Estimation of shale volume from well logging data using Artificial Neural Network

fication. To overcome these 
challenges, now computational tools such as 
machine learning (ML) and artificial intelligence 
(AI) are being used more and more in data 
processing, including geophysical processing. 
Specifically, the application of these tools for the 
analysis of well log data has been published by 
Saumen Maiti et al. (2007), Bosch et al. (2013), 
Dekkers et al. (2014), and Aarushi Gupta and 
Utkarsh Soumya (2020). 
_____________________ 
*Corresponding author 
E - mail: vuhongduong@humg.edu.vn 
DOI: 10.46326/JMES.2021.62(3).06 
 Duong Hong Vu, Hung Tien Nguyen /Journal of Mining and Earth Sciences 62(3), 46 - 52 47 
In the East Sea, there are also similar studies 
which were proposed by Karmakar et al. (2018); 
Tse et al. (2019). The results obtained by these 
authors show the effectiveness when applying 
these ML and AI techniques to solve geological 
structure interpretation missions. Shale has a 
major effect on reservoir quality because it 
reduces both porosity and permeability of the 
rock. There are several types of shale, and they 
can be distributed in the sand in four different 
ways: laminated, structural, dispersed or any 
combination of these. Each of them has various 
features and physical properties. Therefore shale 
volume estimation is one of the most essential and 
challenging tasks to be solved in formation 
evaluation. So far, many mathematical models 
have been proposed to calculate shale volume 
from Gamma - ray log. However, the results are 
not always accurate due to complicated geological 
conditions. This study aims to propose a new 
approach to estimate shale volume from well log 
data based on the application of an artificial 
neural network. We apply this technique tothe 
1143 data set, the ocean drilling program (ODP) 
in the East Sea (Figure 1). 
2. Methodology 
In this study, a new ANN model was 
developed to predict Vsh from well logging data. 
To demonstrate the effectiveness of the model, 
the prediction result is compared with traditional 
methods. 
Normally, estimating Vsh from the gamma - 
ray log still remains the most preferred approach. 
The procedure is easy, straighforward and likely 
to give reasonable results. There are two 
commonly used equations introduced by Clavier 
et al. (1971) and Steiber (1973). 
VshClavier=1.7 - √3.38 − ((𝐼𝐺𝑅 + 0.7)2) (1) 
VshStieber = 
𝐼𝐺𝑅
3−2𝐼𝐺𝑅
 (2) 
In which IGR shaliness index is defined by a 
function of the GR ((gamma - ray)) gamma ray log 
signal: (a) record of the response of the GR log for 
a nearby known shale body and a nearby known 
clean rock. 
𝐼𝐺𝑅 = 
𝐺𝑅𝑙𝑜𝑔 − 𝐺𝑅𝐶𝑙𝑒𝑎𝑛𝑅𝑜𝑐𝑘
𝐺𝑅𝑠ℎ𝑎𝑙𝑒 − 𝐺𝑟𝐶𝑙𝑒𝑎𝑛𝑅𝑜𝑐𝑘
 (3) 
Figure 1. Research area. (source: Google maps). 
48 Duong Hong Vu, Hung Tien Nguyen /Journal of Mining and Earth Sciences 62(3), 46 - 52 
An ANN network using back - propagation 
training algorithm (BPNN) and logsig activation 
function was proposed to predict the volume of 
shale from well - logging data. We used data from 
well A and B to train the ANN model, then used 
data of well C to evaluate the accuracy of the 
prediction model. Finally, the proposed ANN 
model was used to predict Vsh from input data of 
well C; then its performance was compared to 
Clavier and Steiber model. 
3. Data sets 
In this study, we used data sources from 
International Ocean Discovery Program 
( At this location, 
there are three wells OPD - 184 - 1143 A, B, and C 
(Figure 1), for brevity in this article we named 
them well A, B, C, respectively (Figure 1). 
The data used in this study include physical 
and lithological parameters measured in a 
borehole such as the longitudinal wave velocity 
(Vp), gamma - ray, density, magnetic 
susceptibility, and volume of shale (Vsh) in the 
core sample (Table 1). 
3.1. Data preprocessing 
Abnormal data can be considered as noise 
because they can negatively influence the ANN 
model and may restrict the model in its 
generalization. The data set of three wells are 
tested for anomaly by Z - score outlier detection 
algorithm where a threshold Z - Score of 3 is 
selected (Tripathy et al., 2013). Any data points 
above this threshold are marked as an outlier and 
excluded from the training data. The Z - score is 
the score given to the participant as per their 
performance: 
z = |Xi - Xmean|/ SD (4) 
Where: Xmean - the mean value of the data; SD 
- the standard deviation of the data; SD - the 
standard deviation of the data. 
To simplify the interpretation of the z - scores, 
the following agreements were made as: 
z < 2 implies the result is satisfactory. 
2 < z < 3 implies the result is questionable. 
z > 3 implies the result is unsatisfactory. 
To reduce volatility and eliminate statistical 
noise, the dataset is further processed and 
smoothened by a low - pass second – order 
Butterworth filter (Selesnick and Burrus, 1998). 
Figure 2 shows the example comparing raw 
and smoothened ((P - wave)) Pwave velocity data 
of well A. 
3.2. Data analysis 
The selection of input parameters for the 
training process is an important step, which 
determines the accuracy of the ANN model. To 
decide which parameter to be used as input data, 
the interrelationships between parameters were 
Parameters Well A Well B Well C 
Number of core 242 118 74 
Depth (m) 
Top 24.05 44.05 382.35 
Bottom 399.05 249.49 499.75 
Vp (m/s) 
Min 1550.56 1556.63 1714.9 
Max 2047.57 1803.72 2163.2 
Mean 1733.11 1623.25 1877.8 
Stdev 119.30 56.99 77.35 
GR (API) 
Min 20.25 26.50 24.75 
Max 54.75 54.00 49.00 
Mean 37.43 41.04 33.15 
Stdev 6.85 5.74 4.36 
Density 
(g/cc) 
Min 1.37 1.47 1.61 
Max 1.82 1.83 1.93 
Mean 1.66 1.65 1.77 
Stdev 0.09 0.08 0.07 
Magnetic 
susceptib - 
ility (SI) 
Min 1.00 5.50 3.20 
Max 54.00 29.50 14.50 
Mean 14.66 18.73 8.04 
Stdev 8.89 6.80 2.10 
Vsh (%) 
Min 0.00 5.00 5.00 
Max 98.00 98.00 94.00 
Mean 72.39 78.36 60.89 
Stdev 26.89 24.02 30.58 
Table 1. Summary of well log data. 
Figure 2. Pwave velocity smoothened. 
 Duong Hong Vu, Hung Tien Nguyen /Journal of Mining and Earth Sciences 62(3), 46 - 52 49 
studied using cross plots as shown in Figure 3. A 
regression coefficient closer to 1 represents a 
positive correlation and closer to - 1 represents a 
negative correlation between variables. From 
Figure 3, we can see that all parameters: P - wave 
velocity (m/hr), GR (API), Density (g / cc), 
Magnetic suscept. (SI) are suitable and can be 
retained in the ANN model development. 
4. Predict Vsh model development 
An ANN network using back - propagation 
training algorithm (BPNN) and logsig activation 
function was proposed to predict the volume of 
shale from well logging data (Figure 4). In this 
study, we used data from well A and B to train the 
ANN model, then used data from well C to 
evaluate the accuracy of the prediction model. 
A training data set of 316 samples from data 
of two wells A and B includeseveral parameters: 
longitudinal wave velocity, gamma - ray, density, 
magnetic susceptibility from well logging data, 
and volume of shale from core data. This database 
is divided into 3 sets: 70% of the sample is used to 
train the network, 15% is used for testing and, 
15% for the validation. Four parameters: P - wave 
velocity (m/hr), GR (API), Density (g/cc), 
Magnetic suscept (SI) are considered as input data 
and the output value of the ANN model is the 
volume of shale. The calculated output from ANN 
after a cycle (or iteration) is compared with the 
actual output given in the sample dataset (Vsh of 
core) to trace the error. This error is propagated 
back to output neurons and hidden neurons so 
that these neurons adjust their weights. This 
bidirectional propagation is carried out 
repeatedly, until the error reaches a minimum 
value less than a certain allowable value or until 
the number of loops reaches a predetermined 
value. The accuracy of the data model is 
demonstrated by the root mean square which 
serves as a metric to score the predictions of the 
ANN model with the expected result. 
RMSerror = √
∑ (𝑉𝑠ℎ𝑝𝑟𝑒𝑑𝑖𝑐𝑡−𝑉𝑠ℎ𝑎𝑐𝑡𝑢𝑎𝑙)
2
𝑛
 (5) 
Figure 3. Crossplot between well logging parameters. 
50 Duong Hong Vu, Hung Tien Nguyen /Journal of Mining and Earth Sciences 62(3), 46 - 52 
Determining the number of neurons in the 
hidden layer is a challenging step in model design, 
and there is no rigid rule to do it. In this study, to 
determine the optimal number of hidden neurons, 
different scenarios were carried out with variable 
numbers of neurons in the hidden layer and tests 
for their effect on the final prediction (Figure 5). It 
is worth noting that the number of neurons in the 
hidden layer should be chosen carefully since too 
many neurons in the hidden layer can lead to 
overfitting, making the network lose its 
generalization. Therefore, we decided to use 30 
neurons in one hidden layer, Figure 5 shows that 
the ANN model with one hidden layer including 
30 neurons given the RMSE = 0.002 and R2 = 
0.956. 
5. Results and discussions 
The proposed ANN model was used to 
predict Vsh from input data of well C, then 
compare its performance with Clavier and Steiber 
model. It can be seen that ANN model predictions 
are much more accurate than the other two 
traditional models, as confirmed by both RMSE 
and R2 in Table 2. It is observed from Figure 6 and 
Figure 7 that prediction from the ANN model 
follows the trend of actual Vsh.
 Model RMSE R2 
1 Clavier model 0.2616 0.022 
2 Steiber model 0.29 0.019 
3 ANN model 0.0037 0.92 
Table 2. Model performance comparison. 
Figure 5. (a, b) - Optimum number of neural in hidden layer. 
Figure 6. Vsh prediction by ANN for well C. 
 Duong Hong Vu, Hung Tien Nguyen /Journal of Mining and Earth Sciences 62(3), 46 - 52 51 
Meanwhile, Vsh calculated by Clavier and 
Steiber equations can not reflect this trend and 
has significant gaps with the actual Vsh. It can be 
explained that these traditionally predicted 
equations usually are proposed from a limited 
database in a particular research area; therefore, 
when applying them to other cases which have 
different geological properties, the result is 
usually inaccurate. 
6. Conclusion 
This study presented the practical use of data 
analysis and AI applications to solve geological 
interpretation problems. The ANN model is 
developed to predict Vsh from longitudinal wave 
velocity, gamma-ray, density, and magnetic 
susceptibility. The ANN model shows its 
advantages compared to other traditional 
methods. Therefore it can be recommended as an 
effective and suitable method to determine the 
volume of shale presenting in rock in the vicinity 
of the East Sea. Recommendations for future work 
are to update data from other wells to the ANN 
model to increase its accuracy. 
Author contributions 
The author Duong Hong Vu proposes ideas 
and contributes to the manuscript. The author 
Hung Tien Nguyen constructs the manuscript and 
contributes to the material analyses. The authors 
both declare no conflict of interest. 
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