A neural network based approach to classify VLF signals as rock rupture precursors

doi:10.21203/rs.3.rs-1404707/v1

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A neural network based approach to classify VLF signals as rock rupture precursors

https://doi.org/10.21203/rs.3.rs-1404707/v1

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The advent of novel technologies revealed that other geophysical signals than those directly related to fault motion could be used to probe the state of deformation of the Earth's crust. Electromagnetic signals belonging to this category have been increasingly investigated in the last decade in association to natural earthquakes and laboratory rock fractures. These studies are hampered by the lack of continuous recordings and a systematic mathematical processing of large data sets. Indeed, electromagnetic signals exhibit characteristic patterns on a specific frequency band (the very low frequency, VLF) that correlate uniquely with the paroxistic rupture of rocks specimens under uniaxial laboratory tests and were also detected in the atmosphere, in association to moderate magnitude earthquakes. The similarity of laboratory and atmospheric VLF offers an unique opportunity to study the relation between VLF and rock deformation on at least two different scales and to enlarge the dataset by combining laboratory and atmospheric data. In this paper we show that the enlarged VLF dataset can be successfully used, with a neural network approach based on LSTM neural networks to investigate the potential of the VLF spectrum in classifying rock rupture precursors both in nature and in the laboratory. The proposed approach lays foundation to the automatic detection of interesting VLF patterns for monitoring deformations in the seismically active Earth’s crust.

VLF

Earthquakes

Precursors

Machine Learning

Rock mechanics

Electromagnetic signals

Seismic sequences are characterized by a seemingly irregular occurrence of earthquakes along main faults. This irregularity challenges our understanding of the physical processes governing the seismic cycle and represents a serious limitation in the modeling strategies for predictive purposes. More information can be achieved by observing the mechanical behavior of the rock volume which contains seismogenic faults.

Deformation at surface, ground (or ocean) motion, and geological constraints have been widely used to this end. However, other geophysical signals may contain relevant constraints on transient phenomena coheval to the deformation such as geochemical signatures of permeability and temperature changes (e.g. radon or CO) and electromagnetic anomalies in the ionosphere. The very low frequency range of the electromagnetic spectrum (VLF) represents a very strict and promising example of these types of geophysical signals that could extend our knowledge about transient phenomena associated with the deformation of the Earth’s crust and the seismic cycle. The use of VLF signals as possible earthquake precursors has been widely investigated in the atmosphere and in the laboratory with experiments on rock samples (e.g. (Warwick et al., 1982)-(Nardi et al., 2007; Nardi & Caputo, 2009)). Limitations to the study of the natural VLF have been: the non-systematic data acquisition due to a limited data storage and/or data transmission through the network; processing of large data set, due to the high acquisition rates which are of the order of tens of kS/s; the fact that the study of the electromagnetic signal was mainly focused on the observations of narrow EM bands. These three limitations hampered the research of EM signals as possible detectors of transient geophysical signals. However, EM are actually sensitive to transient phenomena: the sensitivity of the LF becomes apparent for M > = 5.5 (Rozhnoi et al., 2005), whereas in the case of VLF signal this threshold lowers to M > 4.5 (Nardi et al., 2007). Previous studies (e.g (Nardi et al., 2007) suggested a correlation with a magnitude 4.5 earthquake, recorded with 3.6 days delay on average and within 270 km maximum distance from the survey site, during an observation period where no other relevant earthquakes have occurred. In this paper, we show how such correlation can be used to train a neural network to classify VLF signals as possible precursors of rock ruptures.

1.1 VLF spectral patterns detected in the laboratory and in the atmosphere

Experimental observations on EM-VLF have been conducted during rock deformation under uniaxial compression. The first recognition of EM as a precursor in the atmosphere was performed by (Warwick et al., 1982) who also conducted experiments on rocks to verify the correlation of EM emission with rock deformation. Experimental evidence (Nardi & Caputo, 2009) documented that VLF signals associated with rock fracturing occur in the form of mainly two impulsive event types occurring before, during, and immediately after the paroxysmal rupture episode. The observed signals have been divided into two groups (Nardi & Caputo, 2009): a first one made of the so called Orderly Impulsive Sequences (OIS) and the second one, the Disorderly Impulsive Sequences (DIS), appearing immediately after or preceding slightly the OIS (Fig. 1). In this work we will focus on OIS emissions because they are characterized by high frequency almost identical micro-impulses appearing at regular time intervals and composing “pulse trains”. On the spectrogram of a laboratory signal (Fig. 2) they compose a uniform band centered over the average pulses frequency. The signal intensity and the number of OIS pulses are influenced by mechanical and structural characteristics of the material, by the presence of fluids, and to a lesser extent, by the lithology. OIS signals are the most easily sampled and recognized in continuous monitoring work. Importantly, natural observation of VLF documented at least three events (Fig. 3) characterized by signals fitting OIS laboratory models (Nardi et al., 2007). In summary OIS signals manifest similar patterns at different scales as shown in Fig. 4 for a spectral pattern recorded in Serramazzoni and associated with a M 4.5 event that occurred on October 3rd, 2012 at 4:41 UTM. The main difference between OIS from the laboratory (LABset) and those recorded in the atmosphere (AIRset) is the time scale, which lasts minutes for AIRset versus a few seconds in the case of LABset as schematized in Fig. 5. This similarity can be used to better identify VLF signals and characterize its phenomenology under controlled laboratory conditions, on a temporal scale which allows for a statistically consistent database of events, and to test the correlation between the VLF signals detected in the atmosphere with the deformation of rock volumes. VLF spectral patterns appear to be correlated to acoustic emission and related to micro and macro fracturing processes preceding and producing sample failure. Moreover, the magnitude threshold of VLF acts as a natural filter on moderate - to - large events suggesting that VLF spectral patterns have the potential to detect deformation of large rock volumes within the Earth crust at depth.

1.2 The need for a novel approach to measures and analysis: machine learning

VLF has been studied discontinuously and non-systematically using different measuring systems and different frequency bands. Specifically, previous studies were focusing on specific frequencies whereas the evolution of the EM signal during the rupture sequence is only visible using the entire spectra of the ELF-VLF band (Fig. 1, from Nardi & Caputo, 2009). However, the recognition of interesting patterns in the atmosphere and thus their association to transient natural events is largely hindered by the lack of a systematic approach to the measuring systems, the lack of continuous data over a statistically consistent temporal and spatial interval and in general, by the approach to data management. Moreover, although these patterns appear clearly in the spectrogram from visual inspection their mathematical expression is not trivial to the design of “classical analytical” algorithms for signal detection. For the aforementioned reasons in this study we challenge these limitation using:

i. a VLF EM monitoring network termed “Cassandra” which is a systematic instrumented network for VLF detection in the atmosphere. The type of antenna and the network design deployed on the national territory is described in (Nardi & Caputo, 2009)

ii. a machine learning algorithm for automatic signal detection to scan for VLF spectral patterns over the huge amount of signals typically acquired at 44100 Hz in a frequency band 20 Hz − 22 kHz.

Machine learning (ML) techniques have tremendously increased in the last few years with the increasingly large amount of data available. More specifically, the neural networks are used for a wide range of different purposes such as image and text recognition, speech interpretation and many other uses. The main benefits in using ML are:

1. versatility, because by only changing input data they can solve many different problems.

2. automation, in fact once the algorithm is designed, the only requirement is to provide enough data to let the machine learn how to solve the problem and then the system will be able to autonomously and automatically solve the same problem in similar different situations.

3. objectivity, as machines are not “biased by emotions”. For example, medical research procedures require double blinded protocols to avoid biases. When using machine learning techniques there are no specific protocols to be fit.

A particular case of machine learning techniques is represented by neural networks (NN). The neural network “architecture” is inspired by the structure of the primate brain cerebral cortex, in order to learn increasingly abstract features of the input and best support the desired output (O’Shea & Nash, 2015; Rawat & Wang, 2017). The main advantage of using neural networks compared to other types of machine learning techniques is that features relevant for the prediction have not to be selected in advance as they are automatically found by network training. In this work we designed the NN to detect the most typical signal patterns of the natural atmospheric noise as well as OIS patterns in the VLF band. NN was trained on VLF signals which preceded rock failure in the laboratory under uniaxial tests as well as on natural VLF signals which occurred a few days (< 5d) before a moderate magnitude earthquake (M > 4.5) exploiting the apparent scale invariance of the VLF OIS. Laboratory OIS can be used effectively to enlarge the data set and to train the neural network for the detection of OIS signals in the atmosphere.

1.3 Neural network architecture and application

We implemented a Neural Network Architecture (ANN) whose structure is designed to deal with time (using a recurrent neural network, RNN, (Pascanu et al., 2013) and a memory state variable (using the Long short term memory LSTM). The basic idea of RNN shown in Fig. 6 is that a neuron output is not influenced just by the convolution between its input and its activation function but also by the output of its adjacent neuron. A RNN network has a “short term” memory as “previous neurons’ memory rapidly vanishes between neurons. To overcome this limitation we designed a LSTM network (Greff et al., 2016; Huang et al., 2015; Karim et al., 2017). Basically LSTM blocks are an update of RNN ones to keep more sequence memory. An example of a LSTM is explained in (Yildirim, 2018). The LSTM blocks replace the neurons in Fig. 6 to set up the same structure using a different block as shown in (Yildirim, 2018). The main limitation of LSTM networks is that only “past” input in the sequence can affect the “future” neurons. That’s why a further development of LSTM called “bidirectional LSTM” (BI-LSTM) has been designed to put together a forward and a backward LSTM. Both networks are connected to inputs and to outputs. In this case study, neural network application is very simple: after careful data collection, we have signal sequences, some of them classified as rock rupture precursors and some of them not.

It is worth noting that the LABset OIS data labeled as rock rupture precursors showed spectral patterns similar to the AIRset OIS events collected a few days before the Italian earthquakes listed in Fig. 3.

A BI-LSTM neural network with 1000 hidden units has been trained in order to fit the known classification so implicitly understanding the most important features and cut offs to split the “potential events” to “not events”

2.1 LABset data

Part of our case study dataset has been collected by means of laboratory experiments and part from an experimental monitoring network. The first dataset, which we will call the “LABset”, are VLF signals generated by 36 rock samples ruptured under uniaxial compression. The 36 samples belong to 14 different lithotypes including porphyry, granites, basalts, peridotites, limestones and concrete. To detect VLF signals during laboratory tests we used the ELF-VLF spectrum sampled at the frequency of 44100 Hz. Detecting and discriminating DIS and OIS from the background noise, consisting of natural (e.g. atmospheric) and artificial (e.g. electromechanical laboratory noise) signals was a complex procedure requiring a different type of spectrum analysis for OIS and DIS. Therefore, in this first monitoring phase, it was chosen to only focus on the OIS type for reasons explained below. OIS emissions are regular (see also description in section 1.1), the pulses variability in the period determines a band-width of about 3 kHz (Figs. 1 & 2). The regular repetition in the succession of the trains determines the uniformity of the emission that is sharply interrupted at the point where train repetition stops. Considering the time span from the beginning of the test until the rupture of the sample under a constant increment of force, the OIS manifests itself in the first half of this period.

2.2 AIRset data

The second data set, which we will call "AIRset", are VLF signals observed in the atmosphere by the stations of the monitoring network at its earlier testing stages (Nardi et al., 2007; Nardi & Caputo, 2009). These very rare signals have been selected to have characteristics similar to those observed in OIS in the laboratory. VLF were observed on a frequency band ranging between 20 Hz and 20 kHz (ELF-VLF radio bands) and sampled at 44100 Hz from a number of stations deployed in Italy along the central Apennines and belonging to the Cassandra monitoring network. The OIS signal appeared to occur a few days before (seemingly up to 5 days) a moderate magnitude seismic event (M 4.5). A very important point is that OIS are not common signals of the VLF spectrum, they do not belong to any of those signals observed even rarely in the background and were only recorded when followed by a short term (days) significant earthquake (Fig. 3). Despite these relevant observations the association between OIS and natural earthquakes is still hypothetical and needs further observations to be proved.

2.3 The neural network approach and definitions

A machine learning method tries to predict a variable (answer or label) when some others (predictors) are known. In order to make the algorithm “learn”, the first step is collecting data including both the predictors and the answer (labeled data). Such data will feed the algorithm that will “learn by itself” if predictors show patterns (said features) able to predict the answer. This machine learning stage is named training. After the training, if successful, the algorithm is able to automatically predict the answer for any other datasets including all the provided predictors. Such a “trained algorithm” able to predict is named “model”. An example of a machine learning task may be recognizing a person's gender by using his/her bibliometric and anagraphic data. In this case, height, weight, age and other data are the predictors and “male” and “female” are the labels. In order to realize a machine learning model working we need to provide the system with already labeled data. In order to check how the model is able to “generalize” its validity for data not included into the training, a common practice is, before doing the training, randomly choose a part of the available dataset and remove it from the training process. So, when the training has been performed, the excluded data (named test data and containing the labels we are looking for) provide a powerful source to verify the model accuracy as this dataset includes both the true labels and, when used as input for the trained model, the predicted labels. This allows the accuracy percentage computation Accuracy = matched results/total test data. We are here using a Neural Network Architecture (ANN) consisting of a set of layers of neurons (Fig. 6). Input data is inserted into the first layer (each input data into a single neuron) and each neuron changes the input value according to a transfer function depending on the ANN used. Once each data input has been processed by the neuron it is “passed” to the next neuron’s layer where the input is a linear combination of the previous layer outputs. Such linear combinations are determined by a set of coefficients (named neuron weights). The process is iterated along all the layers to the last layer (named “output layer”) and the outputs are compared to the provided labels. According to the discrepancy between the true labels and the ones obtained a backward propagation process starts modifying the weights. Such propagation, which involves the iterative adjustment of a single parameter vector, haswith the goal of minimizing the differences between the observed and predicted values (Cao & Parry, 2009).

A big drawback of the backward propagation process is that input data are considered independent and weights networks updates calculation is not affected at all by input sequences. This makes backward propagation neural networks not particularly suitable for time series analysis, speech recognition or any other application where input sequence sorting does matter. That’s why some network structures dealing with time and using previous states memory have been introduced (Elman, 1990) such as recurrent neural networks (RNN) (Pascanu et al., 2013) and Long short term memory (LSTM) networks (Yildirim, 2018)

2.4 The confusion matrix

When dealing with machine learning, the best way to show methods accuracy is using the “confusion matrix” (Lantz, 2013). A confusion matrix is a table counting where the predicted classes agree or disagree with the true values. Conventionally the rows represent the true classes and the columns represent the predicted ones. The number in the intersection between rows and columns represent how many records characterized by the row true classes have been classified with the predicted one specified by the column. So the numbers along the diagonal show all the records correctly classified and the other numbers the wrong ones. In addition to general accuracy, confusion matrices indicate the accuracy of the method for each single class.

After selecting randomly 402784 blocks (i.e. portions of the signal), they have been used to feed the network and use their label to match at best the results. Each block is an ensemble of 1323 recorded samples. The number 1323 has been evaluated as the correct one to be sure that the signal contains the anomalous pattern. Once the training has been completed, the trained network has been used to predict the classification of 50348 test sequences initially excluded from training. The capability of the NN to distinguish signals of relevance from the background which are possibly related to transient geomechanical properties is very satisfactory as revealed by the confusion matrix in Fig. 7 (see also section 2.4). The accuracy from the confusion matrix (calculated according to the equation in the Material and methods section) shows that 89% of the records were correctly classified.This result implies that an automatic recognition of such signals by means of artificial intelligence is possible and very advantageous. The result of the confusion matrix seems to suggest that laboratory OIS can be used with success to detect atmospheric OIS signals with the advantage that laboratory signals can be acquired and integrated easily under controlled conditions.

The VLF have been proved in the laboratory to be a reliable rock rupture precursor. Indeed, recurrent and regular pulse trains defined as OIS from previous literature seem to systematically anticipate the paroxistic rupture event under uniaxial compressive tests. At the same time, OIS with similar characteristics (period and band width), have been detected in the atmosphere. The similarity of VLF-OIS in the atmosphere and in the laboratory offers the opportunity to investigate the potential of VLF in the study of transient phenomena on scalable temporal scales. However, the recognition of characteristic patterns in the atmosphere and thus their association to transient natural events is largely hindered by i. the lack of a systematic approach to the measuring systems, ii. the lack of continuous data over a statistically consistent temporal and spatial interval and iii. because, although these patterns appear clearly in the spectrogram from visual inspection, their mathematical expression is not trivial to the design of “classical analytical” algorithms for signal detection. That’s the context where neural networks found applications as they are designed to detect features that can be used to classify signals as “human” would do. In this paper we challenged such limitations to show that artificial intelligence and, more specifically LSTM neural networks, are effective “automatic detectors” for OIS. Such characteristic spectral patterns have been correctly classified by our neural network within the defined categories: precursors to rock “rupture” and “quite”. The classification has been proven effective not only for laboratory data but also for atmospheric signals recorded in association with transient natural events involving fracturing of rock volumes (e.g. earthquakes).

A couple of methodology limits have to be mentioned, mostly correlated to events magnitude and distance between events and recording stations.In fact, at the state of the art VLF signals are not able to detect earthquakes having magnitude below 4.5 and the maximum distance range where events are detectable is not yet defined.

Despite these limitations, such results look very promising. Indeed a precursory event can be studied and recognized when the dataset of events is statistically consistent. VLF cannot be studied over a statistically consistent data set because the actual dataset is typically large and relevant signals cannot be easily extracted. The proposed approach has the potential to provide a systematic study of OIS patterns because we demonstrated that the use of NN allows the automatic detection of characteristic signals in the air. The automatic detection would allow real-time monitoring, detection and extraction of characteristic patterns which would remain otherwise hidden. Moreover we demonstrated that these OIS signals can be studied on at least two different temporal and spatial scales, at the controlled conditions of the laboratory and on natural recordings in the atmosphere, providing the opportunity to study their potential to probe the state of deformation of rock samples as well as rock volumes of the seismically active Earth’s crust.

5.1 Funding: This work was partially supported by grant FISR 2016 Ricerca Libera and by MUR 2020-2029 – “Working Earth: geosciences and understanding of the earth dynamics and natural hazards”.

5.2 Authors’ contribution: all the authors have contributed to all the paper content parts and its drafting. Moreover, the manuscript is the result of continuous interaction, proposal and discussion among them. More specifically:

NA developed the idea, designed the antenna, the network and the experimental protocol.

PA has given most of his contribution in designing, tuning the neural network architecture and in coding the procedures to run them with data;

SE developed the idea and contributed to the data interpretation.

5.3 Conflicts of interests/Competing interests: The authors declare no competing interests

5.4 Data availability: All data used to train and test neural network can be found as gitlab public project at the following link: https://gitlab.com/alessandro.pignatelli/cassandradata.

Due to the big memory needed _(more than 3 Gb) they have been saved as matlab binary file and basically the file contains two matrices: “input_data” including each time series window (1323 samples) as columns and “output_data” containing the labels in oneshot format so a two rows matrix having a column for each series and the value 1 on the first row and zero on the second row if the series is a rock break precursore and 0 at the first row and 1 at the second row if vice-versa.

5.5 Code availability: There is no specific code to be shared

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No competing interests reported.

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You are reading this latest preprint version

A neural network based approach to classify VLF signals as rock rupture precursors

Status:

Version 1

Abstract

Figures

1 Introduction

1.1 VLF spectral patterns detected in the laboratory and in the atmosphere

1.2 The need for a novel approach to measures and analysis: machine learning

1.3 Neural network architecture and application

2 Materials And Methods

2.1 LABset data

2.2 AIRset data

2.3 The neural network approach and definitions

2.4 The confusion matrix

3 Results

4 Discussion

Declarations

References

Competing Interests

Status:

Version 1