Determining Neuronal Number in Each Hidden Layer Using Earthquake Catalogues as Training Data in Training an Embedded Back Propagation Neural Network for Predicting Earthquake Magnitude

Abstract

In this paper, the 2000–2010 earthquake catalogue with a Richter magnitude (ML) of 5 and a depth of 300 km in the study region, located at 21°–26° N and 119°–123° E, was used as a training data to construct an initial earthquake Richter magnitude (ML) prediction backpropagation neural network (first IEMPBPNN) model with two hidden layers. By using final weights and biases of IEMPBPNN as initials for an embedded earthquake Richter magnitude (ML) prediction backpropagation neural network (EEMPBPNN) from the 1990–1999 and 2011–2014 earthquake catalogues (ML $\geqq ~5$ and depth $\leqq ~300$ km) for the same region, the IEMPBPNN was updated to EEMPBPNN with 10 neurons in each hidden layer. The predicted Richter magnitude (ML) errors could be reduced with EEMPBPNN, and the data from 2000 to 2010 as the outside test and data from 2011 to 2014 as the inside test were compared with the predicted Richter magnitude (ML) under the EEMPBPNN model, which exhibited high accuracy due to the lower standard deviation (SDV), lower mean squared error (mse), and higher correlation coefficient. The accuracy of the second IEMPBPNN, as trained with the 1990–2014 earthquake catalogue under the same proceeding of the first IEMPBPNN, could not be improved with the accuracy of EEMPBPNN. Moreover, the training process of the second IEMPBPNN consumed significant computing time due to massive amount of training data. In predicting the Richter magnitudes of five earthquakes in 2016 and 2018 (TST), lower SDV, lower mse, and higher correlation coefficients were illustrated with reliable prediction accuracy using EEMPBPNN. The objective of this procedure was to determine the neuronal number in each hidden layer using the earthquake catalogue and the slip rate of the Philippine Sea Plate related to the Eurasian plate as the training data, where the number of neurons has not been determined by the training data in previous works.