Page 145 - Machine Learning for Subsurface Characterization

Stacked neural network architecture Chapter 4 121

uniform noises have a mean of zero, whereas exponential and Rayleigh noises
are generated such that the total distribution has a negative portion symmetric to
the positive distribution. So, each DD log contains 20% noise. Exponential
noise in DD logs has the most adverse influence on the prediction performance,
whereas the Rayleigh noise in DD logs has the least influence (Fig. 4.8). Accu-
racy drop due to the exponential noise is twice that of Gaussian noise.
DD logs are frequency-dependent responses of the geological formation.
Such frequency-dependent measurements contain Gaussian frequency-
dependent noise of various colors, such as violet, white, and brown noise. White
noise has an equal density at all frequencies, violet noise has density that
increases 6 dB per octave, and brown noise has density that decreases 20 dB
per octave [13]. We simultaneously added 20% Gaussian noise of a specific
color to each of the eight DD logs. So, each DD log contains 20% noise. DD
log-synthesis performance is not significantly influenced by the color of Gauss-
ian noise (Fig. 4.9). Finally, Gaussian noises of various densities are simulta-
neously added to each input and output logs. More noise in the training/
testing dataset results in higher mean NRMSE, amounting to a reduction in
DD log-synthesis performance from 10% to 11.5% for an increase in noise den-
sity from 10% to 20% (Fig. 4.10).
Key observations based on the sensitivity study are as follows:

1. Resistivity (RLA3) and shear-wave travel time (DTS) log are important fea-
tures for the DD log synthesis using SNN model.
2. Noise in resistivity (RLA3) and shear-wave travel time (DTS) log leads to
significant deterioration in the DD log synthesis using SNN model.
3. Deep laterolog resistivity logs (RLA3-5) are more important than shallow
ones (RLA0-2) for the DD log synthesis using SNN model.
4. Six resistivity logs, one neutron porosity (NPOR), and two sonic logs (DTC
and DTS) can be used for the proposed DD log synthesis using SNN model
at a prediction performance that is 10% lower than that obtained using all the
15 conventional logs.
5. Exponential noise in target can significantly deteriorate the performance of
DD log synthesis using SNN model.
6. Increase in noise density of Gaussian noise in DD logs from 10% to 20%
does not cause significant change in the performance of DD log synthesis
using SNN model.

3.2 Generalization capability of the DD log synthesis using the
SNN model

In this section, we investigate the performance of SNN model when it is trained
and tested in one well and deployed in another well; this truly assesses the gen-
eralization performance of the data-driven model. For any machine learning or
data-driven modeling task, generalization performance has a greater importance