Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2000-06-30
2002-12-31
Lefkowitz, Edward (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C175S045000
Reexamination Certificate
active
06502038
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to the field of seismic data processing and in particular to a method for moveout-correcting seismic data having non-hyperbolic moveout at longer offsets. Uses of the invention include, without limitation, pre-stack data analysis for AVO applications.
BACKGROUND OF THE INVENTION
AVO is an abbreviation for Amplitude versus Offset, or, as it is sometimes written, amplitude variation with offset. AVO is a seismic data analysis method based on studying the variation in the amplitude of reflected waves with changes in the distance (offset) between the seismic source and receiver. The AVO response of the reflection events associated with the boundaries between the reservoir rock and the surrounding sealing materials often depends on the properties of the fluid stored in the reservoir pore space. Because of this property, AVO analysis is often used as a tool for reservoir fluid prediction.
AVO analysis is performed on Common-Depth-Point (CDP) gathers. Seismic events observed in CDP gathers exhibit a curvilinear shape (moveout). In order for the AVO method to be practically applicable to large data volumes, the gather has to be transformed (moved-out), so that the reflection events become horizontal (flat). In standard practice, this is performed using the Normal Moveout (NMO) method, which assumes that the original moveout of the reflection events is hyperbolic. This assumption works well for a small range of recorded offsets (usually up to about 3km). But for longer-offset gathers that are now commercially feasible to acquire and necessary for effective AVO analysis and reservoir properties prediction, the assumption is not adequate; events exhibit non-hyperbolic moveout over the longer offset ranges. An example is provided in
FIGS. 1A and 1B
. The picked reflection event
10
in
FIG. 1A
is flattened only over a limited range of offsets after NMO in FIG.
1
B. In analyzing the AVO behavior of such data, the valuable far offsets have to be discarded; if they are included without proper flattening, there is a risk of wrong fluid type prediction. There is, therefore, a need for an efficient method that takes into account the non-hyperbolic moveout of the reflection events and flattens them over the complete range of offsets.
Non-hyperbolic reflection moveout has been recognized as a significant problem for a long time, and a large body of geophysical literature has been devoted to it. Current solutions fall into the following categories.
Different Approximations Used for the Moveout of Reflection Events
Normal-moveout is based on the hyperbolic approximation
t
2
=
t
0
2
+
(
X
V
)
2
where t is the reflection time at an offset X, t
0
the zero-offset time for the same reflection and V the Normal-Moveout (NMO) velocity. (Notwithstanding the preceding common terminology, it should be understood that V and t
0
are not necessarily physically meaningful, but rather merely parameters that characterize the observations.) This approach is implemented in standard velocity-analysis packages where measures of reflection signal coherency (semblance) are calculated along hyperbolic trajectories through the seismic data. Trajectories corresponding to maximum coherency (semblance peaks) correspond to seismic events. Identifying the semblance peaks on 2-dimensional velocity analysis displays allows determination of the Normal-Moveout velocity V. If the parameter t
0
is changed, then a different value of V will correspond to the semblance peaks. Thus V can be considered to be a function of t
0
, or V(t
0
).
A commonly adopted method for extending the validity of this equation to longer offsets is the use of the truncated 4-th order Taylor series expansion. (See, for example, Gidlow, P. M., and Fatti, J. L., 1990, “Preserving far offset seismic data using non-hyperbolic moveout correction”, Expanded Abstracts of 60th Ann. Int. SEG Mtg., 1726-1729.) This approach is commercially available in the data processing systems of most seismic contractors. The equation used is:
t
2
=
t
0
2
+
(
X
V
)
2
-
(
X
W
)
4
For each zero-offset time to, two parameters, V and W, need to be defined. Extending the standard semblance-based velocity analysis method to this case would imply picking peaks in 3-dimensional semblance panels (one for each CDP location, the three axes being time, V and W). This would be cumbersome and require special graphics. For this reason the most common approach is to first get an estimate of V, using the near offset data, then fix V and estimate W and then repeat the process until satisfactory alignment of the events has been achieved. The disadvantage of such an approach is that its application is time-consuming, because several iteration steps may be required for converging to a good set of coefficients for 2-nd and 4-th order terms.
Tsvankin and Thomsen derived an expression which they claimed to be an improvement upon the Taylor expansion formula in the presence of velocity anisotropy (wave velocity different for different propagation directions). (Tsvankin, I., and Thomsen, L., 1994, “Nonhyperbolic reflection moveout in anisotropic media”,
Geophysics
, 59, 1290-1304.) This expression was re-written by Alkhalifah. (Alkhalifah, T., 1997, “Velocity analysis using nonhyperbolic moveout in transversely isotropic media”,
Geophysics
, 62, 1839-1854.) Their expression is:
t
2
=
t
0
2
+
X
2
V
2
-
2
η
X
4
V
2
[
t
0
2
V
2
+
(
1
+
2
η
)
X
2
]
where &eegr; is an effective anisotropy parameter and V is the NMO velocity.
In addition to the above formulas, other types of equations have been proposed. Byun et al. introduced a “skewed” hyperbolic moveout formula. (Byun, B. S., Corrigan, D., and Gaiser, J. E., 1989, “Anisotropic velocity analysis for lithology discrimination”,
Geophysics
, 54, 1564-1574.) Castle and de Bazelaire proposed the use of a shifted-hyperbola equation. (Castle, R. J., 1994, “A theory of normal moveout”,
Geophysics
, 59, 983-999; de Bazelaire, E., 1988, “Normal moveout revisited: Inhomogeneous media and curved interfaces”,
Geophysics
, 53, 143-157.) Yilmaz proposes the use of parabolas to describe the residual moveout of reflections after NMO has been applied. (Yilmaz, O., 1989, “Velocity-stack processing”,
Geophysical Prospecting
, 37, 351-382.)
All of the above methods suffer from the following shortcomings:
Non-hyperbolic moveout can be caused by vertical velocity heterogeneity, curvature of the reflecting horizon, lateral velocity variation and velocity anisotropy. Given this number of factors and the geologic complexity of the subsurface, it is unlikely that a single mathematical expression can provide a universal description applicable to all situations. Locations where reflection events exhibit anomalous moveout are often the places where hydrocarbon traps exist (vicinity of faults, salt domes). Failure of moveout algorithms to work adequately under such situations is a significant defect.
Even in cases when such algorithms can work, their application can be cumbersome and time-consuming, because several iteration steps may be required for determining the parameters included in the expressions (see the comments on the truncated Taylor series approach above).
Depth Migration with Detailed Subsurface Velocity Models
Since non-hyperbolic moveout is caused by geologic complexity and heterogeneity, an imaging method that can handle those complications accurately should be able to produce CDP gathers with flattened reflection events. Depth migration is the most accurate imaging method available today, and algorithms are available that can deal with velocity anisotropy and heterogeneity. Yet, depth migration is extremely sensitive to the accuracy of the velocity model used for imaging and very expensive to do in a manner that preserves AVO information. Numerous publications exist on methods for determining velocity models for depth migration. The basic scheme in such methods is to depth migrate with an initial velocity model, inspect the results, modify the velocity model and m
Lazaratos Spyridon K.
Shah Pravin M.
ExxonMobil Upstream Research Company
Lefkowitz Edward
Plummer J. Paul
Taylor Victor J.
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