Geology Reference
In-Depth Information
AI
a)
c)
sand
shale
AI
Backus average
(an average of averages)
Correlated monte carlo simulation
takes into account correlations of rock properties
b)
d)
1
1
Average of monte
carlo results
(10 and 90 percentile =
green and red)
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.02
0
0.02
0.04
0.06
0.08
0.1
R(0)
R(0)
Figure 10.10
The flaw of averages; (a) model using sand and shale acoustic impedance averages from the logs and thickness below
tuning, (b) relationship of N:G varying with normal incidence reflectivity for the model in (a), (c) distributions of AI for sand and shales,
(d) N:G vs normal incidence reflectivity results from a set of models generated using the distributions in (c) and Monte Carlo sampling
(after Mukerji et al.,
2008
).
10.3.3 Reservoir property mapping using
geostatistical techniques
Application of a single regression function to a seis-
mic attribute map assumes spatial independence.
Various forms of kriging, the traditional geostatistical
approach to data interpolation, can be used to address
the issues of fit to wells and spatial variability. Kriging
is an interpolation technique which uses a spatial
variogram to determine the mapped value (e.g.
Dubrule,
2003
). As illustrated in
Section 9.3
, the var-
iogram is a way of describing the spatial continuity of
the data, capturing the rapidity with which the vari-
able changes as a function of lateral or vertical dis-
tance. A large number of wells is required to make
this an effective method for interpolating well data;
with only a few wells it is not possible to estimate the
horizontal variogram. When building reservoir
models, variograms estimated for geological ana-
logues may be used, perhaps from cases that can be
studied at outcrop where measurements can be made
The Mukerji and Mavko (
2008
) example also
highlights the role of well data in the nature of
uncertainty. All too often the perception of uncer-
tainty is gauged from the scatter of points around the
regression line on the crossplot. However, given the
potential for bias in functions that are derived simply
by line fitting through a few points it is necessary to
try and place the well results in the context of geo-
logical variance. To quote Connolly (
2010
),
Uncer-
tainty is too complex to be adequately captured by
analysing the results from a small number of wells
'
.
Given that well data are often limited, a key aspect of
statistical rock physics is the extension of the model
dataset through the application of techniques such as
Monte Carlo simulation (e.g. Mukerji et al.,
2001
)
and the generation of pseudo-wells (e.g. Connolly
and Kemper,
2007
). This provides the context for
understanding uncertainty, at least in terms of the
available data. Ultimately, of course, other uncertain-
ties also need to be considered, including the effect of
seismic noise.
'
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