Scale invariance in complex seismic system and its uses in gaining precursory information before large earthquakes: Importance of methodology

► We studied seismicity scale invariance using four methods including Hurst analysis. ► We show differences in ability to gain usable information among four methods. ► We observed precursory changes of local scaling property before major earthquakes. ► We did not observe precursory changes of correlation dimension before major earthquakes. ► Seeking pertinent selection of methodology is needed to gain precursory information.