Distances between consecutive aftershocks are analysed by means of mono- and multifractal theory with the aim of quantifying the complexity of the physical mechanism governing them, as well as their predictability and predictive instability. Hausdorff, Ha, and Hurst, H, exponents are determined by semivariograms and rescaled analysis, respectively. The exponent β of the power law describing power spectral contents is also quantified. These three parameters permit a generation of fractional Gaussian noise, fGn, simulating distances. The complexity and predictive instability of physical mechanism generating the series of distances is quantified by means of the correlation dimension, μ*, the Kolmogorov entropy, κ, and the Lyapunov exponents, λ_i, which are based on the reconstruction theorem formulation. Additionally, the multifractal detrended fluctuation analysis, MF-DFA, contributes with a different point of view to quantify the complexity of the series, in terms of fractal spectral width, W, spectral asymmetry, B, and the critical Hölder exponent, a₀. By one hand, the MF-DFA is applied to the complete set of distances characterising the whole aftershock process. By the other hand, the MF-DFA is applied to segments of the series of distances with the aim of determining the evolution of the complexity since the mainshock up to the end of the stress relaxation process. Finally, an ARIMA multilinear regression process is applied to obtain some improvements, in comparison with fGn simulations, on the prediction of distances. The database for this analysis is obtained from the Southern California Seismic Network (SCSN) catalogue. Three series of aftershocks equalling to or exceeding magnitudes of 2.0, assuring seismic catalogue completeness, and associated with Landers (06/28/1992), Northridge (01/17/1994) and Hector Mine (10/16/1999) mainshocks are obtained. It is worth mentioning that common mono-multifractal behaviour for the three aftershocks series is not detected, whatever aftershock periods or segments of them are considered.

中文翻译：

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连续余震之间距离的分形行为：以Landers，Northridge和Hector Mine南加州主震为例

借助单分形和多重分形理论分析了连续余震之间的距离，目的是量化控制它们的物理机制的复杂性，可预测性和预测性不稳定性。Hausdorff Ha和Hurst H的指数分别通过半变异函数和重新定标分析确定。描述功率谱内容的幂律的指数β也被量化。这三个参数允许生成模拟距离的分数高斯噪声fGn。的物理机制产生一系列距离的复杂性和预测的不稳定性是由关联维数的手段，μ*时，K熵，κ和Lyapunov指数，λ定量_我，它们基于重建定理公式。此外，多重分形去趋势波动分析MF-DFA以不同的观点做出贡献，以分形谱宽W，谱不对称性B和临界Hölder指数a ₀量化系列的复杂性。。一方面，MF-DFA被应用于表征整个余震过程的完整距离。另一方面，MF-DFA应用于一系列距离的分段，目的是确定自主震起直至应力松弛过程结束的复杂性。最后，与fGn模拟相比，ARIMA多线性回归过程可用于距离预测，以获得一些改进。此分析的数据库可从南加州地震台网（SCSN）目录获得。获得了三个等于或大于2.0的余震系列，确保地震目录的完整性，并与Landers（06/28/1992），Northridge（01/17/1994）和Hector Mine（10/16/1999）主震相关。