GNGTS 2017 - 36° Convegno Nazionale

290 GNGTS 2017 S essione 2.1 PSHA: probabilities of what? The word denoted by the first letter of the acronym PSHA is “probabilistic.” PSHA proponents appear to take for granted that earthquakes occur as if at random in time and space, so it is reasonable and natural to estimate the spatio-temporal probability distribution of events, and to use that estimate as the foundation for risk assessment (see, e.g., Musson, 2012). Estimated probabilities are key inputs to PSHA, which then produces numbers such as “the annual probability of a peak ground acceleration of 0.2 g” at a particular site. PSHA assumes that “the probability of an earthquake at a particular site” or the probability of “how often, both in terms of inter-event time and magnitude-frequency, earthquakes occur” exists. There are data on occurrence dates, locations, and magnitudes (subject to various errors and catalog incompleteness uncertainties) of past earthquakes. Let us call these “frequency” data. PSHA requires the “probability” of future earthquakes. PSHA simply conflates the observed empirical frequencies with probabilities. But frequencies are not probabilities, nor are they necessarily estimates of probabilities. If seismicity were the result of a random process, empirical frequencies could be used to estimate the underlying probabilities. However, unless we have exogenous knowledge that the empirically observed frequency of past seismicity is due to something random, defining a quantity called the “probability of future seismicity” is just an assumption about the mechanism that generates seismicity. There are several conceivable potential justifications for modelling seismicity as random. For instance, there might be an underlying theoretical basis in physics—as there is in quantum mechanics—but so far that is not the case for earthquake physics. Or modelling seismicity as random might lead to a compact and statistically adequate description of the data, but in fact seismicity is empirically inconsistent with random seismicity models that have been proposed (Luen, 2010; Stark, 2013). Or perhaps modelling seismicity as random might lead to useful predictions or hazard analyses, but, as we have discussed above, they do not. For further discussion of the fundamental issues involved here see also Stark (2017). Logic trees: does the sum of ignorance lead to knowledge? Some applications of PSHA seek to combine all possible options into a “logic tree,” somehow assigning a “probability” to each branch over a wide variety of scenarios; these are presumed to provide a thorough basis for decision makers. This approach acknowledges our ignorance, but treats it by trying to reach an expert consensus or combining expert opinions into “probabilities.” Such techniques have their origin in the Delphi Method (Dalkey and Helmer, 1963), which was used to assimilate expert opinions on possible outcomes of a nuclear war. In practice, a large—but not too large— group of experts (typically 7–12 in number) is convened to brainstorming and seek consensus. What the numbers obtained from a logic tree mean is less than clear. Failures of engineered systems with a small number of well-understood components whose failure modes are known might sometimes be fruitfully modelled as a tree with known nodes and branches and estimable probabilities at each node, at least as a thought experiment. But there is no evidence that this is meaningful or useful for phenomena as complex and poorly understood as earthquakes. The use of “expert opinion” in PSHA studies implicitly acknowledges the unscientific nature of such endeavors. For example, expert opinion is not needed to make calculations involving Newton’s law of gravitation; barring computational blunders, a high-school student and a Nobel prize-winning physicist will calculate the same forces from the same input data. Conclusions. In conclusion, while PSHA has been widely used for almost 50 years by governments and industry in applications with lives and property hanging in the balance (e.g., deciding safety criteria for nuclear power plants, making official national hazard maps, developing building code requirements, and determining earthquake insurance rates), PSHArests on assumptions now known to conflict with both earthquake physics and statistics. Moreover, many damaging earthquakes, including the 1988 Spitak, Armenia, event and the 2011 Tohoku, Japan, event, have occurred in regions of relatively low-risk according to PSHA hazard maps. No extant method, including PSHA, produces reliable estimates of seismic hazard. Reliance on