Anisotropy Conventional
6.3 Data conditioning for AVO analysis
6.3.3 Amplitude scaling with offset
Despite the best efforts of the seismic processor, it is often the case that the amplitude variation with offset in the final CDP gathers does not faithfully represent
the amplitude variation that would be expected purely from AVO effects at the individual reflectors. This often leads to uncertainties in how to scale the offset component of the seismic (i.e. AVO calibration). Whilst it may not be necessary to correct the scaling if the purpose of a study is restricted to identifying anomalous AVO behaviour, the issue can become important in situations where some quantitative interpretation of the AVO signature is to be made (Ross and Beale,1994).
Perhaps the most robust approach to offset scaling is provided by well ties (see Section 4.7.5). If the
a)
Initial migrationb)
Higher order NMOc)
With trim static Figure 6.12(a) initial migration, (b) after additionalThree adjacent gathers afterhigher order residual moveout correction and (c) after additional trim static flattening. Gather flatness has been significantly improved (from Gulunayet al.,
2007).
Intercept
before
Gradient
improved
Intercept
improved
Gradient
before
Figure 6.13Intercept and gradient sections calculated from gathers before (top) and after (bottom) trim static flattening. A significant amount of residual energy has been removed from the gradient (Gulunayet al.,2007).
scaling of the seismic has the same relative change as the synthetic (i.e. the seismic scaling is‘correct’) then the amplitude of the extracted wavelets on nears, mids and fars should essentially be the same, although the frequency content and phase may change across the offset range. Corrections can be derived simply from the relative scaling of the extracted wavelets. Clearly, if there are big scaling differences from one well to another then further analysis is needed. If well ties are poor then comparison can be made using RMS ampli- tudes in a window which contains several strong reflectors to avoid the effects of noise or bias from a single dominant reflection.
It is paramount in offset scaling that the effects of noise should be avoided. Figure 6.14 illustrates the problem in the context of the AVO crossplot, where the effects of noise are most apparent. The example is fairly extreme as it is based on an unconsolidated sand target and data with fairly poor signal-to-noise ratio. A crossplot derived from the well synthetic (Fig. 6.14a) shows a background trend at an angle of χ ¼ 53°. Compared to the well crossplot (Fig. 6.4a), the seismic crossplot (Fig. 6.14b) has a much lower angle of trend (around 11°). It might be supposed that the AVO calibration step could involve a rotation of this trend to fit the well data. Unfortunately, this is not
a)
c)
b)
0 -0.1 -0.2 0 0.1 -0.1 -0.2 0.2 0.1 0.2 Intercept Gradient 0 -0.1 -0.2 0 0.1 -0.1 -0.2 0.2 0.1 0.2 Intercept Intercept Gradient 0 80 -80 -160 160 Gradient 0 -80 -160 80 160Figure 6.14 AVO calibration at a well; (a) AVO crossplot generated from well data (note red dot represents top reservoir), (b) seismic AVO crossplot determined from the same time segment as the well crossplot, (c) seismic AVO crossplot calibrated by scaling the reflectivities at top reservoir and re-calculating intercept and gradient. Note how the seismic background trend does not change significantly with calibration as it is contaminated by noise.
the case as the seismic trend is not simply a function of geology but a combination of the geology and noise (e.g. Hendrickson, 1999; Simm et al., 2000). In fact, most of the crossplot data in Fig. 6.14 is heavily contaminated with noise. In such a case the calibra- tion should be done on the reflectivity associated with the target sand (shown as the red point on the plots). Effectively, the calibration is done by deriving differ- ent scalers for near and far angles, then re-calculating the intercept and gradient. Given the noise contamin- ation, the background trend on the calibrated cross- plot (Fig. 6.14c) in this case is no different from the original seismic.
6.3.4 Supergathers
A way of enhancing signal-to-noise ratio is by forming a supergather. This is done by collecting traces from adjacent CMPs and stacking traces with similar offsets or angles. Of course, the lateral stacking element of supergathers means that a certain amount
of lateral resolution is traded for improved signal-to- noise ratio. An example is shown inFig. 6.15.
A practical issue is the amount of fold (or number of traces) available to perform the super- gather operation. In 3D datasets the fold varies across the offset range; typically, fold is low at near and far offsets, and traces with intermediate offsets dom- inate the overall fold. Xu and Chopra (2007) have described how using an adaptive approach, in which traces are borrowed from adjacent CMP locations to create an even fold distribution with offset, provides
TWT (s)
a)
b)
Offset (ft) Offset (ft) 440 10100 440 10100 1.4 1.6 1.8 2.0 2.2 2.4 2.6Figure 6.15 An example of gathers and supergathers (after Allen and Peddy,1993); (a) processed gather, (b) supergather generated by stacking offsets across an odd number of cdps. Noise levels are significantly reduced throughout the traces in the supergather, but lateral resolution is compromised to some extent.
3400 3500 3600 3700 3800 TWT (ms)
a)
b)
0 2 0 -2 -4 -6 0.05 0.1 0.15 0.2 sin2θ Amplitude x 10 3 L R OffsetFigure 6.16 Comparison of AVO intercept and gradient calculation by least squares (L) and by robust fit (R) (after Walden,1991).
extra stability in generating supergathers with attend- ant benefits in the extraction of AVO attributes.
6.3.5 Gradient estimation and noise
reduction
Notionally, it is a simple matter to calculate a volume of intercept R0 and of gradient G traces by making a least-squares fit of the amplitude R (for each TWT sample of each angle gather) to the equation R¼ R0+ G sin2θ, where θ is the angle of incidence. It is important that the angle range used to calculate the gradient has good signal-to-noise ratio and that the linearity assumption is valid. This can be tested by analysing the angle behaviour of amplitudes in the gathers and comparing it to well synthetics. As has been discussed in previous sections a key issue is the role of noise in the variability of the gradient (e.g. Hendrickson, 1999; Cambois, 1998) and various methods have been proposed to improve the robust- ness of the gradient estimate in the presence of noise.
6.3.5.1 Walden’s robust fitting
Walden (1991) proposed a two-stage approach as follows. In the first step the data are divided into two groups: nears and fars, separated at the median value of sin2θ. For each group, the median amplitude and value of sin2θ are calculated. A straight line drawn between the near-group point and the far-group point gives an estimate of the gradient that is robust against the noise, because the median is insensitive to outliers. If this estimate for the gradient
is β, then the residuals calculated by subtracting βsin2θ from each starting amplitude can be subjected to the same median fit calculation. This process could be iterated further, but instead Walden suggests making a maximum-likelihood fit to the residuals at this stage. This differs from a standard least-squares fit by giving less weight to points with high residuals, and zero weight to points with residuals beyond a threshold. An example is shown in Fig. 6.16, where the robust fit has been effective in removing the influence of the high amplitudes on the last few traces.
6.3.5.2 Whitcombe’s noise reduction
Another method for reducing noise in the gradient has been proposed by Whitcombe et al. (2004). It makes use of the fact that the noise is well imaged as a coordinate rotation on the intercept vs gradient crossplot. Filtering of the rotated data is carried out by a process rooted in the hodogram concept (Keho et al.,2001). First, a coordinate rotation is applied to the data in the intercept–gradient domain to align the axes parallel and perpendicular to the noise trend (Fig. 6.17a). Rotation of the axes is achieved by:
R00¼ R0 cos χ+G sin χ, ð6:7Þ G0¼ R0 sin χ þ G cos χ: ð6:8Þ Within a sliding window the rotated values of inter- cept and gradient for adjacent datapoints have a regression line fit through them. The filtered output for the central datapoint is determined directly from
a)
b)
c)
R(0)’ R(0) R(0) G G G’Figure 6.17 Filtering process to improve AVO gradient estimation, after Whitcombeet al. (2004); (a) intercept vs gradient crossplot showing the noise ellipse, (b) determining new values for the rotated gradient based on a regression of rotated intercept and rotated gradient points in a sliding window (five samples in this case), (c) noise ellipse reduced in magnitude after rotation back into intercept gradient space (after Whitcombeet al.,2004).
the regression assuming that the rotated intercept value is correct (red dot in Fig. 6.17b). This is repeated for all samples by sliding the window down one sample at a time. Data are then transformed back to the intercept–gradient domain (Fig. 6.17c). The result is that scatter in the noise trend direction
has been reduced, while there has been much less change in the perpendicular direction. To minimise smoothing through geology, a short time window is chosen (e.g. five samples) but samples are also included from adjacent inlines and crosslines, in a direction parallel to the local dip.
7
7.1 Introduction
The purpose of seismic amplitude interpretation and AVO analysis is to explain changes in seismic signa- tures in terms of fluid and rock variations. In hydro- carbon exploration, the interpreter looks particularly for seismic amplitude changes that may be related to a change in fluid (i.e. from water to hydrocarbon). These seismic effects are often called direct hydrocar- bon indicators (‘DHIs’).
The search for DHIs and the analysis of AVO data go hand in hand to develop a view of the prospectivity of an area. There are a variety of interpretation tech- niques that can be used to exploit AVO phenomena and aid interpretation. Commonly used techniques include:
partial offset and angle stacks (e.g. near, mid, far) (Chapter 2),
AVO crossplot colour coding (e.g. Verm and Hilterman,1995),
AVO hodograms (e.g. Keho et al.,2001),
AVO projections (e.g. Whitcombe et al.,2002; and
Chapter 5),
target/reference ‘relative AVO’ method (e.g. Chiburis,1993).
It should be remembered that confidence in ampli- tude interpretation is to a large extent determined by the geological and spatial context. DHIs are most commonly, but not exclusively, found in relatively shallow unconsolidated and partially consolidated sand/shale sequences, where fluid compressibility can have a significant effect on the whole rock compressibility. In well consolidated sandstone and carbonate situations the fluid tends to make a smaller contribution to whole rock compressibility (Chapters 5and8) and consequently DHI and AVO effects are usually more subtle.
Some of the key factors for the interpreter to consider are:
reservoir porosity, mineralogy and stiffness characteristics,
relative compressibility of hydrocarbon and water, non-reservoir properties,
seismic bandwidth (resolution) and data quality, AVO angle,
reservoir architecture
· layering characteristics (e.g. thick or thin isolated reservoir units vs thick sequences of thin-bedded reservoirs)
· lateral extent and morphology.
Clearly, well calibration is invaluable for understand- ing the seismic response. The preceding chapters have emphasised how seismic modelling with well data is a critical tool in guiding the interpreter in what to expect from local rock and fluid effects. In areas without well calibration detailed interpretations may not be possible but AVO might be used as a scanning procedure to highlight anomalies and rank different areas.
The following discussion focusses on the problem of hydrocarbon detection and examples will be presented of how various techniques might be used in a variety of different geological settings. Given the large variety of expressions of AVO behaviour this discussion is intended to get the interpreter thinking rather than as an exhaustive account of all published approaches to AVO analysis.