Shear-wave velocity estimation
Shear-wave velocity estimation techniques: a comparison
Andrew Royle* and Sandor Bezdan (Geo-X Systems Ltd.)
Summary
Shear-wave velocity prediction techniques are compared for six wells located in Central Alberta.
Each well has a full suite of logs, including shear-wave velocity data. The main purpose of this
study is to establish calibration guidelines and to examine the limitations of the various estimation
methods.
Introduction
The absence of recorded shear-wave data in most cases imposes severe limitations in seismic
interpretation and prospect evaluation. Even when shear logs are directly available their quality is
often poor. The accuracy of the shear-wave velocity estimation schemes is especially important
when performing AVO modeling. Recently, a number of studies have been published on various
aspects of deriving accurate shear velocity information (e.g. Reilly, 1994; Armstrong et al., 1995;
Henning and Powers, 2000; Li et al., 2000). In this study, the availability of high-quality shear logs
provides an excellent opportunity to test and compare the performance of shear-wave velocity
estimation techniques.
Method
Castagna’s Relationship (ARCO mudrock line)
The most common method of shear velocity prediction is defined by Castagna et al. (1985). They
derived an empirical relationship between P-wave and S-wave velocity, which can be written as:
VP = 1.16 VS + 1.36
(km/s)
The parameters of the linear relationship between VP and VS were derived from worldwide data.
This empirical relationship became known as the mudrock equation or the "ARCO mudrock line".
If regional shear-wave velocity is available, a local mudrock relationship can be derived.
Krief’s Relationship
Krief et al. (1990) suggested another linear relationship between the squares of P-wave and Swave velocity; this relationship can be written as:
VP2 = a VS2 + b (km/s)
It is important to note that the regression coefficients are different for distinct lithological zones.
Lithological Log Constrained
If lithology logs such as Spontaneous Potential (SP) and Gamma Ray (GR) logs are present, the
observed sand-shale trends further constrain the estimated VS values. This is an empirical
approach that uses the sand baseline value, the shale baseline value, and the corresponding
theoretical Poisson’s ratio values for sand and shale. Since the P-wave velocity, S-wave velocity,
and Poisson’s ratio are related by definition, if Poisson’s ratio changes, one of the other two must
also change.
Shear-wave velocity estimation
Geostatistical Log Prediction
Log prediction using a multi-attribute transform calculated from other logs. For each of the
selected external attributes (DT, RHOB, etc.) a series of new attributes is created by applying a
set of non-linear transforms in an attempt to predict the target (VS) log. This series of new
attributes is then used to predict VS at the target well. This method only applies when sufficient
well control is available.
Results
The log data were first analyzed by comparing the estimated shear-wave velocities to the
measured shear-wave log (Fig. 1). The global relationships (ARCO and Krief) tend to
overestimate the shear-wave velocity whereas the local relationships (SP constrained and local
mudrock) more accurately estimate the shear-wave velocities. Figure 2 shows the associated
errors of the various estimation techniques. The comparison of the actual to the estimated VP/VS
ratios is displayed in Figure 3. As expected the performance of the local relationships is superior
to that of the global methods. The estimated and measured VS values were also examined using
crossplots of VS and VP (Fig. 4). Well-defined linear trends can be observed on the crossplots.
FIG 1. Comparison of shear-wave velocity estimations for wells 1, 2, and 3
To quantify the effect of the different shear-wave velocity estimations on the AVO response, AVO
synthetic modeling was performed over the target zone of well 3 (Fig. 5). A distinct AVO anomaly
at the reservoir zone is observed using the measured well logs. However, this AVO anomaly is
completely masked on the synthetic seismograms calculated from the global predictions of shearwave velocities. Figure 6 shows the amplitude relationships for the top and bottom of the
reservoir.
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Shear-wave velocity estimation
gas zone
FIG 2. The shear-wave velocity prediction errors for wells 1, 2, and 3
FIG 3. Comparison of VP/VS ratios for wells 1, 2, and 3
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Shear-wave velocity estimation
gas zone
FIG 4. Crossplots of VP and VS for wells 1, 2, and 3
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Shear-wave velocity estimation
Measured VS
ARCO mudrock estimated VS
horizons
top gas zone
base gas zone
FIG 5. Synthetic seismograms for the measured and ARCO estimated VS
top gas zone
base gas zone
FIG 6. Amplitude relationships for the top and base of the reservoir zone
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Shear-wave velocity estimation
Conclusions
In each case the ARCO mudrock equation predicted higher VS values than the measured ones.
Excluding the carbonate and pay zones the average RMS error was 21.1 %. The Krief method
exhibits comparable prediction errors. The locally calibrated coefficients are significantly lower
than those of the ARCO mudrock line. Even the local mudrock line predicts the VS values with an
average RMS error of 10.0 %. Using the SP log as a constraint in the estimation scheme, the
prediction error was further reduced (8.5 %). The error associated with the geostatistical method
was comparable to that of the SP constrained. In our comparison, the SP constrained and the
geostatistical shear-wave estimation schemes were the most accurate.
The AVO modeling results from the locally estimated shear-wave velocities show an increase in
amplitude at the target zone whereas the global relationships do not exhibit this anomaly. If
regional shear-wave information is not available, the global relationships can possibly be used in
conjunction with Biot-Gassmann fluid replacement modeling to improve the estimation of the
shear-wave values at the reservoir zone.
Acknowledgements
We thank PanCanadian Petroleum Limited for providing well log data. The data analysis was
carried out using Hampson-Russell AVO Modeling and Emerge software. We also would like to
thank Geo-X Systems Ltd. for supporting our work.
References
Armstrong, P. N., Chmela, W. and Leaney, W. S., 1995, AVO calibration using borehole data:
First Break, 13, no. 08, 319-328.
Castagna, J.P., Batzle, M.L. and Eastwood, R.L., 1985, Relationships between compressionalwave and shear-wave velocities in clastic silicate rocks: Geophysics, 50, 571-581.
Henning, A. and Powers, G., 2000, Shear-wave velocity estimation in the deepwater Gulf of
Mexico: 70th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1723-1726.
Krief, M., Garat, J., Stellingwerff, J. and Ventre, J., 1990, A petrophysical interpretation using the
velocities of P and S waves (full-waveform sonic): The Log Analyst, 355-369.
Li, Y., Hunt, L. and Downton, J., 2000, Sensitivity of rock properties in AVO analysis and prospect
evaluation: 70th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 186-189.
Reilly, J. M., 1994, Wireline shear and AVO modeling: Application to AVO investigations of the
Tertiary, U.K. central North Sea: Geophysics, 59, 1249-1260.
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