Multifractal characteristic analysis of near-fault earthquake ground motions

This study aims to reveal the multi-scaling behavior and quantify the irregularity of near-fault earthquake ground motions from a new perspective of multifractal theory. Based on multifractal detrended fluctuation analysis, the multifractal characteristic parameters of acceleration time series for typical near-fault ground motions are calculated, and their correlations with two period parameters (i.e., mean period Tm and characteristic period Tc) and box-counting fractal dimensions are analyzed. Numerical results of strong nonlinear dependence of generalized Hurst exponents h(q) upon the fluctuation orders q indicate that near-fault ground motions present the multifractal properties and long-range correlation obviously. Furthermore, the scaling exponent h(2) of near-fault records has a strong correlation with their periods Tm and Tc, and strongly negative correlation with their box dimension. Moreover, h(2) can be regarded as a measure of frequency content and irregularity degree of strong earthquake ground motions. Finally, it is pointed out that the long-range correlation of small and large fluctuation is the major source of multifractality of near-fault ground motions.