Analysis and assessment of ground motion characteristics and similarity using dynamic time warping distance

Due to the complex nonstationarity of ground motion in time–frequency domain, the traditional methods of comparing and evaluating earthquake waveforms have not enough ability and accuracy to distinguish the details and changing features of the similar waves, which makes the similarity evaluation of waveform is difficult to be quantified accurately. The similarity degree of different signals can be calculated precisely according to dynamic time warping (DTW) algorithm, so it can be used for waveform comparison and similarity evaluation. In order to improve the traditional method, a method based on DTW distance is proposed to identify the earthquake waveform and analyze the ground motion characteristics. Based on the statistical analysis of a great quantity of earthquake waves, the changes law of DTW distance considering amplitude, time lag, noise signal ratio, site type, and the comprehensive effect is obtained. DTW distance is proved to be used as a compatible evaluation standard for waveform refinement. It is verified that DTW distance and vector norm are essentially equivalent. In the analysis of ground motion, DTW distance is implicated in the equivalent amplitude and energy of earthquake waves. The physical connotation of DTW distance is demonstrated by analyzing the data of the station array, and the results show that the distribution of DTW distance can accurately imply the time–space variation effect of the earthquake in the region. The reasonable reference range of DTW distance is defined by statistical method, and the corresponding evaluation standard of synthetic multi-point ground motion with real characteristics is proposed. In the synthetic accuracy evaluation of artificial ground motion with spatial variation effect, the combination of ground motions with more real characteristics can be obtained by evaluating and optimizing the waveforms according to the variation rule and range of DTW distance.