Relationship between displacement and velocity amplitudes of seismic waves from local earthquakes

Relationship between displacement and velocity amplitudes of seismic waves was examined with data at stations within 200 km from 142 local earthquakes in and near Japan. The expected value of the coefficient for the logarithmic velocity amplitude to the logarithmic displacement amplitude is 0.5 when a self-similar scaling model is assumed. Observed value of the coefficient is about 0.8∼0.9. This value appears to be valid at least in the magnitude range from 3.0 to 6.5. Although a spectral model simulation suggested that apparent large contents of high-frequency components were required to explain the observed coefficient, no distinct deviation from the ω-square model was found in the observed spectral ratios from earthquakes of different sizes, for which the path effects were virtually excluded. By using an empirical Green’s function which would correct the effects of propagation and site amplification, it was shown that the apparent deviation from the self-similar scaling model was due to propagation effects.