A Statistical Study of the Seismic Intensities of the 1755 Lisbon Earthquake

Substantial tragic effects result from great earthquakes – damage, deaths, tsunamis. Various groups, including seismologists, seismic engineers, government officials and insurers seek to quantify the effects in order to proceed with their work. The quantification methods employed include seismic intensity scales and damageability matrices particularly. Principal intensity scales employed are: the Modified Mercalli, (MMI), the Medvedev-SponheuerKarnik (MSK), and the European Macroseismic Scale. The scale values are typically denoted by roman numerals to reflect the fact that they are derived via verbal descriptions rather than some numerical physical measuring device. It is claimed that theMMI andMSK scales are similar, see e.g. (Sokolov et al. 1998). Intensity scales are ordinal, that is the levels are qualitatively ordered and the level spacing does not matter. Adjacent categories can be merged. A probability approach is adopted and there has advantages. These include: one can examine scientific hypotheses formally, one can assess goodness of fit, one can compute and show uncertainty, one can compare alternate models, and there are often robust/ resistant variants of general techniques. The broadly ranging subject matter of statistics becomes available. One is not meant to employ the intensity values using the rules of ordinary arithmetic. One purpose of this research is to examine the possibility of assessing formally if the datamay be employed as if numerical-valued. Isoseismals are often sketched on a map to indicate, generally, the seismic damage experienced. These isoseismals are meant to be contours of equal intensity, to bound areas within which the predominant intensity is the same. The lines prove useful to quantify the shaking pattern and to understand the damage. Traditionally isoseismal maps had been prepared by hand-drawing curves encompassing the observed intensities. The artist seeks to draw a curve