小波分解与重构在地震活动性研究中的应用

利用小波变换具有的多分辨率特点,将时域信号通过小波分解与重构,分解到不同的频带上.分解步长的确定,采用不同尺度近似信号标准差变化平缓段的最小尺度值,从而避免了人为选择分解阶数可能造成的不完全分解或过度分解.分解后的信号不仅在频率成分上较单一,且平稳性较好.然后对小波分解重构后不同尺度的信号分别采用自回归滑动平均混合模型进行预测,再合成原始信号的预测值.对半年尺度的最大震级序列和地震总释放能量序列的一步预测,结果表明这样做有效地提高了预测精度,一步预测结果与实际观测结果不仅相关性高,而且两者的残差曲线离散性小,以此对未来地震形势的判断较目前常用的方法更为可靠.

Application of wavelet decomposition and reconstruction in studying earthquake activity

Making full use of the multi-resolution characteristics in the wavelet transform, we can divide a signal in the time domain into different bands of frequency by using wavelet decomposition and reconstruction. The best scale of decomposition is decided by the minimum scale in which rms error of approximate signal is little and from this scale to another scale rms error of approximate signal is short odds. The decomposed signal is not only more simple in frequency component but also more stationary in the time domain than original signal. Auto Regressive Moving Average Model is employed to predict the decomposed and reconstructed sub-signals with different bands of frequency. Then the expected signal prediction in time domain is obtained by synthesizing these sub-signals prediction. Experimental prediction result with maximum earthquake magnitude and sum of earthquake release energy indicates that the model improves the prediction accuracy. There is a high correlativity between experimental prediction result and observations. And there is a low discrete distribution in difference between experimental prediction result and observations. This methods provides a relatively accurate forecast for earthquake situation.