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.

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.

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.

Migration velocity analysis in factorized VTI media

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 708-718 ◽  
Author(s):  
Debashish Sarkar ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Migration Velocity ◽  
P Wave ◽  
Velocity Analysis ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Wave Migration ◽  
Vti Media

One of the main challenges in anisotropic velocity analysis and imaging is simultaneous estimation of velocity gradients and anisotropic parameters from reflection data. Approximating the subsurface by a factorized VTI (transversely isotropic with a vertical symmetry axis) medium provides a convenient way of building vertically and laterally heterogeneous anisotropic models for prestack depthmigration. The algorithm for P‐wave migration velocity analysis (MVA) introduced here is designed for models composed of factorized VTI layers or blocks with constant vertical and lateral gradients in the vertical velocity VP0. The anisotropic MVA method is implemented as an iterative two‐step procedure that includes prestack depth migration (imaging step) followed by an update of the medium parameters (velocity‐analysis step). The residual moveout of the migrated events, which is minimized during the parameter updates, is described by a nonhyperbolic equation whose coefficients are determined by 2D semblance scanning. For piecewise‐factorized VTI media without significant dips in the overburden, the residual moveout of P‐wave events in image gathers is governed by four effective quantities in each block: (1) the normal‐moveout velocity Vnmo at a certain point within the block, (2) the vertical velocity gradient kz, (3) the combination kx[Formula: see text] of the lateral velocity gradient kx and the anisotropic parameter δ, and (4) the anellipticity parameter η. We show that all four parameters can be estimated from the residual moveout for at least two reflectors within a block sufficiently separated in depth. Inversion for the parameter η also requires using either long‐spread data (with the maximum offset‐to‐depth ratio no less than two) from horizontal interfaces or reflections from dipping interfaces. To find the depth scale of the section and build a model for prestack depth migration using the MVA results, the vertical velocity VP0 needs to be specified for at least a single point in each block. When no borehole information about VP0 is available, a well‐focused image can often be obtained by assuming that the vertical‐velocity field is continuous across layer boundaries. A synthetic test for a three‐layer model with a syncline structure confirms the accuracy of our MVA algorithm in estimating the interval parameters Vnmo, kz, kx, and η and illustrates the influence of errors in the vertical velocity on the image quality.

Separation and imaging of seismic diffractions using migrated dip-angle gathers

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. S131-S143 ◽  
Author(s):  
Alexander Klokov ◽  
Sergey Fomel
Keyword(s):  
Radon Transform ◽  
Real Data ◽  
Separation Procedure ◽  
Shape Difference ◽  
Depth Migration ◽  
Time Migration ◽  
Reflection Angle ◽  
Radon Space ◽  
Dip Angle ◽  
Analytical Expressions

Common-reflection angle migration can produce migrated gathers either in the scattering-angle domain or in the dip-angle domain. The latter reveals a clear distinction between reflection and diffraction events. We derived analytical expressions for events in the dip-angle domain and found that the shape difference can be used for reflection/diffraction separation. We defined reflection and diffraction models in the Radon space. The Radon transform allowed us to isolate diffractions from reflections and noise. The separation procedure can be performed after either time migration or depth migration. Synthetic and real data examples confirmed the validity of this technique.

Benefits of tilted transverse isotropy prestack depth migration for reservoir evaluation offshore West Africa

First Break ◽  
2008 ◽  
Vol 26 (1289) ◽  
Author(s):  
F. Boudou ◽  
Y. Le Stunff ◽  
J. Arnaud ◽  
P. Esquier ◽  
A. Kenworthy ◽  
...  
Keyword(s):  
West Africa ◽  
Transverse Isotropy ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Reservoir Evaluation

Common-Reflection-Point-Based Prestack Depth Migration for Imaging Lithosphere in Python: Application to the Dense Warramunga Array in Northern Australia

2020 ◽  
Vol 91 (5) ◽  
pp. 2890-2899 ◽  
Author(s):  
Weijia Sun ◽  
Brian L. N. Kennett
Keyword(s):  
Open Source ◽  
Receiver Function ◽  
Function Analysis ◽  
Vertical Component ◽  
P Wave ◽  
Northern Australia ◽  
Reflection Point ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Conversion Point

Abstract We exploit estimates of P-wave reflectivity from autocorrelation of transmitted teleseismic P arrivals and their coda in a common reflection point (CRP) migration technique. The approach employs the same portion of the vertical-component seismogram, as in standard Ps receiver function analysis. This CRP prestack depth migration approach has the potential to image lithospheric structures on scales as fine as 4 km or less. The P-wave autocorrelation process and migration are implemented in open-source software—the autocorrelogram calculation (ACC) package, which builds on the widely used the seismological Obspy toolbox. The ACC package is written in the open-source and free Python programming language (3.0 or newer) and has been extensively tested in an Anaconda Python environment. The package is simple and friendly to use and runs on all major operating systems (e.g., Windows, macOS, and Linux). We utilize Python multiprocessing parallelism to speed up the ACC on a personal computer system, or servers, with multiple cores and threads. The application of the ACC package is illustrated with application to the closely spaced Warramunga array in northern Australia. The results show how fine-scale structures in the lithospheric can be effectively imaged at relatively high frequencies. The Moho ties well with conventional H−κ receiver analysis and deeper structure inferred from stacked autocorrelograms for continuous data. CRP prestack depth migration provides an important complement to common conversion point receiver function stacks, since it is less affected by surface multiples at lithospheric depths.

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 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.

3‐D prestack depth migration on real data

1990 ◽  
Author(s):  
Philippe Julien ◽  
Steve Cole ◽  
Stefan Kaculini
Keyword(s):  
Real Data ◽  
Prestack Depth Migration ◽  
Depth Migration

Depth‐domain velocity analysis in VTI media using surface P-wave data: Is it feasible?

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 897-903 ◽  
Author(s):  
Yves Le Stunff ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Heterogeneous Media ◽  
Wave Reflection ◽  
P Wave ◽  
Model Parameters ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Velocity Models ◽  
Trade Offs ◽  
Vti Media

The main difficulties in anisotropic velocity analysis and inversion using surface seismic data are associated with the multiparameter nature of the problem and inherent trade‐offs between the model parameters. For the most common anisotropic model, transverse isotropy with a vertical symmetry axis (VTI media), P-wave kinematic signatures are controlled by the vertical velocity V0 and the anisotropic parameters ε and δ. However, only two combinations of these parameters—NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η—can be determined from P-wave reflection traveltimes if the medium above the reflector is laterally homogeneous. While Vnmo(0) and η are sufficient for time‐domain imaging in VTI media, they cannot be used to resolve the vertical velocity and build velocity models needed for depth migration. Here, we demonstrate that P-wave reflection data can be inverted for all three relevant VTI parameters (V0, ε and δ) if the model contains nonhorizontal intermediate interfaces. Using anisotropic reflection tomography, we carry out parameter estimation for a two‐layer medium with a curved intermediate interface and reconstruct the correct anisotropic depth model. To explain the success of this inversion procedure, we present an analytic study of reflection traveltimes for this model and show that the information about the vertical velocity and reflector depth was contained in the reflected rays which crossed the dipping intermediate interface. The results of this work are especially encouraging because the need for depth imaging (such as prestack depth migration) arises mostly in laterally heterogeneous media. Still, we restricted this study to a relatively simple model and constrained the inversion by assuming that one of the layers is isotropic. In general, although lateral heterogeneity does create a dependence of P-wave reflection traveltimes on the vertical velocity, there is no guarantee that for more complicated models all anisotropic parameters can be resolved in a unique fashion.

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