The September 2018, M w 7.5 Sulawesi earthquake occurring on the Palu-Koro strike-slip fault system was followed by an unexpected localized tsunami. We show that direct earthquakeinduced uplift and subsidence could have sourced the observed tsunami within Palu Bay. To this end, we use a physics-based, coupled earthquake-tsunami modeling framework tightly constrained by observations. The model combines rupture dynamics, seismic wave propagation, tsunami propagation and inundation. The earthquake scenario, featuring sustained supershear rupture propagation, matches key observed earthquake characteristics, including the moment magnitude, rupture duration, fault plane solution, teleseismic waveforms and inferred horizontal ground displacements. The remote stress regime reflecting regional transtension applied in the model produces a combination of up to 6 m left-lateral slip and up to 2 m normal slip on the straight fault segment dipping 65 East beneath Palu Bay. The time-dependent, 3D seafloor displacements are translated into bathymetry perturbations with a mean vertical offset of 1.5 m across the submarine fault segment. This sources a tsunami with wave amplitudes and periods that match those measured at the Pantoloan wave gauge and inundation that reproduces observations from field surveys. We conclude that a source related to earthquake displacements is probable and that landsliding may not have been the primary source of the tsunami. These results have important implications for submarine strike-slip fault systems worldwide. Physics-based modeling offers rapid response specifically in tectonic settings that are currently underrepresented in operational tsunami hazard assessment.

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Summary A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is proposed. It is developed for general conforming two‐dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a nondestructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well balancing with an innovative velocity‐based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme, even on unstructured grids, and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near‐realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, superlinear convergence, mass conservation, well balancedness, and stability are verified.

Summary How does megathrust earthquake rupture govern tsunami behavior? Recent modeling advances permit evaluation of the influence of 3D earthquake dynamics on tsunami genesis, propagation, and coastal inundation. Here, we present and explore a virtual laboratory in which the tsunami source arises from 3D coseismic seafloor displacements generated by a dynamic earthquake rupture model. This is achieved by linking open-source earthquake and tsunami computational models that follow discontinuous Galerkin schemes and are facilitated by highly optimized parallel algorithms and software. We present three scenarios demonstrating the flexibility and capabilities of linked modeling. In the first two scenarios, we use a dynamic earthquake source including time-dependent spontaneous failure along a 3D planar fault surrounded by homogeneous rock and depth-dependent, near-lithostatic stresses. We investigate how slip to the trench influences tsunami behavior by simulating one blind and one surface-breaching rupture. The blind rupture scenario exhibits distinct earthquake characteristics (lower slip, shorter rupture duration, lower stress drop, lower rupture speed), but the tsunami is similar to that from the surface-breaching rupture in run-up and length of impacted coastline. The higher tsunami-generating efficiency of the blind rupture may explain how there are differences in earthquake characteristics between the scenarios, but similarities in tsunami inundation patterns. However, the lower seafloor displacements in the blind rupture result in a smaller displaced volume of water leading to a narrower inundation corridor inland from the coast and a 15 % smaller inundation area overall. In the third scenario, the 3D earthquake model is initialized using a seismo-thermo-mechanical geodynamic model simulating both subduction dynamics and seismic cycles. This ensures that the curved fault geometry, heterogeneous stresses and strength, and material structure are consistent with each other and with millions of years of modeled deformation in the subduction channel. These conditions lead to a realistic rupture in terms of velocity and stress drop that is blind, but efficiently generates a tsunami. In all scenarios, comparison with the tsunamis sourced by the time-dependent seafloor displacements, using only the time-independent displacements alters tsunami temporal behavior, resulting in later tsunami arrival at the coast, but faster coastal inundation. In the scenarios with the surface-breaching and subduction-initialized earthquakes, using the time-independent displacements also over-predicts run-up. In the future, the here presented scenarios may be useful for comparison of alternative dynamic earthquake-tsunami modeling approaches or linking choices, and can be readily developed into more complex applications to study how earthquake source dynamics influence tsunami genesis, propagation and inundation.

The September 2018, Mw 7.5 Sulawesi earthquake occurring on the Palu-Koro strike-slip fault system was followed by an unexpected localized tsunami. We show that direct earthquake-induced uplift and subsidence could have sourced the observed tsunami within Palu Bay. To this end, we use a physics-based, coupled earthquake-tsunami modeling framework tightly constrained by observations. The model combines rupture dynamics, seismic wave propagation, tsunami propagation and inundation. The earthquake scenario, featuring sustained supershear rupture propagation, matches key observed earthquake characteristics, including the moment magnitude, rupture duration, fault plane solution, teleseismic waveforms and inferred horizontal ground displacements. The remote stress regime reflecting regional transtension applied in the model produces a combination of up to 6 m left-lateral slip and up to 2 m normal slip on the straight fault segment dipping 65° East beneath Palu Bay. The time-dependent, 3D seafloor displacements are translated into bathymetry perturbations with a mean vertical offset of 1.5~m across the submarine fault segment. This sources a tsunami with wave amplitudes and periods that match those measured at the Pantoloan wave gauge and inundation that reproduces observations from field surveys. We conclude that a source related to earthquake displacements is probable and that landsliding may not have been the primary source of the tsunami. These results have important implications for submarine strike-slip fault systems worldwide. Physics-based modeling offers rapid response specifically in tectonic settings that are currently underrepresented in operational tsunami hazard assessment.

In this paper a Godunov-type projection method for computing approximate solutions of the zero Froude number (incompressible) shallow water equations is presented. It is second-order accurate and locally conserves height (mass) and momentum. To enforce the underlying divergence constraint on the velocity field, the predicted numerical fluxes, computed with a standard second order method for hyperbolic conservation laws and applied to an auxiliary system, are corrected in two steps. First, a MAC-type projection adjusts the advective velocity divergence. In a second projection step, additional momentum flux corrections are computed to obtain new time level cell-centered velocities, which satisfy another discrete version of the divergence constraint. The scheme features an exact and stable second projection. It is obtained by a Petrov-Galerkin finite element ansatz with piecewise bilinear trial functions for the unknown height and piecewise constant test functions. The key innovation compared to existing finite volume projection methods is a correction of the in-cell slopes of the momentum by the second projection. The stability of the projection is proved using a generalized theory for mixed finite elements. In order to do so, the validity of three different inf-sup conditions has to be shown. The results of preliminary numerical test cases demonstrate the method's applicability. On fixed grids the accuracy is improved by a factor four compared to a previous version of the scheme. Mathematics Subject Classification (2000)65M12 · 76M12 · 76M10 · 35L65

Summary We reformulate the depth‐averaged non‐hydrostatic extension for shallow water equations to show equivalence with well‐known Boussinesq‐type equations. For this purpose, we introduce two scalars representing the vertical profile of the non‐hydrostatic pressure. A specific quadratic vertical profile yields equivalence to the Serre equations, for which only one scalar in the traditional equation system needs to be modified. Equivalence can also be demonstrated with other Boussinesq‐type equations from the literature when considering variable depth, but then the non‐hydrostatic extension involves mixed space–time derivatives. In case of constant bathymetries, the non‐hydrostatic extension is another way to circumvent mixed space–time derivatives arising in Boussinesq‐type equations. On the other hand, we show that there is no equivalence when using the traditionally assumed linear vertical pressure profile. Linear dispersion and asymptotic analysis as well as numerical test cases show the advantages of the quadratic compared with the linear vertical non‐hydrostatic pressure profile in the depth‐averaged non‐hydrostatic extension for shallow water equations. Copyright © 2017 John Wiley & Sons, Ltd.

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