Statistical Relationship between Tsunami Maximum Amplitudes of Offshore and Coastal Stations

Abstract

   A tsunami warning is issued according to the magnitude, location, and depth of an earthquake as estimated from seismograms. However, there is a large uncertainty of expected tsunami heights because of a lack of information on the rupture process immediately after an earthquake occurs. Actual tsunami heights observed by offshore tsunami recorders can reduce this uncertainty. To make it possible to predict tsunami heights on the coast from offshore tsunami heights, we investigated the statistical relationship between tsunami maximum amplitudes of offshore and coastal stations.
   We used data from ocean-bottom pressure gauges, installed as a part of the ocean-bottom seismometer system off-Tokai and off-Boso by the Japan Meteorological Agency, and off-Muroto by the Japan Agency for Marine-Earth Science and Technology. The data were contaminated with short-period variations accompanied by seismic waves as well as long-period variations, such as the tidal components. To remove noise and extract the tsunami component, we first processed time-series data of the ocean-bottom tsunami recorders with filters, and then compared the tsunami maximum amplitudes observed by the ocean-bottom tsunami recorders off-Tokai, off-Boso, and off-Muroto with those observed at coastal stations. We investigated the statistical relationship by calculating means and standard deviations of the common logarithm of the ratio of coastal to offshore tsunami maximum amplitudes. Next, following Baba et al. (2004), we considered the effects of the installation depth of the ocean-bottom tsunami recorders and the reflection at the coastline. The difference of distances to offshore and coastal stations from sources is also corrected through the tsunami magnitude.
   Making use of AIC (the Akaike Information Criterion), for each combination of offshore and coastal stations, we chose the best fitting statistical relationship between tsunami maximum amplitudes at offshore and coastal stations. As a result, we found a constant ratio or a linear relationship with offshore amplitude and/or epicentral distance, with or without the above-mentioned correction.