Geology Reference
In-Depth Information
Figure 9.4
Generalised flow-chart for
model-based inversion.
Seismic interpretation
Log data
Wavelet
Impedance estimate
(model)
Seismic trace
Model trace
Update
impedance model
Calculate error
Display impedance
Small enough?
Yes
No
not consistent with the seismic data, and examination
of the well-to-seismic ties is needed to try to find out
whether the well data or the seismic are at fault. In the
second case there will be an adjustable weighting
parameter that determines the relative weight given to
deviations of the impedance model from the starting
point on the one hand, and synthetic error on the other.
Trials will be needed to establish the best weighting
parameter; this is implicitly a judgement about noise
levels in the seismic data, and again the well ties are a
key to understanding. Usually a range of parameter
settings will give equally plausible inversion results.
This type of non-uniqueness can easily be explored
on a test dataset, giving at least a qualitative appreci-
ation of the range of possible solutions. Some provision
is also required in the algorithm to prevent solutions
from emerging with high-amplitude oscillations at
very high frequencies, such that they would have negli-
gible effect when convolved with the seismic wavelet.
Within these constraints, model-based inversion
finds a solution for the impedance trace that minim-
ises the synthetic error. Usually there is a range of
impedance trace solutions that provide a fairly good
fit to the seismic data. An issue is whether the algo-
rithm is able to find the solution with the lowest
possible synthetic error. If the process that updates
the model looks only at how small movements away
from the starting point affect the synthetic error, then
it is likely to find a solution fairly close to the initial
model. It will be optimal in the sense that small
changes to the final model cause the error to increase.
However, it may be that a more radical change to the
model would produce a solution with lower error.
Various algorithms are employed to allow the opti-
misation process to jump out of a local minimum and
(it is hoped) eventually find the global optimum with
the lowest possible error. An example is simulated
annealing (e.g. Sen and Stoffa,
1991
), in which model
changes that increase the synthetic error have a defin-
ite probability of being accepted. This probability
decreases as the iterations progress, so the process
starts out by exploring a range of possible solutions
and later homes in on the best of them. The name
comes from the analogy with the physical process in
which a solid is heated and then slowly cooled until
it reaches the global minimum energy state where it
forms a crystal. In practice, if the starting model is
fairly close to the optimum solution, the global
minimum may not be very different from the solution
that would have been found by a simpler algorithm
that looks only for local improvement.
Figures 9.5
9.9
show an example of a model-based
inversion. Horizon picks on the main reflecting inter-
faces are used to establish the starting model for the
inversion (
Figs. 9.5
and
9.6
). The inversion is run with
the appropriate wavelet and constraints. The result is
a micro-layer impedance model (
Fig. 9.7
) which, as a
QC step, needs to be closely compared with the actual
impedance in the well. A final impedance section is
shown in
Fig. 9.8
. A map of average impedance in the
reservoir interval (
Fig. 9.9
) shows tight (high AI)
sands in red and porous (low AI) sands in blue.
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