OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS M.A. Nosov, S.V. Kolesov Faculty of Physics M.V.Lomonosov Moscow State University, Russia

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS [WinITDB, 2007]:

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

INITIAL CONDITIONS or “roundabout manoeuvre” 1. Earthquake focal mechanism: Fault plane orientation and depth Burgers vector 2. Slip distribution Central Kuril Islands, 15.11.2006 [http://earthquake.usgs.gov/]

INITIAL CONDITIONS or “roundabout manoeuvre” 3. Permanent vertical bottom deformations: the Yoshimitsu Okada analytical formulae numerical models 4. Long wave theory Central Kuril Islands, 15.11.2006

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS The “roundabout manoeuvre” means Initial Elevation = Vertical Bottom Deformation ??? There are a few reasons why…

Dynamic bottom deformation (Mw=8) [Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

Dynamic bottom deformation (Mw=8) permanent bottom deformation duration ~10-100 s [Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

Period of bottom oscillations

Time-scales for tsunami generation L is the horizontal size of tsunami source; H is the ocean depth g is the acceleration due to gravity c is the sound velocity in water Tsunami generation is an instant process if finite duration However, if instant ocean behaves as a compressible medium

Time-scales for tsunami generation instant L is the horizontal size of tsunami source; H is the ocean depth g is the acceleration due to gravity c is the sound velocity in water traditional assumptions (i.e. instant & incompressible) are valid Tsunami generation is an instant process if finite duration instant However, if Compressible ocean ocean behaves as a compressible medium

Linear = Incompressible! Elastic oscillations do not propagate upslope Elastic oscillations and gravitational waves are not coupled (in linear case) Linear = Incompressible!

Initial Elevation = Vertical Bottom Deformation ???

“Smoothing”: min~H exponentially decreasing function

Initial Elevation = Vertical Bottom Deformation Due to “smoothing”

Permanent bottom deformations vertical horizontal Central Kuril Islands, 15.11.2006

Sloping bottom and 3-component bottom deformation: contribution to tsunami Normal to bottom Bottom deformation vector

Sloping bottom and 3-component bottom deformation: contribution to tsunami traditionally neglected traditionally under consideration

Linear potential theory (3D model) Tsunami generation problem: Incompressible = Linear Linear potential theory (3D model) 1) Dynamic bottom deformation (DBD) Not instant! 2) Phase dispersion is taken into account Disadvantages: 1) Inapplicable under near-shore conditions due to nonlinearity, bottom friction etc.; 2) Numerical solution requires huge computational capability; 3) Problem with reliable DBD data.

If you can’t have the best make the best of what you have Simple way out for practice Instant generation If you can’t have the best make the best of what you have

Simple way out for practice Instant generation Not only vertical but also horizontal bottom deformation is taken into account Permanent bottom deformations (all 3 components!) “Smoothing”, i.e. removing of shortwave components which are not peculiar to real tsunamis

Linear shallow water theory Initial conditions: Boundary conditions: at shoreline at external boundary Initial elevation

Initial Elevation=Vertical Bottom Deformation 15.11.2006 Initial Elevation=Vertical Bottom Deformation

Smoothing: Initial Elevation from Laplace Problem 15.11.2006 Smoothing: Initial Elevation from Laplace Problem

Initial Elevation=Vertical Bottom Deformation 13.01.2007 Initial Elevation=Vertical Bottom Deformation

Smoothing: Initial Elevation from Laplace Problem 13.01.2007 Smoothing: Initial Elevation from Laplace Problem

Comparison of runup heights calculated using traditional (pure Z) and optimal (Laplace XYZ) approach 15.11.2006 13.01.2007

Conclusions: Optimal method for the specification of initial conditions in the tsunami problem is suggested and proved; The initial elevation is determined from 3D problem in the framework of linear potential theory; Both horizontal and vertical components of the bottom deformation and bathymetry in the vicinity of the source is taken into account; Short wave components which are not peculiar to gravitational waves generated by bottom motions are removed from tsunami spectrum.

Thank you for your attention!

15 Nov 2006 13 Jan 2007

15 Nov 2006 13 Jan 2007