Harddata training image

1
Hard-data training image
Soft-data training image
Figure 1 (left) training image serving as a
prior structural model, (right) result of a
forward modelling of a physical process (e.g.
seismic/flow) on the prior structural model.
2
multi-point data st(u)
s(u)
st(u) s(uha ), a 1, , nt
Figure 2 Scanning of a training image and
definition of a template geometry
3
Hidden layer
Input data
Target output data
t1
?
tK
?
T( )
T

S wkl xl
Figure 3 Architecture of a feed-forward neural
network with one single hidden layer.
4
(a)
s(u)
y(u)
st(u)
Collocated soft data
Hard input data
Figure 4 (a) Procedure used to collect data for
calibration of soft data using neural
networks. At each location u on the left image
(hard information) the facies category s(u) is
retrieved together with its neighboring
categories st(u) as defined by a template. At the
same location u on the right image (soft data)
the collocated soft information y(u) is retrieved.
5
T
yo
Collocated Soft data y(u)
?
(b)
S
T
Hard data input
T
Train neural net 1 with collocated soft data y(u)
Neural net 1
T
yo
?
Hard data input
E Y s(u), st(u)
S
T
(c)
T
Train neural net 2 with data from neural net 1
(E y st(u) - y(u) )2
Neural net 2
T
Var Y s(u), st(u)
Hard data input
S
?
T
Hard input data collocated (to target seismic)
facies data s (u) neighboring facies data st(u)
Figure 4 (b) method 1 the output of the neural
network is the conditional expectation of the
soft data. (c) method 2 two neural networks,
neural net 1 is used for determining the
conditional expectation neural net 2 for the
conditional variance. (d) method 3 the neural
network determines the full conditional
distribution.
6
d
d2 for coarsest grid d0 for finest grid
(a)
d4
(b)
d
d3
(c)
Figure 7 Template geometries for (a) scanning
the hard data training image (b) constructing
the seismic through a linear average procees (c)
scanning the hard data training image for
calibration of soft data
7
Figure 12 (top) angle information used for
conditional simulation (angle information is
shown at selected locations only in order not to
complicate the figure). (bottom) Indicator
kriging with changing anisotropy of the sand
facies based on the angle information and well
data.
8
Seismic predicted with neural network
Seismic from validation data set
Figure 16 (b) given a prediction of the
seismic (indicated by ) the histogram
(top) indicates the uncertainty of the true
seismic due to the modelling error in the neural
network.