2006gl026125-txts01


Details of Tsunami Modeling

Because of the large vertical motions and shorter wavelengths 
associated with landslides, nonlinearity and dispersion equations may 
be more of a concern for landslide-generated tsunamis than for 
seismogenic tsunamis. When the maximum seafloor displacement is much 
smaller than the water depth above the slide, then the weakly 
nonlinear equations [Lynett and Liu, 2002] can be used.  Nonlinearity 
can also be important for accurately determining tsunami run-up, 
especially for large incident waves.  As the tsunami propagates away 
from the source, frequency dispersion also becomes important. 
Landslide-generated waves are typically not the long waves 
characteristic of seismogenic sources, and so energy will be dispersed 
in the direction of wave propagation as different wave components 
(frequencies) travel at different velocities according to a dispersion 
relation (Figure S3; See also Figure 7 in ten Brink et al., 2006). 
Lynett and Liu [2002] use the arbitrary-level velocity computation 
[Nwogu, 1993] to "extend" the validity of frequency dispersion for the 
depth-integrated equations into the intermediate water regime, 
allowing for accurate simulation of waves with lengths greater than 
two water depths.  The extended weakly non-linear equations are 
implemented in the program COULWAVE using a finite-difference 
approximation using a high-order predictor-corrector scheme [Lynett 
and Liu, 2002]. The spatial grid size used for the computations is 300 
m with a time step of 0.3 s.  Bottom friction is accounted for with a 
constant friction factor f=0.01 [e.g., Mercado et al., 2002] using the 
quadratic bottom friction formulation. A moving boundary condition 
[Lynett et al., 2002] is implemented along the coast to represent run-
up and overland flow. For the open-ocean boundary conditions, a 
sponge-layer absorption scheme is used.

The dynamics of submarine slope failures can only be observed with 
permanent ocean observatories [e.g., Xu et al., 2004]. Because we 
model slope failures as regions of progressive depletion and down 
slope regions of debris accumulation, it is difficult to assign an 
effective slide speed as with simple block slides commonly used in 
tsunami studies. We can assign different length scales, such as run-
out distance or horizontal displacement of the slide head, to 
calculate an effective velocity from the slide duration time, td. 
Using an 8 km characteristic length scale for the landslide that spans 
the area of excavation and deposition (Figure 1b) and td = 200 s, our 
effective slide velocity is approximately 8000/200 or 40 m/s. For 
comparison, the following velocities were used in tsunami modeling 
case studies: 75 m/s and 35 m/s for the prehistoric Nuuanu, Hawaii and 
Storegga, Norway slides, respectively [Ward, 2001], 20-60 m/s for the 
landslide component of the 1998 Papua New Guinea tsunami [Heinrich et 
al., 2001], 40-80 m/s for the 1888 Ritter Island volcanogenic tsunami 
[Ward and Day, 2003], and 25-30 m/s for the Storegga slide [Bondevik 
et al., 2005].

References

Bondevik, S., F. Lovholt, C. B.  Harbitz, J. Mangerud, A. Dawson, and 
J. I. Svendsen (2005), The Storegga Slide tsunami: Comparing field 
observations with numerical simulations, Mar. Pet. Geol., 22, 195-208.

Heinrich, P., A. Piatanesi, and H. Hebert (2001), Numerical modelling 
of tsunami generation and propagation from submarine slumps: The 1998 
Papua New Guinea event, Geophys. J. Int., 145, 97-111.

Lynett, P., and P. L.-F. Liu (2002), A numerical study of submarine 
landslide generated waves and runup, Proc. R. Soc. London, Ser. A., 
458, 2885–2910. 

Lynett, P., T.-R. Wu, and P. L.-F. Liu (2002), Modeling wave runup 
with depth-integrated equations, Coastal Eng., 46, 89-107.

Mercado, A., N. R. Grindlay, P. Lynett, and P. L.-F. Liu (2002), 
Investigation of the potential tsunami hazard on the north coast of 
Puerto Rico due to submarine landslides along the Puerto Rico trench, 
report, 432 pp., Puerto Rico State Emergency Manage. Agency and Sea 
Grant Coll. Program, San Juan. 

Nwogu, O. (1993), Alternative form of Boussinesq equations for 
nearshore wave propagation, J. Waterw. Port Coastal Ocean Eng., 119, 
618-638.

Okal, E. A., and C. E. Synolakis (2004), Source discriminants for 
near-field tsunamis, Geophys. J. Int., 158, 899-912.

ten Brink, U. S., E. L. Geist, P. Lynett, and B. Andrews (2006), 
Submarine slides north of Puerto Rico and their tsunami potential, in 
Caribbean Tsunami Hazard, edited by A. Mercado and P. L.-F. Liu, World 
Sci., Hackensack, N. J. 

Ward, S. N. (2001), Landslide tsunami, J. Geophys. Res., 106, 11,201-
11,215.

Ward, S. N., and S. Day (2003), Ritter Island Volcano: Lateral 
collapse and the tsunami of 1888, Geophys. J. Int., 154, 891-902.

Xu, J. P., M. A. Noble, and L. K. Rosenfeld (2004), In-situ 
measurements of velocity structure within turbidity currents, L09311, 
Geophys. Res. Lett., 31, doi:10.1029/2004GL019718.