Abstract
The distribution of tsunami height is an important quantity to estimate a magnitude of the earthquake and tsunami, and to predict a damage level. The present study proves that the distribution of tsunami height near the shoreline follows a log-normal distribution by wave deformations due to shoaling, refraction, diffraction, bottom friction and wave breaking on a complex bottom topography. A new tsunami height similarity index is proposed to estimate the location of earthquake together with the Aida's κ value. The moment magnitude of an earthquake in the Sea of Japan was determined using the relationship between tsunami and moment magnitude and average logarithmic values of the ratio of tsunami height.