TSUNAMI RESEARCH GROUP
Indonesia Tsunami of 26 Dec. 2004
NUMERICAL MODELING OF THE GLOBAL TSUNAMI
Non-Linear Shallow Water (NLSW) numerical simulations
Description:
The model for the global tsunami computation includes a high order of approximation for the spatial derivatives. The boundary condition at the shore line is controlled by the total depth and can be set either to runup or to the zero normal velocity. This model, with spatial resolution of one minute, is applied to the tsunami of 26 December 2004 in the World Ocean from 80oS to 69oN. Because the computational domain includes close to 200 million grid points, a parallel version of the code was developed and run on a supercomputer. The high spatial resolution of one minute produces very small numerical dispersion even when tsunamis wave travel over large distances. Model results for the Indonesian tsunami show that the tsunami traveled to every location of the World Ocean. In the Indian Ocean the tsunami properties are related to the source function, i.e., to the magnitude of the bottom displacement and directional properties of the source. In the Southern Ocean surrounding Antarctica, in the Pacific, and especially in the Atlantic, tsunami waves propagate over large distances by energy ducting over oceanic ridges. Tsunami energy is concentrated by long wave trapping over the oceanic ridges. Our computations show the Coriolis force plays a noticeable but secondary role in the trapping. Travel times obtained from computations as arrival of the first significant wave show a clear and consistent pattern only in the region of the high amplitude and in the simply connected domains. The tsunami traveled from Indonesia, around New Zealand, and into the Pacific Ocean. The path through the deep ocean to North America carried miniscule energy, while the stronger signal traveled a much longer distance via South Pacific ridges. The time difference between first signal and later signals strong enough to be recorded at North Pacific locations was several hours.
Reference: Kowalik Z.,W. Knight, T. Logan and P. Whitmore (2005), Numerical modeling of the Global Tsunami: Indonesia Tsunami of 26 December 2004. Science of Tsunami Hazards,Vol. 23, No. 1, page 40-56. (Download PDF file, size:3.16MB)
Figure 1. Maximum amplitude in World Ocean.
Note: This global maximum amplitude distribution shows that the Indonesian tsunami traveled all over the World Ocean. Although the source directivity pushed most of the wave energy towards South Africa, nonetheless quite a strong signal is directed towards the Antarctica. The tsunami signal tends to propagate toward Antarctica along the oceanic ridges and subsequently continues to transfer higher energy along the South Pacific ridge towards South and Central America. This mode of propagation brings the tsunami amplitude up to 65cm along the Pacific coast of South America. A similar mode of energy transfer is observed in the Atlantic, where the Mid-Atlantic Ridge channels the tsunami to produce 30cm wave amplitude as far north as Nova Scotia. An especially large energy flux is ducted from the South Atlantic Ridge towards Brazil and Argentina. The filaments of energy trapped along the South Pacific Ridges are most spectacular as they duct tsunami energy for many thousands of kilometers. A simple explanation of the energy trapping using the continuity equation leads us to conclusion that the amplitude should increase over the ridges due to shallower depth. At the same time the role of the bottom friction over the 2km deep ridge is negligible and therefore the tsunami can travel long distance without energy losses.
Figure 2. Travel time (in hours) for the tsunami of 0.1cm amplitude.
Note: The tsunami arrival time is computed at every grid points for a signal of 0.1cm amplitude. The computed travel time chart shows that even at such small limiting amplitudes the tsunami signal arriving at Alaska and North America did not pass through the Indonesian Straits but rather around the Australia and New Zealand.
SOURCE FUNCTION
Figure 3. Tsunami source deformation contours. Maximum uplift is 507 cm and maximum subsidence approximately 474 cm. Coordinates are given in geographical minutes. Point (0,0) is located at 89oE and 1oN.
Note: The vertical sea floor displacement is computed using the static dislocation formulae from Okada (1985). The earthquake's total rupture extent is estimated by observed tsunami travel times to the northwest, east, and south of the slip zone. This method indicates a fault zone approximately 1000km by 200km. The epicenter location lies on the southern end of the fault zone. To accommodate trench curvature, the fault plane is broken into two segments.
VIDEO/ANIMATION
a) Indian Ocean tsunami wave propagation (Plan view)
Note: Observe the strong wave reflection from Sri Lanka and Maldives Islands. (Download high resolution version. MOV file size: 14.2MB)
b) Indian Ocean tsunami wave propagation (West view)
Note: Notice wave refraction and energy concentration at the lee side of islands. (Download high resolution version. MOV file size: 9.74MB)
c) Global tsunami wave propagation
Note: Notice tsunami signals in the Northern Atlantic and Southern Pacific have been reorganized into coherent waves after passing through the narrows between Africa and South America, and Australia and Antarctica. (Download high resolution version. MOV file size: 83.9MB)
Modified 4 October 2007. Website questions or comments to Juan J. Horrillo.