GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 2.1 289 PSHA? No, thanks F. Mulargia 1 , P.B. Stark 2 , R.J. Geller 3 1 Dipartimento di Fisica e Astronomia, Settore di Geofisica, Università di Bologna, Italy 2 Department of Statistics, Code 3860. University of California, Berkeley CA, USA 3 Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Japan This abstract is excerpted and slightly modified from Mulargia et al. (PEPI, 2017). The method called Probabilistic Seismic Hazard Analysis (PSHA) is based largely on work by Cornell (1968). PSHA is in extremely widespread use as a standard part of the “due dili- gence” process for designing and building critical structure (e.g., Solomos et al. , 2008; Hanks et al. , 2009). PSHA has been extensively debated over the years, but most debate has been focused on mathematical issues, which basically involve questions of internal consistency, giv- ing for granted its physical and statistical bases, which are elastic rebound and the feasibility of some probability distribution. None of these applies, since earthquakes are ruptures in the crust governed not by linear elasticity, but by the highly nonlinear fracture mechanics, while the probability of an earthquake is itself statistically difficult to define. PSHA: an empirical tool? PSHA could in principle still be viable as a merely empirical tool, a black box mysteriously capable of producing useful numbers. However, PSHA can only produce estimates of the seismicity rates of a given region based on data on past earthquakes. Ideally, this would require a complete catalog of all significant earthquakes for an extensive time period. Unfortunately, however, catalogs based on instrumental recordings are available only since about 1900, and are only reliable after about 1960. Historical data for about 2000 years are available for some countries (e.g., Italy, China, Japan), but even though the dates and approximate epicenters are probably reliable, it is difficult to obtain reliable magnitudes and focal mechanisms, and the catalogs are incomplete in unknown ways. Even the Italian macroseismic catalog, which for historical and geographic reasons is of high quality—the area of Italy is small and it has been a site of civilization for over two millennia—rarely reports more than one significant occurrence in any given seismic region. In principle, palaeoseismology can extend the time span of seismic catalogues to thousands of years, allowing the inclusion of several large earthquakes on the same tectonic structure (Sieh et al. , 1989). However, exposed faults are rare, so such direct estimates are generally unavailable (Mulargia and Geller, 2003). An indirect estimate can be made by extrapolating the G-R law from lower magnitudes, making use of the main phenomenological feature of earthquakes: scale invariance. Thus, the behavior of large earthquakes, for which data are insufficient, might be estimated from small seismicity, for which data are available. However, in addition to the general uncertainty inherent in any extrapolation, this approach produces widely different estimates depending on whether a maximum event size (Wang, 2008) or a corner magnitude (Kagan, 2002) is assumed. The lack of a sufficiently long time series may lead to errors, since often “the largest historic magnitude” is inappropriately treated as an upper limit (Mulargia, 2013). The 2011 Tohoku earthquake is a good example of a magnitude 9.0 earthquake happening where a maximum magnitude 8.0 had been wrongly specified by official Japanese government forecasts (Geller, 2011; Stein et al. , 2012; Kagan and Jackson, 2013). If seismic catalogs 10 5  years long were available, seismicity might appear to be nearly time independent on that time scale, because the time scale of geological processes, on the order of 10 6  years, is much longer than that of inter-earthquake intervals in seismically active regions, 10 2 - 10 3 years. Unfortunately, only relatively short seismic catalogs are available, so it is unlikely that the available seismicity data reflect the long-term rates of the underlying processes. Indeed, there is evidence that rates of seismicity vary on historical timescales: Liu et al. (2011) found considerable variability in the spatial pattern of seismicity in North China over the past 2000 years. In conclusion, even if PSHA had no methodological problems, which, as we discuss below, is not the case, the insufficiency of the available seismicity data means that it is highly questionable whether PSHA can provide reliable and accurate hazard analyses.