Variable Star Symbols for Seismicity Plots

Abstract

Online Material: Maps of seismicity and cities; test sheet; list of earthquakes; Fortran 77 code. At least since Mallet (1858) seismicity maps have been a way of showing earthquake activity, but, because earthquake size varies greatly, it is difficult to provide an accurate representation of the spatial variation of total seismic energy or moment release. The most common approach, using for each earthquake a single geometric figure of varying size, creates substantial overlap between large symbols. To reduce overlap and provide a more distinctive gradation, I propose a family of symbols in which size and shape vary together, from polygonal to star shaped as their size increases. Two functions determine how symbol size and shape vary with value, and even a simple parametrization gives considerable flexibility in symbol design. Tests show that, given an appropriate key, the symbol value can be estimated to within better than 5% of the range covered. Symbolization in seismicity maps is challenging. Using identical symbols plotted at the epicenters (or, in a cross section, the hypocenters) shows where there are more or fewer earthquakes but not how (say) moment release is distributed. This can be done by spatially smoothing the amount of energy or moment release and contouring the result (e.g., Allen et al. , 1965), but this in turn removes fine details. Most seismicity maps use a simple geometrical figure, usually a circle or square, to symbolize for each earthquake and vary its size with the earthquake magnitude. The interior of each symbol can be filled with a color to denote depth (or, in Web displays, recency of occurrence). One problem with this approach is that one large symbol can easily cover many small ones. Some seismicity maps use two geometrical figures, one (often a scaled circle) for events less than some magnitude and another …