A new empirical equation for predicting the maximum initial amplitude of submarine landslide-generated waves

The accurate prediction of landslide tsunami amplitudes has been a challenging task given large uncertainties associated with landslide parameters and often the lack of enough information of geological and rheological characteristics. In this context, physical modelling and empirical equations have been instrumental in developing landslide tsunami science and engineering. This study is focused on developing a new empirical equation for estimating the maximum initial landslide tsunami amplitude for solid-block submarine mass movements. We are motivated by the fact that the predictions made by existing equations were divided by a few orders of magnitude (10−1–104 m). Here, we restrict ourselves to three main landslide parameters while deriving the new predictive equation: initial submergence depth, landslide volume and slope angle. Both laboratory and field data are used to derive the new empirical equation. As existing laboratory data was not comprehensive, we conduct laboratory experiments to produce new data. By applying the genetic algorithm approach and considering non-dimensional parameters, we develop and examine 14 empirical equations for the non-dimensional form of the maximum initial tsunami amplitude. The normalized root mean square error (NRMSE) index between observations and calculations is used to choose the best equation. Our proposed empirical equation successfully reproduces both laboratory and field data. This equation can be used to provide a preliminary and rapid estimate of the potential hazards associated with submarine landslides using limited landslide parameters.

3D Linked Subduction, Dynamic Rupture, Tsunami, and Inundation Modeling: Dynamic Effects of Supershear and Tsunami Earthquakes, Hypocenter Location, and Shallow Fault Slip

Physics-based dynamic rupture models capture the variability of earthquake slip in space and time and can account for the structural complexity inherent to subduction zones. Here we link tsunami generation, propagation, and coastal inundation with 3D earthquake dynamic rupture (DR) models initialized using a 2D seismo-thermo-mechanical geodynamic (SC) model simulating both subduction dynamics and seismic cycles. We analyze a total of 15 subduction-initialized 3D dynamic rupture-tsunami scenarios in which the tsunami source arises from the time-dependent co-seismic seafloor displacements with flat bathymetry and inundation on a linearly sloping beach. We first vary the location of the hypocenter to generate 12 distinct unilateral and bilateral propagating earthquake scenarios. Large-scale fault topography leads to localized up- or downdip propagating supershear rupture depending on hypocentral depth. Albeit dynamic earthquakes differ (rupture speed, peak slip-rate, fault slip, bimaterial effects), the effects of hypocentral depth (25–40 km) on tsunami dynamics are negligible. Lateral hypocenter variations lead to small effects such as delayed wave arrival of up to 100 s and differences in tsunami amplitude of up to 0.4 m at the coast. We next analyse inundation on a coastline with complex topo-bathymetry which increases tsunami wave amplitudes up to ≈1.5 m compared to a linearly sloping beach. Motivated by structural heterogeneity in subduction zones, we analyse a scenario with increased Poisson's ratio of ν = 0.3 which results in close to double the amount of shallow fault slip, ≈1.5 m higher vertical seafloor displacement, and a difference of up to ≈1.5 m in coastal tsunami amplitudes. Lastly, we model a dynamic rupture “tsunami earthquake” with low rupture velocity and low peak slip rates but twice as high tsunami potential energy. We triple fracture energy which again doubles the amount of shallow fault slip, but also causes a 2 m higher vertical seafloor uplift and the highest coastal tsunami amplitude (≈7.5 m) and inundation area compared to all other scenarios. Our mechanically consistent analysis for a generic megathrust setting can provide building blocks toward using physics-based dynamic rupture modeling in Probabilistic Tsunami Hazard Analysis.

Influence of Tsunami Aspect Ratio on Near and Far-Field Tsunami Amplitude

This study presents a numerical investigation of the source aspect ratio (AR) influence on tsunami decay characteristics with an emphasis in near and far-field differences for two initial wave shapes Pure Positive Wave and N-wave. It is shown that, when initial total energy for both tsunami types is kept the same, short-rupture tsunami with more concentrated energy are likely to be more destructive in the near-field, whereas long rupture tsunami are more dangerous in the far-field. The more elongated the source is, the stronger the directivity and the slower the amplitude decays in the intermediate- and far-fields. We present evidence of this behavior by comparing amplitude decay rates from idealized sources and showing their correlation with that observed in recent historical events of similar AR.

Tsunami Efficiency Due to Very Slow Earthquakes

Often, tsunami “sources” have been treated as a quasistatic problem. Initial studies have demonstrated that, for earthquake rupture velocities in the span of 1.5–3 km/s, the kinematic and static part of the tsunami can be treated separately. However, very slow earthquake rupture velocities in the span of 0.1–1 km/s have not been included in tsunami analytical or numerical modeling. Here, we calculated the tsunami efficiency, extending Kajiura’s definition for different models. We demonstrated that rupture velocity cannot be neglected for very slow events, that is, rupture velocities slower than 0.5 km/s. We also examined the relation of magnitude, earthquake rupture velocity, and tsunami amplitude to the efficiency of very slow tsunamigenic earthquakes. Hypothetical megathrust earthquakes (Mw>8.5) with very slow rupture velocities amplify energy from 10 to 60 times larger than moderate to large earthquakes (7.0<Mw<8.5) in the direction of rupture propagation.

Study on Analytical Modelling of Tsunami Wave Propagation

Modelling of tsunami wave propagation plays a vital role in forecasting of disastrous tsunami. The earlier identification and prediction of tsunami provides more time for taking preventive measures and evacuation. On December 26, 2004, massive destruction of lives and properties due to tsunami increases the needs to develop a fast and accurate modelling of tsunami wave propagation. The modelling of waves provide the amplitude of tsunami, speed, arrival time and power of the wall of water and also run up distance and height. It also used to predict vulnerable buildings to tsunami. In this paper describes the modelling of tsunami wave propagation from generation to run-up. Numerical and analytical methods used for modelling and simulation. Tsunami is serious of wave (wave train) which has a long wavelength >500 km and celerity of wave more than 800 km/hr in deep ocean and in shallow coast, their wavelength and celerity diminishes but the amplitude of wave increases above 30m. The scope of this study is to determine the areas which are going to hit by tsunami, amplitude of wave and their arrival time for early forecasting and alert the people within a short time after an earthquake happened.

Comparison of local amplification factors for fast forecast coastal tsunami amplitude modeling based on the extended Green’s law

<p>In the framework of operational conditions, the real time coastal modeling in near field is challenging to obtain accurate and reliable tsunami warning products for flooding hazard. Two main approaches are usually developed to generate maps of forecasting inundation and impacts for planning community response. One produces coastal predictions with run-up computation by solving numerically high-resolution forecast models in real time, taking into account all local effects. However, these runs depend on the availability of fine bathymetry/topography grids along the shore and are too time consuming in near field and operational context. The second approach is based on early prediction tools of the coastal wave amplitude calculated from empirical laws or transfer functions derived from these laws. Such tools are suitable in near field context (almost ten times faster than the high-resolution runs), but all local effects are not well taken into account and the assessment of run-up is missing. The linear approximations of coastal tsunami heights are provided very quickly, with global and conservative estimates.</p><p>Within the French Tsunami Warning Center (CENALT), a forecast method based on coastal amplification laws is being implemented. This fast prediction tool provides a coastal tsunami height distribution, calculated from the numerical simulation of the deep ocean tsunami amplitude and using a transfer function derived from the Green’s law. The method involves maps of regionalized values of the empirical correction factor function of the coastal configuration, as a way to amplify or attenuate specific local geometries. Due to a lack of tsunami observations in the NEAM basin, coastal amplification parameters are defined by trial and error regarding high resolution nested grids simulations on the basis of a set of historical and synthetic sources. A method to optimize these local amplification factors by minimizing a cost function is being developed at UCD. Comparisons are shown for several French coastal sites.</p><p>The local tsunami wave heights modeled from the extended Green’s law present a good agreement with the time-consuming high resolution models. The linear approximation is obtained within 1 min and provides estimates within a factor of two in amplitude. Although the resonance effects in harbors and bays are not reproduced and the horizontal inundation calculation needs to be studied further, this method is well suited for an early first estimate of the coastal tsunami threat forecast.</p>

Assessment of the peak tsunami amplitude associated with a large earthquake occurring along the southernmost Ryukyu subduction zone in the region of Taiwan

The southernmost portion of the Ryukyu Trench near the island of Taiwan potentially generates tsunamigenic earthquakes with magnitudes from 7.5 to 8.7 through shallow rupture. The fault model for this potential region dips 10∘ northward with a rupture length of 120 km and a width of 70 km. An earthquake magnitude of Mw 8.15 is estimated by the fault geometry with an average slip of 8.25 m as a constraint on the earthquake scenario. Heterogeneous slip distributions over the rupture surface are generated by a stochastic slip model, which represents the decaying slip spectrum according to k−2 in the wave number domain. These synthetic slip distributions are consistent with the abovementioned identical seismic conditions. The results from tsunami simulations illustrate that the propagation of tsunami waves and the peak wave heights largely vary in response to the slip distribution. Changes in the wave phase are possible as the waves propagate, even under the same seismic conditions. The tsunami energy path not only follows the bathymetry but also depends on the slip distribution. The probabilistic distributions of the peak tsunami amplitude calculated by 100 different slip patterns from 30 recording stations reveal that the uncertainty decreases with increasing distance from the tsunami source. The highest wave amplitude for 30 recording points is 7.32 m at Hualien for 100 different slips. Compared with the stochastic-slip distributions, the uniform slip distribution will be highly underestimated, especially in the near field. In general, the uniform slip assumption only represents the average phenomenon and will consequently ignore the possibility of tsunami waves. These results indicate that considering the effects of heterogeneous slip distributions is necessary for assessing tsunami hazards to provide additional information about tsunami uncertainties and facilitate a more comprehensive estimation.