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.

In this study, an active probability backpropagation neural network model (PBNNM) was built by training a backpropagation neural network (BPNN) to predict the probability distribution of the probabilistic seismic hazard analysis (PSHA) monthly. The four-layered BPNN framework was determined using training data that were obtained from an earthquake catalogue for the time period of 1990-2015 (Taiwan Standard Time, TST). The studied region was divided into 500 small grids, each 0.2°x 0.2° in size, which is approximately 20 × 20 km ² . Each grid was assigned a predicted earthquake occurrence probability for a month between 2015 and 2018 by the PBNNM. The PBNNM successfully predicted the Tainan earthquake (2 February 2016 TST) and Hualien earthquake (2 February 2018 TST) with probabilities of 94% and 95%, respectively. A quantitative analysis of the reliability of the PBNNM, the standard error of the mean (SEM), and the normalised mean square error (NMSE) were used as statistical approaches to evaluate predicted probability errors of the PBNNM. The SEM (1.79) and NMSE (1.45) of 2015 were the inside test and within the time period of the training data. The SEM (2.11) and NMSE (2.03) of 2016, the low SEM (2.17) of 2017, the NMSE (2.13) and SEM (2.17) of 2017, and the SEM (1.71) and NMSE (1.32) of 2018 were the outside tests and not within the time period of the training data. These low SEM and NMSE values confirmed the accuracy of the PBNNM. In addition, the PBNNM does not consider the prerequisite conditions of past studies (e.g., the return period and assumed probability density model). Therefore, the PBNNM can be commercialised with relatively low cost and minimal resources and equipment compared with the methods presented in previous studies; only earthquake catalogues would be necessary.

Daily total electron content (TEC) images created by splitting TEC maps for three time periods from September 1 to 24, 1999; from February 1 to 24, 2003; and from May 1 to 24, 2003 (Taiwan Standard Time TST) as training images (inputs) were used to create two convolutional neural network (CNN) models. However, splitting the TEC maps of the three time periods into daily TEC images caused wedge effects. The wedge effects were reduced using a low-pass filter called the Butterworth filter. This resulted in clearer TEC precursors for earthquakes, facilitating the identification of earthquakes of magnitude Mw ≥5.0 that exhibited associated TEC precursors during three periods, particularly for the Chi-Chi earthquake of September 21, 1999. The results of this study were compared with those of Lin et al. (2001) and Lin (2010) associated with the Chi-Chi earthquake. Simultaneously, two CNN models that were developed were verified to be rational due to the high accuracy of their predictions. These two models were used to verify each other’s accuracies and to demonstrate the reliability of the method in this study. Therefore, statistical analysis was not the aim. The final outputs of the two CNN model were defined as similarities. Similarities, which are larger than 0.5, were defined as TEC precursors of earthquakes. TEC precursors described as temporal TEC multi-precursors (TTMPs) by Zoran et al. (2018) were detectable on the 1st, 3rd, and 4th days (that is, on September 17, 18, and 20, 1999, respectively) prior to the Chi-Chi earthquake of September 21, 1999. These results are consistent with those of Liu et al. (2001) and Lin (2010). A TEC precursor on May 13, 2003, (TST) was detectable 2 days prior to the earthquake on May 15, 2003, (TST) with the magnitude (Mw) of 5.52. The low standard deviation (STD) and mean square error (MSE) confirm the reliability of both CNN models. Regarding mechanical principles, the TTMPs related to the Chi-Chi earthquake were caused by an electric field (Liu et al., 2001). The cause of the TEC precursor on May 13, 2003, prior to the earthquake on May 15, 2003, was an argument without any corresponding study for comparison.