Wavelet-Aggregated Signal in Earthquake Prediction

The concept of aggregated signal is introduced. Quantitatively, an aggregated signal can be defined as the scalar signal: it accumulates in its own variations only those spectral components that are presented simultaneously in each scalar time series of the multidimensional signal to be analyzed. Moreover, an algorithm of aggregation is proposed to suppress the spectral components that are present in any of the scalar components but absent in others (these components can be called local disturbance signals, for instance of technogenic nature). The main purpose of constructing the aggregated signal is to make clearer the common tendency of low-frequency data-flow in geophysical networks, which indicates an increase in collective behavior.It is known that almost all models of the process of earthquake preparation have pointed out an increase in collective behavior of components of geophysical fields in the region of preparation when the coming geocatastrophe has entered its long- and mid-term stages. Long- and mid-term precursors have the feature of rather gradual and smooth changes in the behavior of geophysical fields; therefore, it is possible to extract them from the noise by the multivariate spectral method. As for short-term precursors that have the most important practical meaning, they usually have the character of impulsive changes caused by, for instance, the breakage of bridges between cracks within the future earthquake source area. This explains why it is impossible to extract them by the spectral method.The theory of wavelets provides a way to get rid of this situation. In this paper the procedure of aggregation, i.e., to build a scalar aggregated signal of the components of multidimensional time series, is suggested. The main idea involved in this procedure is the same as the previous method of aggregation. The difference lies in that the Haar and Daubechies wavelets are used as basic functions in place of harmonics. Such an approach allows us to extract from multivariate geophysical data-flow common signals which cannot be detected by spectral methods, in particular short-term earthquake precursors. The effectiveness of the method proposed is verified by the example of extracting short- term precursors from multiple time series (10 geophysical parameters) before the catastrophic Tangshan earthquake (North China, M=7.8, July 28, 1976).