Given a distribution of earthquake-induced seafloor elevations, we present a method to compute the probability of the resulting tsunamis reaching a certain size on shore. Instead of sampling, the proposed method relies on optimization to compute the most likely fault slips that result in a seafloor deformation inducing a large tsunami wave. We model tsunamis induced by bathymetry change using the shallow water equations on an idealized slice through the sea. The earthquake slip model is based on a sum of multivariate log-normal distributions, and follows the Gutenberg-Richter law for moment magnitudes 7--9. For a model problem inspired by the Tohoku-Oki 2011 earthquake and tsunami, we quantify annual probabilities of differently sized tsunami waves. Our method also identifies the most effective tsunami mechanisms. These mechanisms have smoothly varying fault slip patches that lead to an expansive but moderately large bathymetry change. The resulting tsunami waves are compressed as they approach shore and reach close-to-vertical leading wave edge close to shore.

翻译：针对地震引起海底地形变化的分布模型，我们提出了一种计算方法，用于评估海啸在近岸达到特定高度的概率。该方法无需采样，而是通过优化求解能够产生最大海啸波的海底变形对应的最可能断层滑移量。我们采用浅水方程在理想化海洋剖面中模拟海底地形变化引发的海啸过程。地震滑移模型基于多元对数正态分布叠加，并遵循矩震级7-9级的古登堡-里克特定律。以2011年东北-冲地震海啸为参照的模型问题中，我们量化了不同规模海啸波的年度发生概率。该方法还能识别出最具影响力的海啸机制，其特征是平滑变化的断层滑移区域，能够触发规模可观但适度广域的海底地形变化。由此产生的海啸波在接近海岸时发生压缩，并在近岸区域形成近乎垂直的前缘波面。