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Tsunami source parameters versus earthquake magnitude and depth: Monte Carlo simulation
Mikhail Nosov and Anna Bolshakova
M.V.Lomonosov Moscow State University, Faculty of Physics, Moscow, Russian Federation (m.a.nosov@mail.ru)

European Geosciences Union General Assembly 2011 Vienna | Austria | 03 08 April 2011

Studying tsunamis and other oceanic phenomena of seismotectonic origin it is often necessary to know general relationships between parameters of the tsunami source and characteristics of the earthquake such as magnitude and depth. Among all possible parameters of a tsunami source we consider only those parameters which can be unambiguously calculated from the vertical component of co-seismic bottom deformations. There are three of them: double-amplitude of vertical bottom deformation, displaced water volume, potential energy of the initial elevation. Co-seismic bottom deformations we calculate making use of the Okada formulae for a finite rectangular fault. In order to diminish number of the input parameters, we involve the scaling laws by Kanamori and Anderson and the definition of the seismic moment. Specifying a certain values for earthquake magnitude and depth, the rest of the input parameters (dip and rake angles) were chosen randomly. As a result of Monte Carlo simulation we obtain synthetic distributions of the tsunami source parameters which allow us to determine the maximal and the most probable values. Ultimately, we reveal simple relationships between the maximum and the most probable values of tsunami source parameters and earthquake magnitude and depth. Scaling relations [Kanamori and Anderson,1975]

Parameters under consideration:
1. Amplitude of vertical bottom displacements

Synthetic distributions of the tsunami source parameters

L /W = / L = 2, D 5? 10
Seismic moment definition
M
0

5

=LW m D

=1 0 P 83 , m ? a;

10

Empirical relation [Kanamori, Brodsky, 2004]

h a x[ y ) Mh m ax = z ( x , h=h h m in m ax

] r h i n [ y )] { h z } = z ( x, M h , h ,h ? y ,h m in x
2. Displaced water volume

log10 M 0 Mw = 6 .0 7 1 .5
L-length of the fault plane, W-width of the fault plane D- Burgers vector, Л- Lame constant M0-seismic moment, Mw-moment magnitude

lo g 10 L [ k m ] =w -A = 2 . 0 7 ; 0 .5 M AL ; 1 .9 2 L

r AD = 3 . 3 7 . 3 .2 2 log10 D [ m ] = 0.5M w AD ;
h = 0 k m, 3 0 k m, 5 0 k m, 1 k m, 1 1 0 0 k m, 1 5 0 k m, 2 0 0 k m 7 <9 MW < 0° < <90° d ip -rake < 90° < 90°

log10 W [ km ] = -AW = 2 . 3 7 ; 0.5 M w AW ; 2 .2 2 -

r r (xd V =x d y =n )y » x d y x d h ,d h d z oo oo o o
3. Potential energy of the initial surface elevation

r g2 r g 2 E = ( x, y )d x d y »z ( x, y )d x d y x h o 2o o o 2

Maximum and most probable values versus earthquake magnitude and depth
i
m ax

Examples of co-seismic vertical deformation of bottom due to finite rectangular fault
h= 30 km MW = 9 d ip = 30° ra ke = 30° hm = 9 .3
References Bolshakova A.V., Nosov M.A. Parameters of tsunami source versus earthquake magnitude // Pure and Applied Geophysics, 2011, DOI 10.1007/s00024-011-0285-3. Kanamori, H., Anderson, D. L. (1975), Theoretical basis of some empirical relations in seismology, Bulletin of the Seismological Society of America, 65, 10731095. Kanamori, H., Brodsky, E. E. (2004), The physics of earthquakes, Rep. Prog. Phys., 67, 14291496. Okada, Y. (1985), Surface deformation due to shear and tensile faults in a half-space, Bulletin of the Seismological Society of America, 75(4), 11351154. Okada, Y. (1995), Simulated empirical law of coseismic crustal deformation, J. Phys. Earth, 43, 697-713

j

m ax

h= 10 km M
W

j

log 10 Q =a , h [ km ] ah a ij M W
i= 0 j= 0
3

j

i

= 8

i

lo g 10 h ] m ax [ m ?? -0 4 .9 1 1 0 9 .3 ? 1 c - 0 - 0 .0 2 9 7 1 .4 1 3 c? c 56 0 1 .4 7 e .0
6 5

lo g
m o s t p ro b a b l e

10

E

m ax

[J] 3 .6 ? 10 0 .1 3 6 .2 9
4

d ip = 90° ra ke = 30° hm = 2 .2

4 .4 ? 10 0 .1 5 7 .4 4

4

o g 10 V lo ? ? ? o

m ax

[ m ] =V lo g 10 = 1 .5 M
w

? 10 3 [ m ] =.5 9 ? c
3

6

1 .8

0. c0 0 1 c. 0 6 e0
lo g

-0 7 .2 ? 1 0 .0 2 3 3 .0 5
10

5

o ? ? ? o

l o g 1 0 h b le [ m ] m o s t p ro b a
6 4 4 ? ? -1 0 -7 .7 6 ?o 8 .2 9 1 0 - 1 .6 1 ? 10 c ? 3 -1 0 - 0 .0 3 9 1 .8 3 ? -? 0 .2 c c.0 6 ? 0 1 .4 8 -o 7 .4 1 e

E

m o s t p ro b a b l e

[J]

5 3 3 ? ? -? 1 .2 2 ? o 1 .5 6 1 0 3 .3 6 1 0 10 c ? 0. 0 .0 6 2 -? 0 .3 c0 3 4 c0 3 4 0. 2 .5 8 -? 4 .2 5 o e