresponding to thin cracks and negligible equant porosity. Also, P‐wave moveout alone is sufficient to constrain γ if either dipping events are available or the velocity in the symmetry direction is known. Determination of the splitting parameter from P‐wave data requires, however, an estimate of the ratio of the P‐to‐S vertical velocities (either of the split shear waves can be used). Velocities and polarizations in the vertical symmetry plane of HTI media, that contains the symmetry axis, are described by the known equations for vertical transverse isotropy (VTI). Time‐related 2-D P‐wave processing (NMO, DMO, time migration) in this plane is governed by the same two parameters (the NMO velocity from a horizontal reflector and coefficient ε) as in media with a vertical symmetry axis. The analogy between vertical and horizontal transverse isotropy makes it possible to introduce Thomsen parameters of the “equivalent” VTI model, which not only control the azimuthally dependent NMO velocity, but also can be used to reconstruct phase velocity and carry out seismic processing in off‐symmetry planes.

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