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Lithology identification technology using BP neural network based on XRF

Abstract

The element content obtained by X-ray fluorescence (XRF) mud-logging is mainly used to determine mineral content and identify lithology. This work has been developed to identify dolomite, granitic gneiss, granite, limestone, trachyte, and rhyolite from two wells in Nei Mongol of China using back propagation neural network (BPNN) model based on the element content of drill cuttings by XRF analysis. Neural network evaluation system was constructed for objective performance judgment based on Accuracy, Kappa, Recall and training speed, and BPNN for lithology identification was established and optimized by limiting the number of nodes in the hidden layer to a small range. Meanwhile, six basic elements that can be used for fuzzy identification were determined by cross plot and four sensitive elements were proposed based on the existing research, both of which were combined to establish sixteen test schemes. A large number of tests are performed to explore the best element combination, and the result of experiments indicate that the improved combination has obvious advantages in identification performance and training speed. The author’s pioneer work has contributed to the neural network evaluation system for lithology identification and the optimization of input elements based on BPNN.

Introduction

With the continuous improvement of the measurement accuracy of the logging tool and the enrichment of the element types, under the requirements of environmental protection measurement, XRF plays a more and more important role in complex lithologic stratum and evaluation of unconventional oil and gas reservoirs (Yarbrough et al. 2019). A significant body of research (Khajehzadeh et al. 2017; Tiddy et al. 2019) has been published on the methods of lithology analysis and mineral content calculation using XRF mud-logging data, and achieved good application results.

At present, the interpreting method of stratigraphic elements is based on an optimization algorithm, using the data of core analysis, to determine the mineral model that reflects the distribution of mineral content to identify the lithology. However, identifying lithology in wells without core becomes extremely difficult, which can be solved by artificial neural network (ANN) with its own unique sample learning ability.

ANNs for both classification and prediction have become a tool supporting comprehensive interpretation of well-logging and mud-logging data in petrophysical and petrochemistry issues. Element content (Alnahwi and Loucks 2019), mineral properties (Silva et al. 2013) and conventional logging curves (Luo et al. 2018; Puskarczyk 2019), e.g., natural gamma (GR), self-potential (SP), acoustic time (AC) are used as input variables to establish a lithologic identification sample database.

Milad et al. (2020) used a principal component analysis (PCA), elbow method, and self-organizing map (SOM) to improve the electrofacies and chemofacies from the outcrop and a subsurface uncored well based on XRF. This paper continues to optimize the types of elements that are input to back propagation neural network (BPNN) for lithology identification, two-step analysis method was proposed to determine the basic and sensitive elements in the study area, and performance evaluation system was established to objectively evaluate the performance of BPNN.

Measurement method

X-ray fluorescence measurement

Mud-logging is a detailed record of a borehole by examining the drill cuttings of rock brought to the surface by the circulating drilling medium. The content of elements in the drill cuttings can be quantitatively analyzed based on XRF technology, which provides the basic conditions for lithology identification. XRF on-site measurement mainly includes three steps: (1) drill cuttings sampling; (2) scouring, drying, grounding and pressing into sample to remove surface contaminants; (3) XRF measuring and analyzing. According to different dispersion methods, XRF can be divided into wavelength dispersion type and energy dispersion type, in which energy dispersive X-ray fluorescence spectrometer does not require a spectroscopic system, the sample is close to the detector, the optical path is short, and the detection efficiency is high. It reduces the requirements for the excitation source and improves the sensitivity. The structure of the entire spectrometer is simpler, lighter, and more suitable for the needs of on-site operations.

The CIT-3000 energy dispersive XRF spectrometer is used in this study, SDD electric refrigeration semiconductor detector is adopted, and the energy resolution is better than 128 eV (55Fe). The measurement time is set to 90 s, and the element detection content range can reach 0.001–99.99%. In order to improve the stability of the detector and the measurement sensitivity of low-order elements, the drill cutting and detector are placed in a vacuum chamber with a size of Φ165*40 mm, the filter device can be automatically selected according to the test material and the element content analysis adopts multi-parameter linear regression method. In addition, 24 certified reference materials (CRMs) recognized by Standardization Administration of the People’s Republic of China, which have clear lithology and known content of different elements were used as the calibration of the XRF analysis system (Mejia-Pina et al. 2016).

In order to reduce the influence of matrix effect and geometric effect during XRF measurement, the relative humidity of the drill cuttings to be tested needs to be controlled below 20RH% and ground to a particle size of less than 200 mesh. Then, the dried and ground cuttings are put into the sample loop, compressed at a pressure of 5 MPa using a sampler and placed in a vacuum measurement chamber for measurement.

Data set

A total of 906 drill cuttings in this study were sampled at the depth of 5200–5756.8 m in well No.122 and at the depth of 5220–5600 m in well No.125 in Nei Mongol, China. The lithology of the drill cuttings located at different depths are based on the results of the laboratory analysis of the cores at corresponding depth, which are mainly dolomite, granitic gneiss, granite, etc., totaling 8 types of lithology as shown in Table 1. Due to the small amount of rock such as aegirine-nepheline syenite and gabbro, which do not meet the training conditions of neural network, this study selects 6 types of lithology, including dolomite, granitic gneiss, granite, limestone, trachyte, and rhyolite.

Table 1 The number of drill cuttings from Nei Mongol

Methodology

The mineral composition and elemental distribution of rocks in different wells with similar geological environment within a certain regional limit are relatively stable, cores from several wells are sampled to determine the lithology of rocks, and XRF data of drill cuttings at corresponding depths are obtained, both of which form the training set for the BPNN in order to perform machine identification of drill cuttings and formation depth prediction of the other wells in the same region.

Back propagation neural network

ANN is a mathematical model for distributed parallel information processing that mimics the behavioral characteristics of animal neural networks, which relies on the complexity of the system to process information by adjusting the interconnecting relationships between a large number of internal nodes. BPNN is a kind of multilayer feed-forward ANN that features forward propagation of the signal and backward propagation of the error. In 1986, Rumelhart et al. (1986) proposed the BPNN, which realizes the relationship mapping between input and output layer without the mathematical equation in advance (Bahadır 2016) and consists of three parts: the input layer, the hidden layer and the output layer.

The structure of BPNN, as shown in Fig. 1, has one input layer, two hidden layers and one output layer, each layer is connected to each other, W and θ represent the weight and threshold of the neuron node, respectively.

Fig. 1
figure1

The structure of BPNN with two hidden layers

After entering BPNN from the input layer, the training sample will continue to flow in the BPNN, enters each hidden layer neuron node through the weight channel, each neuron in the hidden layer will use an activation function to perform weighted summation processing on it, and then enters the output layer through the weight channel between the hidden layer and the output layer to produce a result after processing. During the propagation of training samples from the input layer to the output layer, the process of gradually updating the state of each layer from the input layer to the output layer is the forward propagation process. BPNN will calculate the error between the output result and the expected result, if the error is greater than the set accuracy threshold, the error will be backpropagated layer by layer along the path and the network weight will be corrected. BPNN continuously iterates forward propagation and error back propagation until the sum of error squares of all training samples meets the accuracy requirements (Ren et al. 2014).

BPNN parameter optimization

The key of BPNN training is the selection of training parameters and the avoidance of saddle points in the optimization procedures. The number of nodes in the input and output layers of the neural network, the activation function, and the complexity of the problem may affect the determination of the number of nodes in the hidden layer. The number of hidden layers of BPNN was set to two, since there is a discontinuous function between XRF data of drill cuttings and lithologies (Wang et al. 2018). For the discussion of the optimal number of nodes in the hidden layer, Wang et al. (2018) have given some empirical formulas:

$$\left\{ {\begin{array}{*{20}c} {\mathop \sum \limits_{i = 0}^{n} C_{h}^{i} > k} \\ {h = \sqrt {n + m} + a} \\ \end{array} }, \right.$$
(1)

where k is the number of training samples, m is the number of nodes in the output layer, n is the number of nodes in the input layer, a is a constant between 1 and 10, and \(C_{h}^{i}\) = 0 when i > h. m, n, and k can be set according to the attributes of neural network, when the BPNN for lithology identification is determined, therefore, the number of hidden layer nodes can be determined in a small range by formula (1), then verify and calculate the minimum error value for each integer solution in the interval, which is the optimal number of hidden layer nodes.

Elemental data normalization and lithology vectorization

There is great difference between the content of each element in the drill cutting, which leads to different weights of the influence of each element on the lithology identification, and the influence of elements with low content may be buried by the elements with large content. Thus, it's necessary to normalize the input data as shown in formula (2) in order to adjust values measured on different scales to a notionally common scale:

$$Y = \left( {L_{max} - L_{min} } \right)\frac{{X - X_{min} }}{{X_{max} - X_{min} }} + L_{{{\text{min}}}},$$
(2)

where X is the input data, Y is the normalized data, Xmax is the maximum among the input data and Xmin is the minimum. Lmax is the maximum of notionally common scale and Lmin is the minimum, Lmax is set to 1 and Lmin is set to 0 in this paper which means the notionally common scale is the interval [0, 1].

BPNN is a kind of method based on mathematical function, the problem cannot be described by mathematical methods when there is category data in dataset to be analyzed, therefore, pre-vectorization of categories is necessary, lithologies are mapped with multi-dimensional vector in binary (Zhang et al. 2019), as shown in Table 2.

Table 2 Lithology binary sign

Each dimension of the output in the interval [0, 1] from BPNN represents the possibility that the sample being identified as a certain lithology. A unit circle as shown in Fig. 2 can be created for each sample, and lithology can be judged according to the distribution of six possibilities in the circle.

Fig. 2
figure2

Schematic diagram of lithology judgment

Neural network evaluation system

The nature of BPNN for lithology identification is a multi-classification system, and confusion matrix (Fig. 3) is usually used as a visual tool to evaluate the classification accuracy (Ruuska et al. 2018), thus, Accuracy, Recall, and Kappa are used as model evaluation indicators in this article.

Fig. 3
figure3

Schematic diagram of confusion matrix

Accuracy represents the proportion of all samples with correct prediction in all test samples:

$$Accuracy = \frac{a + e + i}{{a + b + c + d + e + f + g + h + i}}.$$
(3)

Recall represents the proportion of all positive examples of a certain type of sample that are matched, which measures the classifier’s ability to recognize positive examples. Recall of different categories can be obtained by formula (4):

$$Recall_{A} = \frac{a}{a + b + c}, Recall_{B} = \frac{e}{d + e + f}, Recall_{C} = \frac{i}{g + h + i}.$$
(4)

Cohen's kappa coefficient (Kappa) is usually used as a standard for evaluating classification consistency in statistics (Landis and Koch 1977), which can be calculated by formula (5):

$$\left\{ {\begin{array}{*{20}c} {P_{e} = \frac{{\left( {a + b + c} \right) \cdot \left( {a + d + g} \right) + \left( {d + e + f} \right) \cdot \left( {b + e + h} \right) + \left( {g + h + i} \right) \cdot \left( {c + f + i} \right)}}{{\left( {a + b + c + d + e + f + g + h + i} \right)^{2} }}} \\ \\ {Kappa = \frac{{Accurary - P_{e} }}{{1 - P_{e} }}} \\ \end{array} } \right..$$
(5)

The calculated result of Kappa ranges from -1 to 1, but it usually falls within the interval [0, 1]. There are different explanations about the magnitude of Kappa (Fleiss et al. 2003; Landis and Koch 1977), and the explanation of Landis and Koch (1977) is adopted in this paper, which regards Kappa < 0 as indicating no agreement, 0–0.20 as slight consistency, 0.21–0.40 as fair consistency, 0.41–0.60 as moderate consistency, 0.61–0.80 as substantial consistency, and 0.81–1 as almost perfect agreement.

Analysis of input elements

Choosing an appropriate combination of elements is very important to the effect and stability of BPNN for lithology identification. As the input of the neural network, the selection of formation elements has a great influence on the convergence of the neural network (Wu et al. 2005). More than 20 elements such as Na, Mg, Al, Si, P, S, K, Ca, Mn, Fe, etc., can be measured in the formation through XRF analysis technology, and if too many elements are selected, the complexity of the neural network will increase and overfitting will easily occur. Therefore, a lithology identification plate was established to determine the combination of basic elements by cross plot at first, and then, the sensitive elements of the rock are analyzed to optimize the combination of elements that are input to BPNN.

Basic element combination analysis by cross plot

The cross plot is a quick and intuitive way to explain lithology (El-Khadragy et al. 2014) which can draw a two-factor or multi-factor intersection diagram through the mineral or element content of the rock. According to the XRF data of drill cuttings, the statistical distribution range of certain element contents is shown in Table 3, which indicates that different lithologies have different distributions of element content and it is possible to visually distinguish the lithologies by establishing plates with different elements and observing the distribution of scatter.

Table 3 The distribution range of certain element content in drill cuttings

The total content of Ca and Mg in sedimentary rocks is 23.9–59.83%, which in igneous rocks is 3.83–36.28%; the content of Si in sedimentary rocks is less than 16.42%, which in igneous rocks is 7.22–36.90%. Therefore, the dividing line L1 (y = 1.5∙− 36.5) is introduced. When the element intersection point is above L1, the rock is identified as igneous rock; when the element intersection point is below L1, the rock is identified as sedimentary rock, as shown in Fig. 4a.

Fig. 4
figure4

Lithology identification plate of a sedimentary rock and igneous rock, b sedimentary rock and metamorphic rock, c limestone and dolomite, d rhyolite, granite and trachyte. The variable w represents the mass fraction of the element in the drill cutting, which was calculated by CIT-3000

The content of Ca in metamorphic rocks is 2.50–23.94%, which in sedimentary rocks is 20.50–45.54%; the total content of Si, Al, and K in metamorphic rocks is 6.68–50.47%, which in sedimentary rocks is less than 18.75%. Therefore, the dividing line L2 (y = 4∙x − 81.5) is introduced. When the element intersection point is above L2, the rock is identified as metamorphic rock; when the element intersection point is below L2, the rock is identified as sedimentary rock, as shown in Fig. 4b.

Among sedimentary rocks, the total content of Ca and Si in dolomite is 20.67–56.78%, which in limestone is 24.05–54.83%; the total content of Mg and Fe in dolomite is 4.24–18.84%, which in limestone is 0.74–20.84%. Therefore, two dividing lines L3 (y = 0.9∙x-22.5) and L4 (y = 0.32∙x-8) are introduced. When the element intersection point is above L3, the rock is identified as dolomite; when the element intersection point is below L4, the rock is identified as limestone; when the element intersection point is between L3 and L4, it is a mixed zone of dolomite and limestone, and the plate cannot accurately identify this type of rock, as shown in Fig. 4c.

Among igneous rocks, the total content of Ca and K in trachyte is 2.37–29.39%, which in granite is 12.59–22.00%, while that in rhyolite it is 20.48–23.74%; the total content of Mg, Al, and Si in trachyte is 8.6857.27%, which in granite is 21.66–45.12%, while that in rhyolite is 20.89–28.96%. Therefore, the discriminant parameter R = (w (Mg) + w(Al) + w(Si))/(w(Ca) + w(K)) is introduced. When R > 3.52, the rock is recognized as trachyte; When 1.16 < R < 3.52, the plate is identified as granite; when R < 1.16, the plate is identified as rhyolite, as shown in Fig. 4d.

The lithology can be identified by six elements of Mg, Al, Si, K, Ca and Fe based on the cross plot. However, the types of discriminant elements for lithology identification are different, the dividing line is difficult to confirm and there are certain indistinguishable areas, which leads to a large amount of computing resources being consumed in practical engineering applications. For such classification problems with multi-input, multi-output, multi-variable and causality difficult to describe, BPNN is a suitable solution.

Sensitive element determination by mineral analysis

In addition to the six elements involved in the lithology identification plate above, the content levels of the nine elements (Ba, Zr, S, Na, P, Sr, Ti, V and Cl) in different samples have certain differences. In igneous rocks, with the increase of acidity, the content of Si in the rock increases while the content of Ti decreases. Moreover, due to the part of biotite in its composition, a small amount of S appears, at the same time, Ba accumulates in the rock in the diagenesis process as an incompatible element (Kelemen et al. 1990). In acidic rocks, granite and rhyolite can be divided into calc-alkaline and alkaline series according to the similarities and differences of Na, K and Al (Irvine and Baragar 1971; Shand 1927). The content of plagioclase in rhyolite is relatively low, while the content of potassium feldspar is relatively high, and its element characteristic is that the content of K is much higher than Na. Therefore, Na, S, Ba and Ti were selected as sensitive elements and combined with the six basic elements to establish a BPNN for lithology identification based on the differences in element characteristics between different lithologies.

Result

Based on the abovementioned six kinds of basic element content and preliminary judgment of sensitive elements, in order to explore the influence of different input element combinations on the lithology identification effect, the following schemes were performed:

  • K, Ca, Mg, Al, Si, Fe were selected as the basic element combination as the input for BPNN, and three sensitive elements Na, S, Ba and Ti were added to establish sixteen element combinations respectively, as shown in Table 4;

  • 70% data of each lithological were divided into training set, and 30% data were divided into test set by random sampling method;

  • The largest number of BPNN training iterations was set to 1000, the training target (mean square error) was set to 10–5, the learning rate was set to 0.15, and the 'trainlm' training algorithm was used, the hidden layer transfer function was set to 'tansig', the output layer transfer function was set to 'purelin', the number of hidden layer nodes was calculated and verified using the method described above;

  • Each scheme was repeatedly established and tested 50 times, and the average value of Accuracy, Recall of each lithology, Kappa and training time were taken as the experimental evaluation results.

Table 4 Element input scheme of BPNN

A large number of networks were tested to determine the optimal performance with different number of hidden layer nodes and find the optimal input element type with different combinations of input elements. Figure 5 shows the histograms of Accuracy and Kappa of the samples under different scheme. Accuracy of all schemes is above 87.8%, and the lowest Kappa still satisfies substantial consistency, which is consistent with the above statement that there is a certain indicative relationship between lithology and element content.

Fig. 5
figure5

Comparison of Accuracy and Kappa in different schemes

The analysis of the average values of Accuracy and Recall (as shown in Fig. 5) shows that:

  • Kappa has a clear positive correlation with Accuracy;

  • The performance of BPNN is not better with more input elements, but with some special combinations of elements;

  • Ba has an obvious positive effect on lithology identification, and the results of the experimental scheme containing Ba are significantly higher than those without Ba;

  • S and Ti have a negative effect on the identification effect and cause the misjudgment of BPNN, regardless of whether S and Ti is added alone or both;

  • The effect of an element on lithology identification is not absolute. If the input elements contain both positive and negative elements, the experimental results are uncertain, which is determined by the internal self-learning of neural network.

For more detailed information about identification performance, Recall of each lithology was selected to explore the elemental response of each lithology, and the training time was selected to judge the convergence ability and training speed of the network. Recall and training time of different schemes in Fig. 6 and Fig. 7 indicate:

  • Recall of lithology is related to the number of samples. Dolomite has the highest Recall due to its large number of samples. Rhyolite with only 22 samples gets the lowest Recall. The number of other lithologies is similar, but far less than the number of dolomites, so Recall of them also reflect the same trend;

  • Ba has a significant positive effect on Recall of limestone and rhyolite; besides, S, Na and Ti have a negative effect on limestone, which may be determined by the element response characteristics of lithology itself;

  • Recall of dolomite is steadily maintained at a high level regardless of the change in input elements, which indicates that the basic elements are sufficient for precise identification of dolomite;

  • Recall of granite and trachyte is steadily maintained at a moderate level regardless of the change in input elements, which may be caused by the small number of training samples;

  • In this case, the changes in Accuracy and Kappa are mainly caused by the influence of different input elements on limestone and rhyolite.

Fig. 6
figure6

Comparison of Recall of lithology in different schemes

Fig. 7
figure7

Comparison of train time in different schemes

Discussion on lithology prediction in the well

The network evaluation system proposed in this paper can objectively analyze the results of lithology identification, and the method of two-step optimization of input element can screen lithology sensitive elements and improve the identification effect.

The above experimental results show that Ba element has an absolute positive influence on limestone and rhyolite, but the influence of Na, S and Ti seems to be more complicated. Compared to the combination of basic elements, whether these three disputed elements are added separately or mixed together, it will reduce Recall of limestone, while adding Ba will increase Recall by about 10%; on the other hand, Na and S have little positive effect on the identification of rhyolite, while Ti has a negative effect.

The thirteenth input element scheme (Mg/Al/Si/K/Ca/Fe/Na/S/Ba) shows Accuracy of 92.3%, Kappa of 0.83 and training time of only 4.0 s, which not only has a great network performance, but also has a faster training speed. Therefore, the thirteenth plan was used as the best combination of input elements in this case.

The thirteenth input element scheme was adopted, with well No.125 as the training set and well No.122 as the test set for lithology prediction. Figure 8 shows the variation trend of basic elements and mineral content in well No.122 with the increase of sampling depth, and shows the comparison between the real lithology of the formation and the lithology prediction result from BPNN. The neural network evaluation system for lithology prediction shows that the prediction Accuracy is 91.41%, training time is 4.01 s and Kappa is 0.81, which indicates that the prediction network has almost perfect consistency; however, the evaluation system still considers that rhyolite has a low Recall, which corresponds to the fact that rhyolite has fewer samples.

Fig. 8
figure8

Results of element mud-logging analysis and lithology prediction of well No.122. The 6 lithologies represent, respectively: a rhyolite; b limestone; c granite; d granitic gneiss; e trachyte; f dolomite

Unfortunately, our results lack the support of a large amount of XRF mud-logging data, resulting in a significantly lower Recall of lithologies with a small number of samples than those with a large number of samples. Despite its limitations, this study can clearly indicate that the two-step analysis method of input elements, the neural network optimization method and evaluation system are effective.

Conclusions

On the basis of BPNN and analysis of basic and sensitive elements, Mg/Al/Si/K/Ca/Fe/Na/S/Ba is inferred to be the best combination of input elements in this example, and separated 6 types of lithology, finally, a BPNN trained by a known well successfully predict another unknown well.

In conclusion, the obtained results were found:

  • It is feasible to identify lithology based on the element content measured by XRF using BPNN;

  • The lithology identification method based on BPNN has high accuracy and almost perfect consistency;

  • Due to the diversity of the elements in the XRF measurement results, element analysis is necessary before BPNN is established and the two-step analysis method of basic and sensitive elements proposed in this paper is effective;

  • The neural network evaluation system composed of Accuracy, Kappa, Recall and training time proposed is effective, which can objectively reflect the changes in training performance of different programs;

  • Due to the uneven distribution of the number of different lithologies, which leads to a low Recall of rhyolite, more mud-logging data needs to be further trained.

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Acknowledgements

The author would like to thank Prof. Yingjie Ma from Chengdu University of Technology for providing mud-logging data. This study was supported by the National Natural Science Foundation of China (No. 41704171, No. 12075055), Defense Industrial Technology Development Program (No. JCKY2018401C001), Natural Science Foundation of Jiangxi Province (No. 20192BAB202009).

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Communicated by Prof. Jadwiga Jarzyna (ASSOCIATE EDITOR) / Prof. Michał Malinowski (CO-EDITOR-IN-CHIEF).

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Wang, Q., Zhang, X., Tang, B. et al. Lithology identification technology using BP neural network based on XRF. Acta Geophys. (2021). https://doi.org/10.1007/s11600-021-00665-8

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Keywords

  • Lithology identification
  • BP neural network
  • XRF
  • Cross plot