# 3D Convolution Recurrent Neural Networks for Multi-Label Earthquake Magnitude Classification +
###### Abstract
We propose, by using regression analysis, the earthquake magnitudes can be modeled into multiple classes, i.e., after dataset conversion, an earthquake of magnitude \"1\" can belong to class \"0\", \"1\" or \"2\" simultaneously, which in this particular study is considered as a multilabel classification problem (see Figure 1). Although the labels can be interpreted as intensities, however, they are not the actual intensities measured by the instrument. To avoid ambiguity, we do not label them as intensities. This study only uses the magnitude information from which we convert the single label information to multi-label information. The uncertainty associated with these border seismic signals makes it impossible to distinguish earthquakes even from a human viewpoint, and no prior study has addressed this issue. Moreover, many researchers [18] find ways to employ low-cost ground motion sensors in cities to monitor seismic activity in urban areas. The primary motivation to conduct this study is to pave the way for data-centric approaches and deploy an efficiently trained deep learning model on personal seismometers where seismic noise is high. We believe that using deep learning models on these sensors to categorize earthquake severity in an urban environment will significantly increase the response time. Furthermore, categorizing earthquakes into multiple classes is a time-consuming operation in a classical method. For example, in classifying the earthquake into several categories, the earthquake magnitude must be estimated using the following steps: firstly, we  
Figure 1: Multiclass to multi-label data transformation: examples of converted multiclass earthquake categories to multi-label categories. An earthquake signal first belongs to a single category. However, after transformation, it belongs to multiple categories. compute the sensor response; secondly, we convolve the estimated response with a signal response from a [PERSON] instrument (specialized to measure the signal response accurately) [19], thirdly, transform the original signal counts to acceleration. Moreover, to estimate the correct earthquake magnitude, we need to apply the attenuation models for each region and introduce some correction terms. Finally, we average the measurements from multiple nearby single stations to accurately estimate the earthquake magnitude. Motivated by the reasons mentioned above, we propose to view earthquake magnitude categorization as a multi-label classification task, assigning several labels to a seismic signal based on its reported magnitude by a seismograph. We propose to solve this task using a 3-dimensional convolutional recurrent architecture (3D-CNN-RNN). Encouraged by the significant advancements in convolutional neural networks (CNN) [20; 21; 22; 23; 24; 25], we utilize CNN as the earthquake feature extractor. On the other hand, numerous earthquake classes demonstrate high co-occurrence correlations in seismic data. For example, earthquakes having magnitude 1.5-2.5 can exhibit the same seismic pattern and have similar effects, while magnitudes 1.5 and 4.5 can never have indistinguishable fallout. With the recent success of recurrent neural networks (RNN) [26; 27; 28] in modeling the dependencies, we propose to employ separate RNNs on each kernel of the last convolutional layer to model the dependencies among labels and predict earthquake categories step by step. In this way, the network can implicitly integrate the information inferred using the previous hidden states when recognizing the subsequent labels. Due to the acoustic nature of the seismic signal, it exhibits similar properties as an audio signal; therefore, we propose to extract log-Mel features for algorithm training. The signal is easily convertible to a log-Mel spectrogram and is treated as an input to the CNN. Moreover, it is imperative to make the earthquake signal discriminative and preserve the spatial information of the spectrogram.