Morphotectonics III Determining the time evolution of fault slip 1 Techniques to monitor fault slip 2 EQs phenomenology 3 Slow EQs phenomenology 4 Paleoseismology 5 Paleogeodesy ID: 804412
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Slide1
GE177b
I. Introduction
II. Methods in
Morphotectonics
III.
Determining the time evolution of fault slip
1- Techniques to monitor fault slip
2- EQs phenomenology
3- Slow EQs phenomenology
4-
Paleoseismology
5-
Paleogeodesy
Appendix:
‘Elastic Dislocation’ modeling
Slide2III.2-Earthquake Phenomenology
Slide3Hector Mine 1999 earthquake (California), Mw= 7.1
Slide4Landers 1992 earthquake (California), Mw= 7.3
Slide5Terminology, components and measurement of a slip vector
Slide6Yet, these measurements only give a ‘partial’ vision of the slip distribution on the rupture fault, for they only represent the (small?) portion of the slip that has reached the surface.
Besides, such
complete
measurements are quite
rare and really reliable for strike slip faults only.
(
Manighetti
et al, 2007)
Mw=7.3
Mw=7.6
Mw=7.1
Mw=7.3
Mw=6.5
Mw=7.1
Slide7C
o-seismic
displacement
field due to the 1992, Landers EQ
G. Peltzer
(based on
Massonnet
et al, Nature, 1993)
Slide8Co-seismic displacement field due to the 1992, Landers EQ
G. Peltzer
Here the measured SAR
interferogram
is compared with a theoretical
interferogram
computed based on the field measurements of co-seismic slip using the elastic dislocation theory
This is a validation that
coseismic
deformation can be
modelled
acurately
based on the elastic dislocation theory
(based on
Massonnet
et al, Nature, 1993)
Slide9A common approach to investigate earthquake physics consists of producing
kinematic source models
from the inversion of seismic records jointly with geodetic data.
Seth Stein’s web site
Slide10Kinematic Modeling of Earthquakes
Slide11Kinematic Modeling of Earthquakes
Parameters to find
out (assuming a propagating slip pulse)
Slip at each
subfault
on the fault
Rise time
(the time that takes for slip to occur at each point on the
fault).
Rupture velocity
(how fast does the rupture propagate)
Slide12Landers (1992, Mw=7,3)
Hernandez et al., J.
Geophys
.
Res
., 1999
Slide13Slide14Sud
Nord
Joined
inversion of
geodetic
,
inSAR
data and
seismic
waveforms
Hernandez
et al., J.
Geophys
.
Res
.,
1999
Slide15Sud
Nord
Slide16Sud
Nord
Slide17Sud
Nord
Slide18Sud
Nord
Slide19Sud
Nord
Slide20Sud
Nord
Slide21Sud
Nord
Slide22Sud
Nord
Slide23Sud
Nord
Slide24Sud
Nord
Slide25Sud
Nord
Slide26Sud
Nord
Slide27Sud
Nord
Slide28Sud
Nord
Slide29Sud
Nord
Slide30Sud
Nord
Slide31Sud
Nord
Slide32Sud
Nord
Slide33Sud
Nord
Slide34Sud
Nord
Slide35Sud
Nord
Slide36Sud
Nord
Slide37Sud
Nord
Slide38Sud
Nord
Hernandez et al., J. Geophys. Res., 1999
Slide39Observed and predicted waveforms
Strong motion data
Hernandez et al., J. Geophys. Res., 1999
Slide40(Bouchon et al., 1997)
Slide41This analysis demonstrates weakening during seismic sliding
Slide42Some characteristics of the Mw 7.3 Landers EQ:
Rupture length:
~
75 km
Maximum slip:
~
6m
Rupture duration:
~
25 seconds
Rise time: 3-6 seconds
Slip rate: 1-2 m/s
Rupture velocity:
~
3 km/s
Slide43Kinematic inversion of earthquake sources show thatSeismic ruptures are “pulse like” for large earthquakes (Mw>7) with rise times of the order of 3-10s typically
(
e.g
, Heaton, 1990)
the rupture velocity is variable during the rupture but generally close to Rayleigh waves velocity (2.5-3.5
kms
) and sometimes ‘
supershear
’ (>3.5-4km/s)
Seismic sliding rate is generally of the order of 1m/s
Large earthquakes typically ruptures faults down to 15km within continent and down to 30-40km along
subduction
Zones.
Slide44P = D.S (Integral of slip over rupture area)
Quantification of
EQs- Moment
Slip Potency (in m
3
):
Seismic
Moment tensor
( in
N.m
):
Scalar seismic Moment (
N.m
):
M
0
=
.D.S
where D is average slip, S is surface area
and
m
is elastic shear modulus (30 to 50
GPa
)
M
w
= 2/3 * log
10
M
o
- 6.0
Moment Magnitude:
(where M0 in N.m)
Slide45Quantificatio
n of EQs:
The
Elastic
crack
model
See Pollard et
Segall
, 1987 or
Scholz
, 1990 for more details
A
planar
circular crack of radius a with
uniform
stress drop,
Ds
,
in a perfectly elastic body (Eshelbee, 1957)
NB: This model produces
un realistic infinite stress at crack tips
The predicted
slip
distribution is
elliptical
D
mean
and
D
max
increase linearly with fault length (if stress drop is constant).
Slip
on the crackStress on the crack
Slide46See Pollard et
Segall
, 1987 or
Segall
, 2010 for
more details
A rectangular fault extending from the surface to a depth h, with uniform stress drop (‘infinite Strike-Slip fault)
The predicted
slip
distribution is
elliptical with depth
Maximum slip should occur at the surface
D
mean
and
D
max
should increase linearly with fault width (if stress drop is constant) and be
idependent
of fault length.
Quantification of EQs: The Elastic crack model
Slide47Coseismic surface displacements due to the Mw 7.1 Hectore
Mine EQ measured from correlation of optical images
(
L
eprince
et al, 2007)
Quantification of EQs: The Elastic crack model
Slide48Quantification of EQs: The Elastic crack model
Slide49Ds
of the order of 5
MPa
Quantification of EQs: The Elastic crack model
Slide50The crack model works approximately in this example, In general the slip distribution is more complex than perdicted from this theory either due to the combined effects of non uniform prestress, non uniform stress drop and fault geometry.
The theory of elastic dislocations can always be used to model surface deformation predicted for any slip distribution at depth,
Quantification of EQs: The Elastic crack model
Slide51Quantification of
EQs- Stress drop
Average
static stress drop
:
S
is rupture area;
a
is characteristic fault length (fault radius in the case of a circular crack, width of
inifinite
rectangular crack).
C
is a geometric factor, of order 1, C= 7
p
/8 for a circular crack, C=½ for a infinite SS fault.
is equivalent to an elastic stiffness (1-D spring and slider model).
Given that
The stress drop can be estimated from the seismological determination of M
0
and from the determination of the surface ruptured area (geodesy, aftershocks).
Slide52M
0
~
Δσ
S
3/2
M
0
linked to stress drop
Es ~ ½
Δσ
D
mean
Seismic
Energy
M
0
= μ
DS
Es/M
0
~
Δσ
/2μ
Stress
Drop
Stress
drop is generally in the range 0.1-10
MPa
Slide53But S not always well-known; and all
type of faults
mixed
together
Modified from
Kanamori
& Brodsky, 2004
M
0
scales indeed with S
3/2
as expected from the simple crack model.
Ds
of the order of 3
MPa
on average
Bigger Faults Make Bigger Earthquakes
Stress
drop is generally in the range 0.1-10
MPa
Quantification of
EQs- Scaling Laws
Slide54Bigger Earthquakes Last a Longer Time
From
Kanamori
& Brodsky, 2004
M
0
scales
approximately with
(duration)
3
M
0
=
.D.S
2004, Mw 9.15 Sumatra Earthquake (600s)
Quantification of
EQs- Scaling Laws
Rupture velocity during seismic ruptures varies by less than 1 order of magnitude
Slide55(
Wesnousky
, BSSA, 2008)
Bigger Earthquakes produce larger average slip
The mean slip,
D
mean
, is generally larger for larger earthquakes, but not as linear as expected from the crack model. Recall:
where here L is fault Length (2a for a circular crack)
We expect the circular crack model not to apply any more as the rupture start ‘saturating’ the depth extent of the
seismogenic
zone (M>7).
Quantification of
EQs- Scaling Laws
Slide56(
Manighetti
et al, 2007)
The maximum slip,
Dmax
, is generally larger for larger earthquakes, but not as linear as expected from the crack model. Recall:
where here L is fault Length (2a for a circular crack)
The
pb
might be that the estimate of
D
mean
is highly model dependent. Also the circular crack model should not apply to large magnitude earthquakes (Mw>7,
Dmax
>3-5m).
Slide57Seismogenic
depths
typically
0-15km
within continent
probably primarily thermally controlled (
T<350°C)
(from Marone & Scholz, 1988)
In oceans, the lower friction stability transition corresponds approximately with the onset of ductility in olivine, at about 600°C.
From Scholz, 1989
Slide59(
Wesnousky
, 2006)
Slide60(
Wesnousky
, 2006)
Slide61(
Wesnousky
, 2006)
Slide62log N(M
w
)=
-
bM
w
+
log
a
w
here b is generally of the order of 1
N(M
0
)=aM
0
-2b/3
Here the seismicity catalogue encompassing the entire
planet. It shows that every year we have about 1 M≥8 event, 10 M>7 events …
Let N (M
w) be number of EQs per year with magnitude ≥ Mw
This relation can be rewritten
From
Kanamori
& Brodsky, 2004
The Gutenberg-Richter law
Slide63The Omori law (aftershocks)
The
decay of aftershock activity follows a
power law
.
Many different mechanisms have been proposed to explain such decay: post-seismic creep, fluid diffusion, rate- and state-dependent friction, stress corrosion, etc… but in fact, we don’t know…
Aftershock decay since the 1891, M=8
Nobi
EQ: the Omori law holds over a very long time!
Same for 1995 Kobe EQ
1
100
10000
Time (days)
0.001
0.01
10
1000
n (t)
Time (days)
n (t)
where p
~
1
Slide64References on EQ phenomenology and scaling laws
Kanamori
, H., and E. E. Brodsky (2004), The physics of earthquakes,
Reports on Progress in Physics, 67(8), 1429-1496.
Heaton, T. H. (1990), Evidence for and implications of self-healing pulses of slip in earthquake rupture,
Physics of the Earth and Planetary Interiors, 64, 1-20.
Wells, D. L., and K. J. Coppersmith (1994), New Empirical Relationships Among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,
Bulletin of the Seismological Society of America
,
84
(4), 974-1002.
Hernandez, B., F. Cotton, M.
Campillo
, and D.
Massonnet
(1997), A comparison between short term (co-seismic) and long term (one year) slip for the Landers earthquake: measurements from strong motion and SAR
interferometry, Geophys
. Res. Lett., 24, 1579-1582.Manighetti, I., M. Campillo, S.
Bouley, and F. Cotton (2007), Earthquake scaling, fault segmentation, and structural maturity, Earth and Planetary Science Letters, 253(3-4), 429-438.Wesnousky, S. G. (2008), Displacement and geometrical characteristics of earthquake surface ruptures: Issues and implications for seismic-hazard analysis and the process of earthquake rupture,
Bulletin of the Seismological Society of America, 98(4), 1609-1632.