Geology Reference
In-Depth Information
(Posterior)
probability density
function
Using Bayesian inference
Facies and rock
property distributions
Markov Chain
Monte Carlo
sampling
Seismic data
Residuals
Detailed model in depth
(facies and reservoir
properties, Phi V
cl
etc)
NO
Trace match
YES
Depth to
time
conversion
Elastic properties
(using rock physics
relationships)
Synthetic
trace
Multiple impedance
realisations with facies and
reservoir properties
that fit the wells and seismic and
honour the geostatistics within the
stratigraphic framework
Seismic
noise
Velocity
model
Figure 9.34
A geostatistical inversion workflow incorporating Bayesian inference (derived from the work of Saussus and Sams (
2012
)
and Sams et al.
(
2011
))
measures might be used, such as absolute error, mean
squared error or correlation coefficient or combin-
ations thereof. Typically a cross-correlation coeffi-
cient similar to that used in well ties is calculated.
As in deterministic inversion an analysis of
implemented faster algorithms such as Markov Chain
Monte Carlo, a random walk method in which the
algorithm is guided (e.g. Contreras et al.,
2005
), or
simulated annealing (e.g. Debeye et al.,
1996
; Torres-
Verdin et al.,
1999
), but creating enough simulations
in a time efficient manner remains a significant
challenge. Francis (
2002
) adopts a hybrid approach,
referred to as Multi-Point Stochastic Inversion
(MPSI), in which traditional inversion methods are
used to condition model realisations to the seismic in
the time domain and within the seismic bandwidth.
Although a variety of geostatistical methods might be
used to generate these realisations, a Fast Fourier
Transform based spectral
the
'
well testing. Data quality is an important issue deter-
mining methodology and parameter choice. With
deterioration in seismic quality the seismic has less
of a constraining effect and the realisations increas-
ingly resemble the results of kriging with well data.
It is not immediately obvious how many realisa-
tions are sufficient for geostatistical inversion results
to be statistically meaningful. Effectively, there need to
be enough realisations to generate smooth cumulative
distributions of parameters derived from the
realisations. The minimum number of realisations
is usually of the order of 100 or greater. Whilst
Sequential Gaussian Simulation is a useful way of
understanding how geostatistical inversion works, as
a practical implementation it has the drawback of
being computationally slow. Some authors have
'
residuals is a useful QC as well as the use of
blind
frequency method is
preferred.
Since the mid 1990s there have been significant
developments in the way that geostatistical inversion
is approached particularly from the view point of data
integration and the conditioning of reservoir models
with seismic and prior rock physics information. In a
sequential workflow populating reservoir models with
seismic conditioned reservoir properties is done by
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