Attenuation of ground motion in the central United States has to be determined principally using the Modified Mercalli (MM) intensity observations because of the absence of instrumental strong ground-motion data. Nuttli's previous studies of Mississippi Valley earthquakes indicate that higher-mode surface waves produce the largest ground motion except possibly in the near-field region. Particle velocity rather than acceleration correlates directly with intensity and the coefficient of anelastic attenuation has an average value of 0.10 per degree. Using data from isoseismals of the November 9, 1968, southern Illinois and the December 16, 1811, New Madrid, Missouri earthquakes and assuming a linear relationship between log(A/T) and MM intensity, attenuation is expressed by the equation, valid for I(R) ≧IV (MM), I ( R ) = I 0 + 3.7 − 0.0011 R − 2.7 log R ; for R ≧ 20 k m where R is the epicentral distance in kilometers. This relationship shows fairly good agreement with isoseismals of many large earthquakes in the central United States and may therefore be useful in providing realistic estimates of spatial attenuation and hence of design earthquakes for a given site. It can also be sometimes useful in estimating the epicentral intensity of an earthquake whose maximum intensity is not reliably known.
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Gupta et al. (1976) studied this question.