Page 155 - Machine Learning for Subsurface Characterization

130 Machine learning for subsurface characterization

PLS Partial least squares
LASSO Least absolute shrinkage and selection operator
MARS Multivariate adaptive regression splines
ANN Artificial neural network
DBSCAN Density-based spatial clustering of application with noise
SOM Self-organizing map
GMM Gaussian mixture model
RE Relative error
t-SNE t-Distributed stochastic neighbor embedding
y i Original log response at depth i
0
y i Normalized value of the log response (y) at a depth i
^
y i Synthesized value of the log response (y) at a depth i
β Coefficient of OLS model
w Coefficient/parameter vector
X Feature vector
Y Target vector
N Gaussian distribution
R 2 Correlation coefficient
Subscripts
i Formation (i)
j Formation parameter (j)

1 Introduction
Well logging is essential for oil and gas industry to understand the in situ
subsurface petrophysical and geomechanical properties. Certain well logs,
like gamma ray (GR), resistivity, density, compressional sonic travel time,
and neutron logs, are considered as “easy-to-acquire” conventional well logs
and deployed in most of the wells. Other well logs, like nuclear magnetic
resonance, dielectric dispersion, elemental spectroscopy, and shear wave
travel-time logs, are deployed in limited number of wells.
Sonic logging tools transmit compressional and shear waves through the
formation. These waves interact with the formation matrix and fluid.
Compressional waves travel through both the rock matrix and fluid, whereas
shear waves travel only through the matrix. The time taken by the wave to
travel from the transmitter to the receiver, referred as travel time, depends
on the geomechanical properties, which are influenced by the matrix
composition, fluid composition, and microstructure. Compressional and shear
travel-time logs (DTC and DTS, respectively) can be computed from the
waveforms recorded at the receiver. Sonic travel-time logs contain critical
geomechanical information for subsurface characterization around the
wellbore. The difference in the DTC and DTS logs is a function of the
formation porosity, rock brittleness, and Young’s modulus, to name a few.
Both shear and compressional travel-time logs are not acquired in all the
wells drilled in a field due to financial or operational constraints. Under such
circumstances, machine learning-generated synthetic DTC and DTS logs can