new multiple dimension stress release statistic model based on co-seismic stress triggering
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New Multiple Dimension Stress Release Statistic Model based on co-seismic stress triggering. Mingming Jiang Shiyong Zhou ITAG, Peking University Email:[email protected]. Outlines. - PowerPoint PPT PresentationTRANSCRIPT
New Multiple Dimension Stress Release Statistic Model based on co-seismic stress triggering
Mingming Jiang Shiyong Zhou
ITAG, Peking University Email:[email protected]
Outlines Physical interpretation for the risk
function in the stress release model
Upgrading the stress release model with the co-seismic stress triggering model
Application to the historic catalogue of North China and results
Stress release model
Coupled stress release model
Is it the real situation that the stress will all release in the whole region after one earthquake?
))((exp)( tStt
))()((exp)( 2211 tSctSctt
depends on mechanisms
Review the stress release model in the physics view
What is the nature of the risk function of the stress release model? How can the stress variation correlated to earthquakes be modeled correctly ?
Evidence from the laboratory
In static fatigue studies, the data are generally reported as the mean fracture time <t> (Scholz, 1968)
The risk function of stress release model
)(exp * Sbat T
)exp( X
Num. of the events per time unit
real stress
Conclusions 1
The risk function could be an expression of the static fatigue in the crust
The stress level X in the risk function could be the real stress
Upgrading SRM with the co-seismic stress triggering model
),,(exp),,( tyxttyx S
the induced shear stress on the fault plane due to earthquakes
),,(),,()( yxtyxtStS s
How to get ? The procedure of Okada (1992, based
on static displacement field of the elastic medium triggered by a slip) was used to get induced shear stress
),,( tyxs
How to get the loading term
L ρ(x,y)
azimuth=16.5°
N
L
Historic catalogue from 1300 to 1997 in North China
Ms≥6.0
64 events
Ms≥6.5
37 events
N
i
N
i
T
S
iiii dxdydttyxmftyxL1 1 0
),,()(ln),,(lnln
Fitting results
α ν (10-7) σ L(103Pa) b Num. of events
Ms≥6.5 -6.899 7.502 5.050 0.810 37
Ms≥6.0 -7.040 7.463 5.118 0.665 64
2.0% 0.5% 1.3% 17.9%
kLAIC 2log2
AIC AICSRM ΔAICS AICPoisson ΔAICP
563.70 583.88 20.18 586.00 22.30
Be extended to spatial-time domain
The variation of conditional intensity with time
1300 1400 1500 1600 1700 1800 1900 2000
0.02
0.06
0.1
Year
Ev
en
ts/Y
ea
r
New SRMClassic SRMPoisson model
1300 1400 1500 1600 1700 1800 1900 2000
6
8
Year
Ms
S
dxdyyxtt ),,()(
Results more than the classic stress release model
We can get the spatial distribution of the conditional intensity at any time
),,( tyx
an example 1997),,( 00 ttyx
High risk is reasonable here?
The weighted conditional intensity
A try, we took the kernel estimation of spatial distribution of seismicity as the spatial weight function. (stock and smith, 2002)
),,(),(),,( tyxyxwtyxw
Data:Ms≥4.0 1970-2005
too high due to the aftershocks of Tangshan Eq. ??
at t=1997
Reasonable now
Might be higher due to weight function
We are still seeking for a reasonable spatial weight function
),,(),(),,( tyxyxwtyxw
),,( tyxwDistribution of at the times before and after M8.0 earthquake of Sanhe of Beijing in 15th century
before after
Distribution of at the times before and after Tangshan M7.8 earthquake in 1976
),,( tyxw
before after
Conclusions 2 The multiple dimension stress release model could be
got based the multiple dimension physical model instead of the simple physical model.
The spatial distribution of the conditional intensity could be very useful in the hazard analysis, if it could be express in a proper way.
Fitting data better than the classic SRM (lower AIC)
The additional sorts of data are needed besides the traditional catalogues. These data can be easily got in modern catalogues, but the problem is the modern catalogues are not long enough.
Data processing depth (feng, 1981)
strike and dip angle (Shen, 2004) Ms≥6.5: data from geologic and seismic survey Ms≤6.5: the same as the nearest event whose strike and dip is known
sediment 4.2km depth
40.3km
moho
Data processing
Slip angle the same as the slip angle of the outside
loading
Rupture length and width, displacement
the empirical relationships between magnitude and them. (Donald et al, 1994)