250th Anniversary of the 1755 Lisbon Earthquake

A probabilistic method that takes account of the ordinal character of the MSK Scale has been adapted to generate a 1755 seismic intensity map for the Iberian Peninsula. Statistical models are employed to estimate isoseismals and to compute standard error uncertainties. The output includes intensity maps, estimates of the effects associated with each intensity level, and estimates of the distribution of intensity levels a given distance from the hypercenter. It is applied to a data set of Portugese and Spanish intensity values. It is shown how the analysis may be employed to include explanatory variables such as regional and local geological effects. INTRODUCTION 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, the 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. Intensity scales are ordinal, that is the levels are qualitative ordered, the level spacing does not matter, and adjacent categories can be merged. One is not meant to employ the values using the rules of ordinary arithmetic. One purpose of this research is to examine the possibility of assessing formally if the data may be employed as if numerical-valued. A probability approach is adopted and there are 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. Isoseismals are often on a map to indicate seismic intensity 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 encircling, say all the VIII value locations, ignoring scattered VIIIs. Professor Bolt once emphasized to this writer, [Brillinger, 1993], that a critical aspect of existing isoseismal maps, namely that they are conservative in two senses. First, the indicated intensity level at a location is the highest noted. Second, the isoseismals themselves are drawn as far out from the source as reasonable to include all locations with given intensity. However as [Reiter, 1990] states, “... drawing isoseismals can be a subjective process that may lead to different outcomes for different analyses.” and this provides a motivation for the present work. [Perkins and Boatwright,1995] list some of the factors on which seismic intensities depend, namely, size of the earthquake, distance of the site from the earthquake source, the focusing of the earthquake energy and the regional and local geological effects. There is a falloff in severity of effect with distance from the source and substantial variability is inevitably present. The event of concern is the Lisbon 1 November 1755 tragedy. General descriptions of the event can be found abound. Its magnitude has been estimated as 8.7, depth 20-40km and epicentre at (-10.0,36.5) a point about 90km SW of Sagres. The data employed in the work were provided by J. M. Miranda, who acknowledged Mezcua. There are 810 observations in Portugal and Spain. The counts of the numbers of the various MSK intensities recorded are provided in Table 1 at the end of the paper. There are intermediate levels in the data set but because such are not part of the MSK scale they are not included in the analyses presented. Figure 1, also at the end of the paper, shows the locations of the measurements for the integral intensities. The clusters are associated with population centers. One sees a falloff from level X to level II as one moves north and east from Sagres. Other references using intensity values to understand this event include: [Mendes-Victor et al., 1999], [Baptista et al, 2003], [Matrinez Solares, Lopez Arroyo, 2004]. There is discussion of seismic damage scales in [Bullen and Bolt, 1985, pp. 433-437], and [Reiter, 1990].