Документ взят из кэша поисковой машины. Адрес оригинального документа : http://ocean.phys.msu.ru/science/nosov/EGU2010_initial_condition.pdf Дата изменения: Thu Jan 12 20:24:35 2012 Дата индексирования: Mon Oct 1 19:50:29 2012 Кодировка:

Specification of Initial Condition in Numerical Simulation of Seismotectonic Tsunamis
Mikhail Nosov and Sergey Kolesov
M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow, Russian Federation (m.a.nosov@mail.ru) Numerical simulation of tsunami is normally based on the shallow water theory. As for the description of tsunami generation, an earthquake is considered to instantly cause residual deformations of the ocean bottom. Then, the assumption is made that the displacement o f the bottom is simultaneously accompanied by formation at the surface of the ocean of a perturbation (initial elevation), the shape of which is fully similar to the vertical residual deformations of the bottom. The initial elevation, thus obtained, is then applied as the initial condition in resolving the problem of tsunami propagation. A logical development of the traditional approach is to calculate the initial elevation from the solution of the 3D problem taking into account all three components of the bottom deformation vector and the distribution of depths in the vicinity of the source. The suggested method of calculation of the initial elevation in tsunami source does not violate the traditional scheme of tsunami simulation but just optimize it. The first point of optimization consists in the removal from tsunami spectrum of the shortwave components which are not peculiar to real tsunami waves The second point of optimization consists in taking into account not only vertical bottom deformation but all three components of the deformation vector and bathymetry in source area. The Central Kuril Islands tsunamis on November 15, 2006 and on January 13, 2007 are taken as examples to demonstrate the efficiency of the new method.

H / g

Dynamic problem


Static problem
F dt
0

F 0
F n

, n , z H ( x , y ) t

0 0, z 0
0 , n , z H ( x , y ) n

2F F g , z0 2 z t

1 F ( x , y ,t ) g t v ( x , y , z ,t ) F

0
z 0

z

z 0

Free surface disturbance caused by residual deformat ion of rectangular shape (potential analyt ical solut ion). Surface disturbance and deformat ion are shown in the same scale. Displac the free surface is much smoother as compared bottom deformations: init ial elevat ion has amplitude and spreads over a rather wide area.

bottom theory, bottom ement of with the smaller

F ­ velocity potential, H ­ depth, ­ vector of bottom deformation, 0 ­ initial elevation

a

.

b

Bottom topography November 15, 2006 is shown by iso lines m) is depicted in the

and vector fields of residual bottom deformat ion for the tsunamigenic Centr al Kuril Islands earthquakes o f (a) and of January 13, 2007 (b). The isobaths are drawn with an interval o f 1 km. Vertical bottom deformat ion drawn in steps of 0.2 m (a) and 1 m (b). Black arrows stand for horizontal bottom deformat ion; scale arrow (4 right down corner.

Init ial elevat ion of water surface in tsunami sources of November 15, 2006 (left co lumn) and of January 13, 2007 (right column). a, b ­ vertical bottom deformation: 0 z ; c, d ­ contributions of vertical and horizontal bottom deformat ion: ( n , ) n x x n y y n z z ; e, f ­ the Laplace smoothing algorithm: 0 ( x, y) .

Snapshots of the simulated propagation of January 13, 2007 tsunami at time mo ment 3000 s after the earthquake. The init ial elevation assumed to be equal to the vertical bottom deformat ion (a); calculated with use of the Laplace smoothing algorithm (b).

Synthetic (curves) and in-situ measured (gray squares) run-up heights along the coasts of Simushir and Ketoi Islands. Red curves stand for the t raditional method of specificat ion of the init ial elevation; blue curves ­ the Laplace smoothing method. Green curves denote difference in run-up heights of tsunamis originated fro m the init ial elevation calculated with account of horizontal and vert ical co mponents of bottom deformat ion and with account of the vertical component on ly. Relief maps of the islands; starting points (white circles), where the distance along the coast is equal to zero, and the direct ion of "traveling" along the coasts (black arrows).

Publications:
Nosov M. A., Kolesov S. V. Optimal initial conditions for simulation of seismotectonic tsunamis, Pure and Appl Geophys (In print) Nosov, M.A., and Kolesov, S.V. (2009), Method of Specification of the Initial Conditions for Numerical Tsunami Modeling, Moscow University Physics Bulletin, 64(2), 208­213.