Effectiveness of Real-Time Near-Field Tsunami Inundation Forecasts for Tsunami Evacuation in Kushiro City, Hokkaido, Japan - Post-Tsunami Hazard: Reconstruction and Restoration - page 160

parameters, earthquake fault model, or tsunami source model can be estimated from
real-time observations of seismic waves, crustal deformation, or sea level.
A tsunami source model inferred from tsunami waveforms directly estimates the
tsunami source, whereas earthquake fault or source models from seismic wave data
or GPS data indirectly estimates the tsunami source. The sea-fl oor deformation
caused by fault motion can be calculated by the elastic theory (Okada 1985 ), using
the earthquake fault parameters of longitude, latitude, depth, strike, dip, rake, slip
amount, fault length, and fault width. We may assume that the sea-fl oor deformation
is the same as the sea-surface deformation because, in most cases, the wavelength is
much greater than the water depth. The velocity of rupture propagation is much
faster than the propagation of a tsunami wave; therefore, the sea-surface deformation
can be assumed to occur instantaneously.

11.3.1 Scaling Relations

A scaling relation is needed to estimate rupture area from the earthquake's moment
magnitude. The moment magnitude (Mw) to fault area (A) relation of Wells and
Coppersmith ( 1994 ) is widely used in seismic hazard analysis. The scaling relation
was derived from a database that includes all slip types of continental interplate or
intraplate earthquakes, with the exception of subduction zone earthquakes, both
those at the interface and those within the oceanic slab. Other recently developed
scaling relations focus on continental events (Hanks and Bakun 2002 ) and on sub-
duction zone events (Blaser et al. 2010 ; Murotani et al. 2013 ). Table 11.1 shows the
scaling relations of Hanks and Bakun ( 2002 ), Blaser et al. ( 2010 ), and Murotani
et al. ( 2013 ) and those used by the JMA. From the scaling relations of Hanks and
Bakun ( 2002 ) and Murotani et al. ( 2013 ), we may obtain area from moment magni-
tude, and then to obtain fault length (L) and width (W), we may assume L = 2 W. In
the NearTIF algorithm, we used the scaling relation of Hanks and Bakun ( 2002 )
because it gives a rupture area that is consistent with the major slip region of the
2011 Tohoku earthquake (Gusman and Tanioka 2013 ).

Table 11.1 Scaling relations
for fi rst-order approximation
of rupture area from
earthquake moment
magnitude

Authors Scaling relation
Hanks and Bakun ( 2002 ) Mw = 4/3 × log A + 3.03
Blaser et al. ( 2010 ) log L = 0.57 × Mw - 2.37
log W = 0.46 × Mw - 1.86
Murotani et al. ( 2013 ) A = 1.34 × 10 −10 × Mo 2/3
D = 1.66 × 10 −7 × Mo 1/3
JMA (Kamigaichi 2011 ) log L = 0.5 × M - 1.8
log W = 0.5 × M - 2.1
log D = 0.5 × M - 3.3
Area (A) is in km 2 , length (L) and width (W) are in km, and slip
amount (D) is in m