Seismic Intensity Calculator

Intensity measures what an earthquake does at a place, not what it released at the source. The Modified Mercalli scale runs in twelve ordinal degrees, from I, not felt, through VI, where plaster cracks and poorly built masonry is damaged, to X and above, where most structures are destroyed. A single earthquake has one magnitude but an entire field of intensities decaying outward from the source. The attenuation form used here separates the two ways amplitude is lost: a term in ln(R) for geometric spreading of the wavefront, and a term linear in R for anelastic absorption, both evaluated at hypocentral distance R = sqrt(d^2 + h^2) so that focal depth is properly included. A deep event produces markedly lower intensity at the epicentre than a shallow one of the same magnitude. Site response is the third control. Building codes classify ground by Vs30, the average shear wave velocity in the top 30 metres; soft soils below about 180 m/s can amplify shaking two to three times relative to rock, which is why damage maps often follow buried river channels and filled ground rather than distance contours. Because intensity is ordinal rather than a physical quantity, arithmetic on MMI values is only approximate, and the PGA and PGV figures derived from it inherit wide scatter. A generic relation of this form should not replace region-specific ground motion prediction equations in engineering work, and it cannot capture rupture directivity or sedimentary basin resonance.

Intensity scales predate instrumental seismology because observed damage was the only thing that could be recorded systematically. The Rossi-Forel scale of the early 1880s was the first in wide use. Giuseppe Mercalli published a ten-degree scale in 1902, Adolfo Cancani extended it to twelve degrees in 1904, and August Sieberg elaborated the degree descriptions in 1912, producing the Mercalli-Cancani-Sieberg scale long used across Europe. The American adaptation came in 1931, when Harry Wood and Frank Neumann rewrote the descriptions to match United States construction practice, creating the Modified Mercalli Intensity scale; Charles Richter revised the wording again in 1956. Other regions retained their own systems, including the Japan Meteorological Agency shindo scale and the European Macroseismic Scale of 1998. The link to instrumental ground motion is comparatively recent: David Wald and colleagues published regressions between MMI, peak ground acceleration and peak ground velocity for Californian earthquakes in 1999, which let the USGS ShakeMap system render instrumental intensity within minutes of an event. The Did You Feel It system, launched by the USGS in the same period, reversed the flow by gathering questionnaire responses over the web and assigning community intensities from them, and the 2007 analysis of that accumulated dataset by Gail Atkinson and Wald produced magnitude-distance intensity relations of the kind used here.