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Stacked neural network architecture Chapter 4 123

3.3 Petrophysical and statistical controls on the DD log synthesis
using the SNN model

The conventional and DD logs used to develop the data-driven model are
recorded more than 10,000 feet in the subsurface using logging tools that are
run at different times in the rugose boreholes filled with drilling fluids. In such
conditions, the logging tools sense certain properties of the near-wellbore geo-
logical formation volume. The logs are affected by the heterogeneity, complex-
ity, noise, and uncertainty due to the surrounding borehole and near-wellbore
environments that adversely affect the accuracy and robustness of the DD log
synthesis using the SNN model. In Well 1, relative error (RE) is used to evaluate
the performance of DD log synthesis at each depth. RE is formulated as
j P Mj
RE ¼ (4.5)
M
where P is the predicted value and M is the measured value. Mean RE for the
four conductivity-dispersion logs and that for the four permittivity-dispersion
logs are calculated at all depths resulting in two REs at each depth. When both
the REs are less than 0.2, the depth belongs to the category of good prediction
performance (65% for Well 1). When both REs are higher than 0.3 or either of
them are higher than 0.4, the depth belongs to the category of poor prediction
performance (24% for Well 1). The rest of the depths belong to moderate pre-
diction performance (11% for Well 1). Table 4.4 lists the statistical properties of
the formation zones for which the SNN model exhibits good (G), medium (M),
and poor (P) performances. Following petrophysical and statistical factors
are found to control the performance of the DD log synthesis using the SNN
model [14]:
1. Depths with low resistivity exhibit better performance. Low-resistivity
depths exhibit larger conductivity dispersion. These depths also exhibit
less-noisy dispersion data.
2. Depths having higher conductivity and higher relative permittivity measure-
ments exhibit better performance.
3. Zones exhibiting better performance tend to have lower absolute skew-
ness of DD logs. Lower skewness (symmetric distribution of data)
ensures relatively limited bias in the data and uniformly distributed noise
in data and that the bounds are equally distant from the mean. Symmetric
data are more suited for training the ANN models as compared with
asymmetric data.
4. Depths where porosity and water saturation are high exhibit better perfor-
mance. These depths are related to regions of low resistivity and limited
cementation. At a depth of high porosity, dispersion in DD logs is large,
the relative permittivity is high, and the dielectric tool response is more sen-
sitive to variations in porosity and pore-filling fluids. The data at such
depths are less noisy and more suited for building robust models.