Page 312 - Machine Learning for Subsurface Characterization

Classification of sonic wave Chapter 9 273

discontinuities (lower row). Three concentration parameters (kappa, k, and
inverse of dispersion) equal to 0, 5, and 1000 are selected for this study. When
the kappa equals 0, the orientations of discontinuity follow a uniform distribu-
tion. When the kappa equals 5, the orientations are centered at 0 degree and pri-
marily dispersed between 50 and 50 degrees. When the dispersion parameter
equals 1000, all the fractures are almost parallel to the y-axis, which is 0 degree.
These three types of materials represent high, intermediate, and low dispersivity
of discontinuities around the primary orientation.
When compressional wave propagates through such materials containing
discontinuities, the multipoint measurements of compressional wavefront travel
times are too complicated for humans to recognize and differentiate in terms of
the dispersion of the embedded network of discontinuities that give rise to the
measured travel-time signature. There do not exist simple simulation techniques
and physical law to characterize such embedded network of discontinuities
based on the measurements of the travel times. Machine learning provides a
possible way to extract complex relationships/patterns from the multipoint
wavefront travel-time measurements and relate them to the dispersion of the
embedded network of discontinuities. To that end, DFN model was used to gen-
erate 10,000 samples (realizations) for each of the three types of dispersion
around the primary orientation. In total, the training/testing dataset contains
30,000 samples. The compressional wavefront travel times originate from
one source and are measured at 28 sensors/receivers located on the three bound-
aries of the material, as shown in Fig. 9.22. The boundary on which one trans-
mitter/source is placed is known as the source-bearing boundary. There are no
receivers on the source-bearing boundary. The receivers are referred using indi-
ces ranging from 0 to 27. For purposes of developing data-driven models, each
sample in the dataset contains 28-dimensional feature vector, representing the
travel times measured at the 28 receivers. Each sample was assigned a label,
denoting a material type, for purpose of model training and testing. The
user-assigned label categorically represents the dispersion around primary ori-
entation of the embedded network of static discontinuities in a sample. The
dataset of compressional wavefront travel times with associated user-assigned
labels is processed by the nine classifiers to learn to noninvasively characterize
the material containing discontinuities in terms of dispersion around primary
orientation. The classification task is to classify the 28-dimensional travel-time
measurements into the four classes representing the dispersion of the embedded
network of discontinuities.

5.1.2 Model accuracy
Nine classifiers are applied to the dataset: KNN, SVM with linear kernel, SVM
with radial basis function (RBF) kernel, decision tree, random forest, AdaBoost,
Naı ¨ve Bayes, ANN, and voting classifier. These nine classifiers cover the most
popular classifiers used in machine learning and data-driven approaches.