Muography. Группа авторов
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standard deviation and the daily number of eruptions with gray impulses for the data collection period from 20 October 2018 to 29 June 2020. The muon flux images and average flux values are excluded from this analysis for those days on which the MMOS did not operate reliably or maintenance work was performed in SMO.
Significant change in the muon flux observed before or during the occurrence of eruption may reveal the underlying volcanological process. Consequently, it is worth investigating how the muon flux changes across the selected regions before and during the eruption. We selected 47 consecutive three‐day periods days in which the volcano did not erupt on the first two days and did erupt on the third day. Fig. 4.4 shows the average flux values for the three regions, divided by the average flux value measured on days when there is no eruption within ± 2 days. This quantity is called the averaged relative flux. As shown in Fig. 4.4a, the averaged relative flux increased by approx. 2.5σ standard deviations across the Minamidake crater one day before the eruption relative to the averaged relative fluxes measured on the other two days. The observed muon flux increase hints at the blasting of the magmatic plug located beneath the craters (Oláh et al., 2019b). The relative muon flux is decreased across the Showa crater below 2σ standard deviations (Fig. 4.4b). The role of this region in the eruption mechanism of Minamidake is an open question that should be addressed in future studies. As is expected, the averaged relative muon flux is around 1 across the Surface region, in which volcanological processes do not occur (Fig. 4.4c).
The data were organized as rows consisting of the seven daily muographic images or seven averaged flux values for the selected regions, and the corresponding eruption labels (“0” or “1”) for the eighth day. These rows were shuffled to avoid possible effects due to the change in the internal structure of crater region. The data set was divided into three smaller ones: (i) a training data set was selected for 394 days with 146 eruption days; (ii) a validation data set was selected for 110 days with 48 eruption days for tuning of hyperparameters; and (iii) a test data set was selected for 109 days with 56 eruption days for testing of tuned models and quantifying of the accuracy of eruption forecasting.
Figure 4.3 Average muon flux values are plotted with 1σ standard deviation (black error bars) for the erupting Minamidake crater (a), the deactivated Showa crater (b), and the Surface region of Sakurajima volcano (c) for the data collection period between 20 October 2018 and 29 June 2020. Daily number of eruptions of Minamidake are shown with gray impulses (a).
Figure 4.4 Averaged relative flux values for eruption days and the two days before that for the erupting Minamidake crater (a), the deactivated Showa crater (b), and the Surface region (c).
4.4 MUOGRAPHIC DATA PROCESSING WITH MACHINE LEARNING
In this section, we present the application of three different ML techniques to the processing of muographic image data. The significant variation of averaged relative flux values through the erupting Mindamidake crater (Fig. 4.4) suggested the application of conventional classifier models for processing of averaged flux values. Thus, we applied SVM and an artificial neural network (ANN) for the processing of average fluxes calculated for the three selected regions. For the processing of daily muon flux images, a convolutional neural network (CNN) model was utilized. Each model was implemented, trained and tested with scikit‐learn version 0.22.1 (Pedregosa et al., 2011), Keras version 2.4.3 (Keras, 2020), and Tensorflow version 2.3.0 (Tensorflow, 2020). Receiver operating characteristic (ROC) analysis was performed on each trained model to evaluate the eruption forecasting performance using the test data (Fawcett, 2006). The performance of each model was quantified by means of calculation of area under the curve (AUC). The optimal cutoff points, i.e. sensitivity and specificity parameters of the ROC curves, were determined with the Youden index (Youden, 1950). In this study, sensitivity (true positive rate) and specificity (1 ‐ false positive rate) correspond to the probabilities of forecasting an occurred eruption and false alarm, respectively.
In the following subsections, we present briefly the core concepts, the results of hyperparameter tuning, and the achieved eruption forecasting performances for the different models.
4.4.1 Processing of Average Fluxes with Support Vector Machine
SVM is a versatile model that constructs a set of hyperplanes to separate the multi‐dimensional input data for the classification, regression, or detection of outliers (Vapnik, 1995). In this analysis, SVM was implemented with radial basis function kernel with a C regularization parameter and a γ kernel parameter. The C parameter represents the cost of training accuracy that regulates the balance between the maximization of distances of data points from the hyperplane and the maximization of correctly classified data points in training data. In case of smaller C, the distance is larger between the data points and the hyperplane, and SVM achieves lower accuracy in classification of training data. In case of larger C, the distance is smaller between the data points and hyperplane, and SVM achieves a better classification in training data; however, it is more sensitive to the unique features of training data, which can result in lower classification accuracy in test data. The γ kernel parameter represents the inverse of the radius of influence of samples selected by the SVM. In case of small γ, SVM cannot capture the complexity of the training data. In case of large γ, the support vector only includes itself that results in over‐fitting with any value of C.
Two hundred trials of parameter tuning were performed for various C − γ pairs in C ∈ [2−5 − 215] and γ ∈ [2−15 − 23] ranges with Bayesian optimization (Snoek et al., 2012). A five‐fold cross‐validation procedure was applied to avoid overfitting of data. A test set was separated from five equally divided training sets. Four out of five sets were used for training of SVM and the fifth set served as the validation set. The latter was cyclically permuted and the average score was calculated for the five cases. The SVM model achieved the best AUC score with C = 925.83 and γ = 1.75 hyperparameters (Fig. 4.5a). The result of the ROC analysis of trained SVM is shown in Fig. 4.5b. The AUC score of SVM reaches a moderated value of 0.6.
4.4.2 Processing of Average Fluxes with Neural Network
An ANN model was also constructed to process average flux values. Conceptually, the ANN is a directed and weighted graph of neurons. Each neuron has multiple inputs and produces one output that can be connected to multiple neurons. The inputs on the first layer are the input data, such as series of numbers or image data. The last layer represents the output of ANN that accomplish the required task, such as prediction or classification. The connections of neurons are corresponding to the synapses of biological brain. The input of a neuron is determined by an activation function, typically by ReLU or sigmoid, that is applied