Institute of Computational Mathematics and Mathematical Geophysics SB RAS

International Conference on Mathematical Methods in Geophysics «MMG-2008»

Akademgorodok, Novosibirsk, Russia, October 13-15, 2008

Abstracts

Mathematical Simulation in Geophysical Problems. Seismic Methods, Problems of Geomonitoring and Geodynamics

Tsunami source restoration: case study of the Peru coastal area.

Voronina T.A.

Institute of Computational Mathematics and and Mathematical Geophysics SB RAS (Novosibirsk)

Abrupt marine invasions such as tsunamis are particularly devastating for coastal areas. Recent tsunami events, e.g. Sumatra 2004 and Java 2006 have demonstrated the need for providing accurate and timely tsunami warnings. There are several components of assessment and mitigation of disasters. One of them for tsunamis is numerical modeling. Tsunami modeling is one of the most important tools needed for assessment of tsunamis, using for warning issues. One of the main needs for developments in tsunami modeling is estimating the characteristic parameters of the tsunami source characteristics (initial water level distribution for the static source). Most of these parameters can only be estimated by compilation of seismic, geophysical and tidal data some time after the event. Since numerical modeling of the tsunami source is one of the available tools for numerical simulation of tsunami propagation and runup. For this reason, we have developed a technique based on the inverse problem by a truncated SVD approach. Mathematically, this problem is formulated as inverse problem of mathematical physics for restoration of the initial water displacement in the source area by the water level oscillations observed at a number of points distributed in the ocean. In this paper to simulate seawater disturbance we have used the bathymetry by the Peru zone. The forward problem, i.e. the calculation of synthetic tide-gage records from the initial water elevation field, is based on a linear shallow-water system of differential equations in the rectangular coordinates. This system is approximated by the explicit-implicit finite difference scheme on a uniform rectangular grid, so the system of the linear algebraic equations is obtained. The ill-posed inverse restoration problem is regularized by means of the least square inversion using the truncated SVD approach. Furthermore, proposed technique allowed estimating the potentialities of sea-level observations system that could be used to support detection and warning. The results of the numerical simulations for the probably scenario on the Peru area are discussed.

Note. Abstracts are published in author's edition

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