Geology Reference
In-Depth Information
a)
Select random x,y point
One realisation
Simulate vertical
impedance trace
(conditional to
well data)
4
AI (km/s . g/cc)
9
b)
Mean
Create synthetic
trace
c)
SD
NO
Trace match
YES
Merge
impedance trace
with 3D model
0
σ
AI
(km/s . g/cc)
0.7
Figure 9.31
An example of geostatistical inversion products;
(a) single realisation, (b) mean of the realisations and (c) standard
deviation of the realisations. Note how the mean solution (b) is
smoothed compared to the single realisation (a) and how the
standard deviation increases away from the well control, consistently
with honouring the data at the well (after Lamy et al.,
1999
).
Figure 9.32
Sequential Gaussian simulation constrained by seismic
data (based on Haas and Dubrule,
1994
).
(
1994
). The methodology, referred to as Sequential
Gaussian Simulation, is based on a random search
method and works as follows. A particular trace is
chosen at random from the set of seismic traces in the
volume to be inverted and a large number of imped-
ance trace realisations are simulated. The simulation
estimates an impedance value at each pixel by kriging of
well data to determine a value with its Gaussian distri-
bution, and subsequent sampling using Monte Carlo.
For each simulated impedance trace, reflectivity coeffi-
cients are calculated and convolved with the seismic
wavelet. When a satisfactory trace match is obtained
the impedance trace is incorporated as a new control
point. Another seismic trace is chosen at random and
the process repeated. A single global realisation is com-
pleted when all the traces have been inverted (
Fig. 9.32
).
Another realisation can then be computed in the same
way, using a different set of random choices.
Geostatistical inversion is commonly done within
a 3D structural/stratigraphic geo-cellular grid (e.g.
Marion et al.,
2000
; Rowbotham et al.,
2003b
). This
allows appropriate control of the histogram model
and spatial relationships in sedimentary layers and
forms an effective basis for the integration of numer-
ous types of data. Sequence stratigraphy and biostra-
tigraphy provide the framework for correlations
between wells and extrapolation away from wells,
whilst depositional environments control the loca-
tion, trends and proportions of facies within the
sequences. Given that the geo-cellular grid is con-
structed in depth, it is important that there is an
accurate 3D time
depth relationship.
An important aspect of any geostatistical approach
is the assumption that the impedances from wells are
statistically representative and the spatial descriptors
are adequately defined. It is clearly important to have
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