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”