Page 128 - Machine Learning for Subsurface Characterization

Stacked neural network architecture Chapter 4 105

where the attenuation and phase shift of the waves due to the electromagnetic
properties of the formation are recorded. Following that, the wave attenuations
and phase shifts at various frequencies are inverted using the tool-physics for-
ward model to compute multifrequency conductivity (σ) and relative permittiv-
ity (ε r ) of the formation in the frequency range of 10 MHz to 1 GHz. Relative
permittivity is computed as the real component of complex permittivity divided
by the vacuum permittivity. Conductivity is computed as the imaginary com-
ponent of complex permittivity multiplied by the angular frequency. Finally,
a physically consistent geo-electromagnetic mixing model or mechanistic
polarization-dispersion model is invoked to process the conductivity- and
permittivity-dispersion logs to estimate water saturation, bound-water satura-
tion, salinity, clay-exchange capacity, and textural parameters [1]. However,
there are several subsurface environments, operational challenges, and project
economic scenarios where DD logging tool cannot be run or where DD logs
cannot be acquired in the borehole. For such situations that prevent the subsur-
face deployment of DD logging tool and DD log acquisition, we propose a
workflow to generate 8 DD logs, comprising 4 conductivity-dispersion logs
and 4 permittivity-dispersion logs, by processing 15 easy-to-acquire conven-
tional logs using a stacked neural network (SNN) model, which combines mul-
tiple artificial neural networks (ANNs).
There are several applications of data-driven models and artificial neural
networks (ANNs) for subsurface characterization. Neural network can detect
conductivity anomalies in sediments [2]. For improved imaging, ANN can
reconstruct the 2D complex permittivity profiles in dielectric samples placed
in a waveguide system [3]. ANN was used to predict the real and imaginary
permittivity components of thermoresponsive materials by processing the mag-
nitude and phase of reflection coefficients measured at various frequencies
ranging from 2.5 to 5 GHz [4]. ANN was used to predict dielectric permittivity
of epoxy-aluminum nanocomposite at different concentrations [5]. An interest-
ing ANN-assisted application used complex-valued neural network (CVNN)
specially designed for generating/synthesizing complex-valued parameters
[6]. CVNN was used in landmine detection and classification by processing
the ground-penetrating radar data [7]. CVNN model was used in the prediction
of soil moisture content [8]. In our study, we designed a novel stacked neural
network (SNN) architecture specially designed for the synthesis of eight dielec-
tric dispersion logs acquired at multiple frequencies. The SNN architecture can
be generalized for the synthesis/modeling of any dispersive properties that are
mathematically represented as real and imaginary (or magnitude and phase)
components as function of an independent parameter (e.g., time, frequency,
count, and energy). The SNN architecture is suited for dispersive electromag-
netic properties where there is direct relationship between the real and imagi-
nary components at any given frequency and there is a strong relationship
between the real/imaginary components at various frequencies. Extensive sen-
sitivity analysis and noise analysis are performed on the SNN model to identify
the best strategy for generating conductivity and permittivity dispersions. When