Page 58 - Machine Learning for Subsurface Characterization

44 Machine learning for subsurface characterization

assemblies are in contact when scanning the frontal surface (Fig. 2.4, right).
Sinusoidal pulses of 6 MHz are transmitted into the Tennessee sandstone by
each source transducer (one at a time), and the transmitted shear waveforms
are measured only by the corresponding sensor, in the same transducer
assembly. Each transducer assembly is active one at a time for transmitting
the pulses and recording the waveforms. Total number of shear waveforms
measured across the axial surface is 133 7 waveforms, whereas that
across the frontal surface is 133 5 waveforms. Prefracture shear
waveforms (Step 1 in the workflow shown in Fig. 2.2) are recorded only for
the axial surface prior to the hydraulic fracturing. Postfracture shear
waveforms (Step 3 in the workflow shown in Fig. 2.2) are recorded for both
the axial and frontal surfaces after the hydraulic fracturing.

4 Clustering methods for the proposed noninvasive
visualization of geomechanical alterations

The goal of the study is to noninvasively visualize the fracture-induced
geomechanical alterations in the sandstone sample by first clustering
the shear-waveform measurements and then using displacement discontinuity
theory to convert the cluster labels/IDs to physically consistent geomechanical
alteration index. The interaction of ultrasonic wave propagating through the
fractured material with the fractures and geomechanically altered zones
influences the amplitude, time delay, and other spatial and frequency-time
characteristics of the transmitted waveforms. At 133 locations on the axial
surface and 133 locations on the frontal surface, the seven and five transducer
sensors, respectively, record the shear waveforms affected by the
geomechanical alterations and fractures induced in the Tennessee sandstone
due to hydraulic fracturing. Clustering methods are used to group similar shear
waveforms, such that waveforms in each group can be assumed to have
interacted with similar fracture intensity/density and geomechanical alterations
as the wave travels from source to sensor. Therefore, these groups generated
using clustering represent the degree of fracture-induced geomechanical
alterations. The present study considers three methods for clustering the shear
waveforms: K-means clustering, agglomerative clustering, and density-based
spectral clustering of applications with noise (DBSCAN). Like any
unsupervised learning method, clustering methods do not have a predefined
outcome and these methods group samples based on certain similarity/
dissimilarity measures.

4.1 K-means clustering
K-means is the simplest and a widely used method for clustering. K-means
algorithm begins with a certain predefined number randomly selected samples
(data points) as cluster centers. Cluster labels are then assigned to each sample
based on the nearest cluster center. Centroid of each newly formed cluster is