Spatial correlation of spectral acceleration of mainshock‑aftershock earthquake sequences

According to certain selection criteria， this paper selects 8 mainshock‑aftershock events and 560 mainshock‑aftershock sequences from NGA‑West2 ground motion database， uses ASK14 ground motion prediction equation to carry out residual analysis on the mainshock‑aftershock sequences， obtains the intra event residual of mainshock‑aftershock sequences at each station， and standardizes them. According to the geostatistical semivariogram method， the exponential semivariogram model and the manual fitting method are used to calculate the spatial autocorrelation of the spectral acceleration period of the mainshock‑aftershock sequence. Since the Pearson linear correlation coefficient can better measure the linear relationship between the fixed‑distance variables， the Pearson linear correlation coefficient is used to calculate the cross‑correlation of the normalized intra‑event residuals between different spectral acceleration periods of the mainshock‑aftershock sequence without considering the spatial cross‑correlation. According to Markov’s hypothesis， the spatial information is introduced into the calculation of the cross‑correlation， and then the expression of the change of the spatial cross‑correlation with the spatial distance （h） is obtained. The results show that the mainshock is significantly different from aftershocks in terms of spatial autocorrelation and cross‑correlation characteristics， and aftershocks generally have higher spatial correlation in the long‑period stage. Neglecting the spatial correlation between the mainshock and aftershocks or using the characteristics of the mainshock to replace the characteristics of the aftershocks will adversely affect the research on earthquake hazard analysis， damage assessment， and the synthesis of main and aftershock sequences.