A macroseismic equation with a convergent solution

Abstract We obtained a macroseismic equation with a convergent solution at a hypocentral distance D ∼ 0 (independent of magnitude) for relative shaking intensity. The logarithmic distance dependence of intensity turned out to be piecewise linear no matter whether it is expressed in relative units of intensity degree or in logarithmic ground motion velocity. The macroseismic intensity shows high correlation with motion velocity. Another result is the magnitude dependence of dominant periods of ground motion velocity for large earthquakes.