# A Novel Method of Seismic Signal Detection Using Waveform Features
## 5 Results  
In the test process, it is crucial to pay attention to select the threshold value. The probability of the noise misjudged as a seismic signal is 5%, known as the false alarm rate. Usually, the threshold of STA/LTA can be obtained directly according to the false alarm rate. Differently, the threshold of the posterior distribution consists of two parts, one is the probability threshold from the fake alarm rate, as marked by the red dot in Figure 6, and the other is the mean of the amplitude feature Gaussian distribution. Due to the symmetry of Gaussian distribution, the threshold acquired by only the false alarm rate will exclude some signals higher than the average value but lower than the probability threshold, as located to the right of the black point in Figure 6. Therefore, the advantage of the double threshold is that the new signal is judged as noise only when it is below both the probability threshold and the mean threshold. Otherwise, it is considered as an earthquake signal, and similarly for other features threshold choices. For the whole multi-features joint probability model, the threshold also consists of two parts. The mean threshold is still the mean of the amplitude distribution. After choosing the suitable threshold, the test results of different methods are obtained, shown in Table 5. From top to bottom is the test result of STA/LTA, STA/LTA with changing characteristic function (C_STA/LTA), single waveform feature (amplitude \(\alpha\), ratio \(\rho\), average energy value of specific frequency band \(\log(\gamma)\), IMF1 energy value \(\log(\lambda)\)) and multiple features. Different characteristic functions lead to various detection in the STA/LTA method. In this paper, the absolute value function as the most commonly used characteristic function is chosen, which is \(CF(i)=|Y(i)|\). Moreover, we select another one defined as \(CF(i)=y(i)^{2}+K(Y(i)-Y(i-1))^{2}\), where \(K\) is a weighting factor that is related to sample rate and station noise characteristics. The test results demonstrate selecting the appropriate feature function will improve the detection effect relatively. In this article, seismic events have specific occurring location and waveform information. For amplitude feature \(\alpha\), we can get the distribution from the Gaussian process using historical seismic signal messages. Then we obtain the mean and variance of distribution about other features in the same ways. In other words, we obtained a posterior distribution of new signals based on prior information, which is shown in  
Figure 10: Training flowchart of optimizing hyperparameters. Hyperparameter training use gradient ascent and the termination contingency of the training process is that the logarithmic marginal likelihood value reaches the maximum. Figure 6. Furthermore, using the distribution can predict the probability of a new signal occurring. The detection rate of most single features does not have too much improvement compared to STA/LTA, which can be enhanced by combining multiple features. We combine multiple features to form a seismic signal detector, as shown in Equation (16). The false alarm rate of 5% provides the probability threshold, and the mean of amplitude distribution obtained by GP is the other part of the threshold. In Table 5, we show the test results of various methods. We can see the STA/LTA detector generates correctly 123 signal detections and 190 noise detections, while the algorithm in this paper successfully achieves 136 signal detection and 190 noise detections. Comparing to the traditional STA/LTA and C_STA/LTA, the detection rate is increased by 3.7% and 2.3% respectively. In this paper, the results of the two methods only provide 0 or 1, the square errors between the predicted value and the true value are also 0 or 1. Then we cannot get the error statistical distribution and its cumulative distribution function (cdf) for the waveform features and STA/LTA. Therefore, the KSPA cannot be used to evaluate whether there is a significant difference between the two methods.