Abstract
Tsunami propagation in the open ocean is most commonly modeled by solving the shallow water wave equations. These equations require initial conditions on sea surface height and depth-averaged horizontal particle velocity or, equivalently, horizontal momentum. While most modelers assume that initial velocity is zero, Y.T. Song and collaborators have argued for nonzero initial velocity, claiming that horizontal displacement of a sloping seafloor imparts significant horizontal momentum to the ocean. They show examples in which this effect increases the resulting tsunami height by a factor of two or more relative to models in which initial velocity is zero. We test this claim with a “full-physics” integrated dynamic rupture and tsunami model that couples the elastic response of the Earth to the linearized acoustic-gravitational response of a compressible ocean with gravity; the model self-consistently accounts for seismic waves in the solid Earth, acoustic waves in the ocean, and tsunamis (with dispersion at short wavelengths). Full-physics simulations of subduction zone megathrust ruptures and tsunamis in geometries with a sloping seafloor confirm that substantial horizontal momentum is imparted to the ocean. However, almost all of that initial momentum is carried away by ocean acoustic waves, with negligible momentum imparted to the tsunami. We also compare tsunami propagation in each simulation to that predicted by an equivalent shallow water wave simulation with varying assumptions regarding initial velocity. We find that the initial horizontal velocity conditions proposed by Song and collaborators consistently overestimate the tsunami amplitude and predict an inconsistent wave profile. Finally, we determine tsunami initial conditions that are rigorously consistent with our full-physics simulations by isolating the tsunami waves from ocean acoustic and seismic waves at some final time, and backpropagating the tsunami waves to their initial state by solving the adjoint problem. The resulting initial conditions have negligible horizontal velocity.Graphical abstractGRAPHICAL ABSTRACT CAPTION
Highlights
Tsunamis from earthquake sources pose a significant threat to coastlines around the world and have killed hundreds of thousands of people in the last few decades
The first approach involves running comparable tsunami simulations with a full-physics model and a linearized shallow water wave model, and selecting the initial condition on horizontal velocity for the shallow water model using the expressions presented by Xu and Song (2013), Titov et al (2016) and Song et al (2017)
We vary the rise time parameter τ, which scales the amplitude of v0(x), and compare the tsunamis predicted by the shallow water and full-physics simulations
Summary
Tsunamis from earthquake sources pose a significant threat to coastlines around the world and have killed hundreds of thousands of people in the last few decades. Promoted an alternative theory of tsunami generation that includes, in addition to the processes encapsulated by Eq (6), an additional horizontal momentum transfer from the solid Earth to tsunamis in the ocean that leads to non-negligible initial velocity v0(x) They suggest that this momentum transfer increases the kinetic energy of the ocean and substantially contributes to tsunami wave heights. In the full-physics model, the earthquake source and all waves are simultaneously generated, unlike the typical approach of first modeling the earthquake and using the final displacement from the earthquake model to set initial conditions for the tsunami We use this model to simulate the full seismic, ocean acoustic, and tsunami wavefields.
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