IEEE Signal Processing - March 2018 - 76

Overview of the prediction stage
The prediction stage involves two significant steps: first, selection
of an appropriate prediction/classification tool and training of the
corresponding parameters, as appropriate for the chosen ML
algorithm; second, repeated testing, validation, and adjustment of
parameter values for ensuring the generalization capability. Each
sample of a data set consists of a tuple containing predictor and
target attributes pertaining to a particular time (depth) instant.

Selection of the ML scheme
The literature [1], [3], [6]-[12] suggests applications of several ML
algorithms to the RC problem. It is difficult to find a single ML
method working for all RC problems because of the wide variation
of lithology and geology. Generally, the initial selection of an ML
method can be done heuristically using the domain knowledge of
the experts for a given data set. After implementing a number of
ML algorithms on the data set, the user finalizes the model yielding
the best performance. There can be two different approaches for
prediction: 1) prediction of continuous values (generally referred
to as prediction) and 2) class-based prediction (known as classification). For prediction of continuous values, the cost function
can be designed by computing the error between the values of the
target and obtained vectors. On the other hand, the number of misclassifications can be used as the cost function for the class-based
prediction approach. Several ML algorithms such as an artificial
neural network (ANN) and its variants [3], [13], neuro-fuzzy systems [1], [8], support vector regression (SVR) [14], [15], support
vector machines (SVMs) [16], [17], support vector data description (SVDD) [10], [11], genetic algorithms [18], hybrid systems
[9], [18]-[20], and so on have been applied to learn the nonlinear
mapping between the seismic and lithological attributes.

Prediction of continuous values
Next, we summarize three important ML algorithms-the ANN,
the adaptive neuro-fuzzy system (ANFIS), and SVR-applied
in various RC frameworks. The ultimate goal of prediction is to
yield the functional relationship between the predictor and target
variables so that targets can be estimated for unknown predictor
values. Figure 4 describes a workflow for continuous and classbased predictions using ANN, ANFIS, or SVM algorithms.

The ANN
The ANN has gained popularity over the last few decades to
solve RC problems due to its simplicity. Learning an ANN using
a backpropagation algorithm has two phases:
1) Forward phase: The input signal propagates to the output
node through the hidden layers.
2) Backward phase: The error signal between the target and the
output is computed at the output layer and propagates back to
the input layer.
The network structure, e.g., the number of hidden layers,
numbers of neurons, and activation functions, is tuned by the
users to achieve acceptable performance. The selection of different activation functions such as hyperbolic tangent sigmoid
and log sigmoid transfer functions may affect the performance
as well [3]. The parameters of an ANN can be calibrated using
76

efficient learning algorithms like the scaled conjugate gradient
method [3]. The ANN can also be used for classification purposes, where the target log contains discrete class labels instead
of continuous values.

The ANFIS
The ANFIS has also been extensively used in the field of RC by
researchers [1], [8]. A detailed description of the fuzzy logic theory, membership functions (MFs), ANFIS system, and its application on a real hydrocarbon field data set is given in [8]. Unlike the
ANN, fuzzified values of inputs and target variables are fed to
the ANFIS; and the final output is defuzzified before comparing
with the target log for evaluating the performance. The ANFIS
workflow is given in Figure 4. It starts with the initialization of
MFs, rule base, and fuzzy inference system (FIS). The updating
of ANFIS parameters is carried out by training, testing, and validation until the optimum performance is yielded. The choice of
MFs, the FIS inference method, and rule base can be crucial for
the efficient tuning of an ANFIS.

SVR
SVR has gained attention among researchers to predict petrophysical properties, e.g., porosity and permeability, for RC [14],
[15]. SVR tries to learn the relationship between the predictor and
target attributes by means of a function in a higher-dimensional
space. The effects of the training data set size and various parameters on the SVR performance are investigated in [14]. The kernel
functions and associated parameters are calibrated by a three-step
approach: training, testing, and validation as in ANN and ANFIS.
There are also several other ML algorithms reported in the RC
literature. Some of them are the committee model [9], Bayesian
inversion [19], ensemble ML [20], and neural network adaptive
wavelet (wavenet) [21], which have been used to predict porosity,
permeability, water saturation, and so on. Though the training
of most of these methods is based on supervised learning, unsupervised ML algorithms, e.g., self-organizing-maps (SOMs) have
also been used for seismic facies analysis [22]. To correctly estimate the oil production capacity of a reservoir, the prediction of
asphaltene precipitation is important in RC [23], [24]. Similar to
lithological property prediction, the modeling of compressional
and shear wave velocities from well logs has been carried out
by neuro-fuzzy systems and metaheuristic algorithms such as
ant colony optimization (ACO), among others. [25], [26].
In the case of RC, horizontal boreholes also contribute to
hydrocarbon reservoirs along with their vertical counterparts
[27]. In the case of horizontal well logs, accurate pressure analysis based on a hybrid ML tool such as ANN-particle swarm
optimization (PSO) is essential for estimating the production
capacity of a reservoir [27]. ANN-PSO has also been used for
modeling of equilibrium water dew point of natural gas in RC
[28]. Moreover, in the case of natural gas reservoirs, least square
SVM (LSSVM) is an automatic choice for the researchers for
predicting natural gas dehydration unit and gas/oil relative permeability [29], [30] due to its simplicity. In [31], predictions
of porosity and permeability from petrophysical logs have been
carried out using hybrid models. In this article, we give a concise

IEEE Signal Processing Magazine

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March 2018

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