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：根据地震引发的海平面分布,我们提出一种方法来计算由此造成的海啸在岸上达到一定规模的概率。建议的方法不是抽样,而是依靠优化来计算导致海底巨浪畸形的最可能的断层滑块。我们用海面理想切片上的浅水方程模拟由测深变化引发的海啸。地震滑块模型以多变量日志正常分布的总和为基础,并遵循古腾堡-里希特法,以7-9秒为时标。对于由2011年托霍库-奥基地震和海啸引发的模型问题,我们量化了不同规模海啸波的年度概率。我们的方法还确定了最有效的海啸机制。这些机制的断层偏差偏差差异很大,导致大但中等大水深的改变。由此产生的海啸波在靠近岸边并到达近岸边端的近垂直波脊边缘时会受到压缩。