A tsunami earthquake is an earthquake event that generates abnormally high tsunami waves considering the amplitude of the seismic waves. These abnormally high waves relative to the seismic wave amplitude are related to the longer rupture duration of such earthquakes compared with typical events. Rapid magnitude estimation is essential for the timely issuance of effective tsunami warnings for tsunami earthquakes. For local events, event magnitude estimated from the observed displacement amplitudes of the seismic waves, which can be obtained before estimation of the seismic moment, is often used for the first tsunami warning. However, because the observed displacement amplitude is approximately proportional to the moment rate, conventional magnitudes of tsunami earthquakes estimated based on the seismic wave amplitude tend to underestimate the event size. To overcome this problem, we investigated several methods of magnitude estimation, including magnitudes based on long-period displacement, integrated displacement, and multiband amplitude distribution. We tested the methods using synthetic waveforms calculated from finite fault models of tsunami earthquakes. We found that methods based on observed amplitudes could not estimate magnitude properly, but the method based on the multiband amplitude distribution gave values close to the moment magnitude for many tsunami earthquakes. In this method, peak amplitudes of bandpass filtered waveforms are compared with those of synthetic records for an assumed source duration and fault mechanism. We applied the multiband amplitude distribution method to the records of events that occurred around the Japanese Islands and to those of tsunami earthquakes, and confirmed that this method could be used to estimate event magnitudes close to the moment magnitudes.

海啸地震是一种地震事件，考虑到地震波的幅度，它会产生异常高的海啸波。与典型地震相比，这些相对于地震波幅值的异常高波与此类地震的较长破裂持续时间有关。快速震级估算对于及时发布有效的海啸地震预警至关重要。对于局部事件，通常在第一次海啸预警中使用根据观测到的地震波位移幅度估计的事件幅度，该幅度可在估计地震矩之前获得。但是，由于观察到的位移幅度大约与力矩速率成正比，根据地震波幅值估算的传统海啸震级往往会低估事件的大小。为了克服这个问题，我们研究了几种幅度估计方法，包括基于长周期位移，积分位移和多频带幅度分布的幅度。我们使用根据海啸地震有限断层模型计算出的合成波形测试了这些方法。我们发现，基于观测振幅的方法无法正确估算震级，但是基于多频带振幅分布的方法给出的值接近许多海啸地震的瞬时震级。在这种方法中，对于假定的源持续时间和故障机制，将带通滤波后的波形的峰值幅度与合成记录的峰值幅度进行比较。