Page 285 - Machine Learning for Subsurface Characterization

Classification of sonic wave Chapter 9 247

material containing mechanical discontinuities of various spatial properties,
such as orientation, distribution, and dispersivity; (2) perform fast-marching
(FM) simulations of compressional wavefront propagation through each numer-
ical model of material containing discontinuities to create a dataset of multi-
point compressional wavefront travel times recorded at multiple sensors
when emitted by a single source along with a label that categorically represents
the overall spatial properties of the discontinuities embedded in the material;
and (3) train several data-driven classification methods on the dataset of com-
pressional wavefront travel times with associated labels representing the spatial
characteristics of the embedded static discontinuities to learn to characterize
(categorize) the materials containing discontinuities. The configurations/
arrangement of 1 sonic source and 28 sensors/receivers for the measurement
of travel times are inspired by real laboratory experiments [15].

2.1 Assumptions and limitations of the proposed data-driven fracture
characterization method
a. The method is developed for two-dimensional rectangular materials,
assuming homogeneity in the vertical direction.
b. A discontinuity is a linear element, and the embedded discontinuities can be
represented as discrete fracture network (DFN).
c. The method is developed for compressional wavefront travel times ignoring
the reflection, scattering, refraction, phase change, later arrivals, and
dispersion.
d. The mechanical properties and the velocity of sonic wave propagation are
assumed to be homogeneous and isotropic for the background material.
e. The mechanical properties and the velocity of sonic wave propagation are
assumed to be homogeneous and isotropic for each discontinuity.
f. Discontinuities in material are assumed to follow certain statistical distribu-
tions of spatial properties.
g. Wavefront travel times are simulated using the fast-marching method
(FMM), which can have errors in the presence of large contrasts due
mechanical discontinuities.
h. The method is developed for scenarios when the discontinuities and pores
are filled with air.

2.2 Significance and relevance of the proposed data-driven fracture
characterization method
a. Numerical models of material containing discontinuities and simulations of
wavefront travel times are inspired by real-world laboratory experiments.
b. As a proof of concept, a limited number of source-receiver pairs were used
to generate the labeled travel-time dataset for developing the classification-
assisted fracture characterization method. Characterization performance