Keywords

1 Introduction

Understanding a reservoir to determine where to drill a production well comes under Reservoir Characterisation (RC) domain. RC [11] aims to identify potential location of hydrocarbon presence by modelling earth’s subsurface. To get most comprehensive understanding of a reservoir, geophysical data sources are utilized in RC. Seismic signals obtained from the seismic survey is the most common geophysical data source that is used to interpret the earth subsurface without a direct penetration into the earth crust. Seismic survey is performed by sending the acoustic signals to the earth crust, which are reflected back by the different layers of earth subsurface. The reflected signals are then recorded, analysed and processed to interpret the underlying subsurface characteristics. Interpretation of the earth subsurface in terms of facies classes is important to distinctly define rocks of interest and to build a better understanding of the depositional environments of the earth subsurface [13]. With the emergence of Machine Learning (ML) in various fields of applications in recent years, many researchers suggested the use of data-driven methods in this domain [2, 6, 12, 16,17,18, 20, 24]. Among the data driven models, the Artificial Neural Network (ANN) is one of the research hot spots in recent years. Many researchers are focusing on how to effectively apply ANN [10, 21, 22] in this field to improve the modelling accuracy. The researchers [8, 10, 14] suggests that neural network has the capability to solve complex calculations and can discover very complex relations within the data that the conventional algorithms often fail to discover. The model has also been successfully applied in petroleum engineering even with sparse data [4, 5]. However, in the literature of facies classification [3, 8, 9, 19], it is observed that facies classification is challenging when we try to interpret from seismic data compared to the interpretation from well logs. This is because of the complex relationship between geophysical data obtained from different sources. Moreover, the uncertainty from seismic data interpretation is higher compared to well logs interpretation as the seismic data cannot see the earth subsurface as the same resolution as well logs see. Hence, in the fields of having limited hydrocarbon wells understanding the relation between seismic and facies can be challenging. Moreover, due to the heterogeneous nature of subsurface, the data obtained can be imbalanced in terms of available classes and building a machine learning model over it can lead to a biased model towards the major classes.

In this work, we are considering a case study over a hydrocarbon field that consists of limited hydrocarbon wells (seven wells), having imbalanced data samples. The task here is to classify the three types of facies (shale, brine sand, and hydrocarbon bearing sand) available over the field from the acquired seismic data. To solve this problem, we developed a framework that consists of: Preprocessing to make the data suitable for the ML model applicability; Modelling using ANN to model the complex relationship between seismic and facies classes, Interpretation of the developed model to understand what made the model work as it is. The strategy of the framework used here can be used by any researcher in this field without the need of having much domain understanding and the end result of the framework can be provided to experts to analyse the model for its applicability in their field. It is worth to specify here that the interpretability of the ML model was never been performed in this field unlike other domains of ML. This is an initial work in this field to the best of our knowledge.

The organisation of this paper is as follows. Section 2 provides the data description. Section 3 provides the detailed description of the methodology followed. Section 4 provides details of experimentation performed with the results obtained. Section 5 provides the conclusions and the future work.

2 Data Description

The dataset we have is a confidential dataset provided by GEOPIC, ONGC, that consists of data from seven wells (Total 36000 instances with each well constituting around 5000 to 6000 instances) in a considered hydrocarbon field. The data consists of fourteen seismic attributes and three classes of facies. Class 0 corresponds to shale, Class 1 corresponds to Brine sand, Class 2 corresponds to Hydrocarbon bearing sand. Fourteen seismic attributes consists of: Amplitude Envelope(X1), Amplitude Weighted Cosine Phase (X2), Amplitude Weighted Frequency (X3), Amplitude Weighted Phase (X4), Derivative (X5), Dominant Frequency (X6), Instantaneous Frequency (X7), Instantaneous Phase (X8), Integrate (X9), Integrated Absolute Amplitude (X10), P-Impedance (X11), Quadrature Trace (X12), Seismic (X13), and VpVs (X14) that are extracted from the main reflected seismic signal recorded with respect to Time (X0). With this data, we need to model the relation between the seismic attributes and facies, to correctly identify the facies classes in the hydrocarbon field from seismic data.

3 Methodology

The proposed framework is provided in Fig. 1. The steps consists of Preprocessing, Modelling, and Interpretation. Preprocessing is performed to handle the imbalanced dataset by oversampling the minority classes and undersampling the majority class data, normalisation of the input (seismic) attributes using Z-score normalisation, and converting the output (facies classes) to the one hot encoding to make the data suitable for ML models. The modeling phase consists of applying ANN with different ML models for the comparisons in modelling the complex relationship between the input (seismic) and the output (facies class). The last step, interpretability is performed using Local Interpretable Model-Agnostic Explanations to understand the working of a model. The detailed description and motivation for each step of the framework is provided in Subsects. 3.1 to 3.3.

Fig. 1.
figure 1

Proposed framework

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3.1 Preprocessing

Table 1. Description of classes before and after resampling
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It can be observed from Table 1 that the original dataset distribution depicts a high bias towards class 0 of around 85% whereas other two classes in combined contributed only 14% of the total data. If this dataset is used to build a model, the model will be highly biased towards majority class. This motivated us to use a resampling method. The resampling of the dataset is performed with Synthetic Minority Oversampling Technique (SMOTE) [7]. This is a popular technique in literature to handle imbalance dataset. The technique is used to reduce the imbalance in the dataset by synthetically generating minority class instances based on the feature space similarities between existing minority instances. Table 1 shows the dataset distribution after resampling. SMOTE is used to generate more samples from Class 1 and Class 2. SMOTE alone is not sufficient to sample the data effectively as generating too many samples of a class will lead to dominance on noise in the dataset. Therefore, we also implement random under-sampling on Class 0 to reduce its samples and make a lesser biased dataset [1].

3.2 Modelling

For modelling, we applied various state of the art methods of classification and compared their results. However, due to the state of art performance of Neural Networks as provided in the literature, we preferred neural network over other ML models and compared it with Naive Bayes (NB), Support Vector Machine (SVM), Decision Tree (DT), and Random Forest (RF), to see how effectively they model the relation between seismic and facies. The performance of ML algorithms are typically evaluated using predictive accuracy (Acc). However, this is not appropriate when the data is imbalanced. Hence, the model performance is evaluated using other important evaluation metrics, sensitivity (Se), specificity (Sp) and precision (Pr), suitable for imbalanced dataset.

3.3 Interpretation

The last step of our framework explains the prediction of a model using Local Interpretable Model-Agnostic Explanations (LIME) [15]. LIME explains the model by perturbing the input data and correlating the effect of these changes on predictions made by the model. One advantage of using LIME is that it is model-agnostic technique and can be applied to understand the explanations of any model. Other model-specific methods try to understand the model by studying the internal components and their behavior. For example, investigation of activation units and linking of internal activations to inputs are performed in case of most deep learning models interpretability [23]. This requires deep knowledge of the model and is not applicable to other models. LIME generates a list of explanations, showing the effect of each feature on the output. The explanations are created by using interpretable models like decision trees and linear models. The interpretable models are trained in close vicinity of data instance i.e. understanding complex models by application of simpler models locally. With the use of LIME, we can provide the explanations of our model predictions to the geoscience experts to determine whether the model explanations satisfied their requirements for its deployment in the real world.

4 Experimentation and Results

To build and study the performance of models we first take one well aside (Well 1 with 5645 samples), to use it as test data to evaluate the performance of the models on unknown location. We then combine the data of the remaining six wells (31355 samples as train set) to train the models. To evaluate model performance we keep 30% of train data as validation set. Several runs of training, testing, and validation phases have been carried out in order to decide the best set of hyperparameters and parameters for every ML model. Figure 2 shows the performance on our dataset with resampling as well as without resampling with the considered ML models. NB performed poorly in validation dataset, however its performance is better in test dataset, in comparison to other models. On the contrary, DT and RF performed remarkably better (almost 100%) on the validation data but performed very poor on the test dataset. It looks a classic case of overfitting that the models could not generalise to the samples that belong to a different well from training wells. Coming to the ANN model performance, its performance is not as worse as NB in validation set, and does not overfit like DT and RF. Hence, the model is able to outperform all these models on the test dataset. We can also observe that ANN with more number of hidden layers (also called as deep neural network (DNN)) is able to improve accuracy on the test set but could not provide better Precision, Sensitivity and Specificity compared to its shallow version. This can be due to the more number of layers in DNN helping towards improvement of accuracy due to further improvement in loss function, but it is ignoring other important performance criteria of the model in imbalance dataset. However, in the scenario of balanced dataset, DNN has got the capability to improve performance in every aspects. Hence we can infer that ANN approximated a very good relation between seismic and facies classes as they can build more complex boundaries which is required for a real world dataset. ANNs generalises well, which can be seen as the improved accuracy of the test dataset. The above observations are true for both, with sampling as well as without sampling. However, better performance is obtained with the resampled dataset. The accuracy of the models remained almost similar, however, the sensitivity and specificity improved by almost 3% to 6%, which are the major evaluation criteria for imbalanced dataset. From the analysis, we came to a conclusion that ANN provided the best performance. However, being a black box model, the geoscientists find it difficult to gain trust in the model to make it deployable for the real world. So, we have used LIME interpretation as provided in Fig. 3 to explain about the predictions of the model. Figure 3 presents one explanation for each of the classes using LIME. The variables occurring in the right side of the axis represents positive contribution, whereas the variables occurring in the left side represents negative contribution. From the interpretation result of Class 0, it can be seen that features X11, X6, X0, X9, X1 and X2 contributes positively, whereas feature X13 and X10 contribute negatively for the prediction of Shale class. Other attributes have very negligible contribution or no contribution at all. Similarly, the result of model prediction belonging to Class 1, depicts that features X11, X6, and X10 contribute positively, whereas X0, X4, and X12 contribute negatively to the classification of this instance to Brine Sand Class. The result of model prediction belonging to Class 2 depicts that features X9, X11, and X8 contribute positively, whereas X12 and X4 contribute negatively to the classification of this instance to Hydrocarbon Sand Class. Moreover, Values of these features belonging to a certain range (as specified) is the sole reason behind classifying these instances to a particular class. This kind of interpretation can be helpful for geoscientists to validate if the reason for the classification of the instance should be trusted or not, and hence they can accordingly decide the models applicability for the real world.

Fig. 2.
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Model evaluation using performance metrics: precision, accuracy, sensitivity, and specificity

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Fig. 3.
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LIME explanations for instances of (a) Class 0, (b) Class 1, (c) Class 2

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5 Conclusion and Future Work

This paper presents a data driven based framework on facies classification. The challenge of having imbalanced classes in the data is successfully handled with an upsampling method, namely SMOTE. The method effectively deals with bias in the dataset towards specific classes. ANN is built for the purpose of modelling complex relationship within the data, provided the best performance measure on the test data that belongs to a completely new well. As important decisions on drilling a new well have to be taken based on model predictions, this paper also presented LIME results to interpret the predictions made by the model. It is observed from the interpretation that, not all seismic attributes are affected by facies characteristics. Some facies classes effect some seismic attributes more than the other. This is a very initial work on interpretation in this field. However, more analysis can be performed on interpretation of model that comprises the domain knowledge. Also, it’s worth mentioning that the composition beneath the earth subsurface varies greatly from location to location that limits the applicability of a model from one field to another, that opens new avenues for more research on modelling the complex underlying relation in this field.