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*** N.B. The material presented in these lectures is from the principal textbooks, other books on similar subject, theresearch and lectures of my colleagues from various universities around the world, my own research, and finally,numerous web sites. I am grateful to E. Calais, E. Garnero and S. Ford for some material I used in this lecture. Iam thankful to many others who make their research and teaching material available online; sometimes even asingle figure or an idea about how to present a subject is a valuable resource. Please note that this PowerPointpresentation is not a complete lecture; it is most likely accompanied by an in-class presentation of mainmathematical concepts (on transparencies or blackboard).***
LECTURES 10 and 11 - Seismic SourcesHrvoje Tkalčić
Exercise 1: Locating a local earthquakeDue next Tuesday, 10:10 AM in class
1. Measure time between P and S wave on seismogram
2. Use travel-time curves to get distance to epicenter
3. Draw circle on a map with radius of that distance
4. Three or more circles should intersect at EQ!
What is an earthquake?
elastic reboundelastic rebound
- plates are continually moving & fault is stuck
- crust starts deforming (stores elastic energy)
- fault breaks, releases elastic energy
fault
Seismic Sources
Seismic Sources
These are, of course, fictitious forces.
Seismic Moment Tensor Mij
Seismic Sources
Seismic Sources
Seismic Sources
ε - the strength of CLVD component (from 0 to 0.5)
Seismic moment tensors
Double-couple(DC)
y z
x
Compensatedlinear vectordipole (CLVD)
Isotropic
y z
x
y z
x
Model Source M Couples Focal
Ring Fault
Explosion
Strike-slip
Mechanism
Moment tensor decomposition
Full Isotropic DC CLVD
Seismic Sources
“Strike”, “Dip” and “Rake” angles
Strike, Dip and Rake anglesAki & Richards (an advanced seismology book) definition of strike, dip, and rake
(adapted from page 106 of Aki & Richards (1980), Quantitative Seismology - Vol 1)
Strike - the fault-trace direction in decimal degrees (0 to 360, relative to North), defined so that the fault dips to the right side of thetrace. That is, the fault always dips to the right when moving along the trace in the strike direction (from one point to the next). Thismeans that the hanging-wall block is always to the right. This is important because rake (which gives the slip direction) is defined asthe movement of the hanging wall relative to the footwall. For a vertical, strike slip fault (for which "hanging wall" has no physicalmeaning) we still call the right-side block the hanging wall to distinguish between right lateral and left lateral motion.
Dip - the angle of the fault in decimal degrees (0 to 90, relative to horizontal).
Rake - the direction the hanging wall moves during rupture, measured relative to the fault strike (between -180 and 180 decimaldegrees). Rake=0 means the hanging wall, or the right side of a vertical fault, moved in the strike direction (left lateral motion); Rake =+/-180 means the hanging wall moved in the opposite direction (right lateral motion). Rake>0 means the hanging wall moved up(thrust or reverse fault). Rake<0 means the hanging wall moved down (normal fault).
Basic Examples:
Dip=90 & Rake=0 -----> left lateral strike slipDip=90 & Rake=180 -----> right lateral strike slipDip=45 & Rake=90 -----> reverse faultDip=45 & Rake=-90 -----> normal fault
Seismic Sources
Seismic Sources
Seismic Sources
“Beach Balls”
Types of focal mechanisms vs. boundaries
Transform faults (e.g. San Andreas)
Earthquake - slippage along a fault
Earthquake focus - fault slip location
Fault - crack in Earth where slip occursTurkeyAug 1999M 7.4
Subduction zones and ridges)
Earthquake “belts”
95% of energy from earthquakes from thin zones (plate edges) Some are quite deep (subduction zones)
You are here: check out that unbeatable ray-path coverage for tomography
Earthquake “belts”
95% of energy from earthquakes from thin zones (plate edges) Some are quite deep (subduction zones)
Earthquake “belts”
notice the orientation of tectonic forces on this map
volcanoes
- cliff from nearly vertical slip on fault
Hmm. How canwe calculate thescalar seismicmoment?
!
M0
=µAD
Earthquake Intensity and magnitude
Mercalli intensity scale
Magnitude
Intensity of shaking & damage at a specific location
A measure of the energy released in an earthquake
Depends on distance to earthquake& strength of earthquake
Depends on size of fault that breaks
Earthquake Intensity and magnitude
Mercalli intensity scale
Magnitude
Intensity of shaking & damage at a specific location
A measure of the energy released in an earthquake
Depends on distance to earthquake & strength of earthquake
Depends on size of fault that breaks
Earthquake Intensity and magnitude Mercalli intensity scale
Magnitude
Intensity of shaking & damage at a specific location
A measure of the energy released in an earthquake
Depends on distance to earthquake & strength of earthquake
Depends on size of fault that breaks
Regional moment tensor inversiondn(x,t) = Mkj [ Gnk, j * s(t) ]
If we assume a point sourceand now in matrix form
d = Gm
d = seismic observations of displacementG = Green’s functions representing propagation effectsM = moment tensor elements
m = vector of 6 independent moment tensor elements
m = (GTG)-1GTd
Full waveform moment tensor inversion
Displacement u can be written:
where u is displacement, SS is vertical strike-slip, DS is vertical dip-slip,DD is 45º dip-slip, and EP is the explosion Green’s functions with Z, R,and T refering to vertical, radial and tangential components. Miso is(Mxx+Myy+Mzz)/3. Ai is given by
Now put the coefficients into the displacement equations and rearrange
!
uz = Mxx
ZSS
2cos(2az) "
ZDD
6+ZEP
3
#
$ % &
' (
+Myy "ZSS
2cos(2az) "
ZDD
6+ZEP
3
#
$ % &
' (
+Mzz
ZDD
3+ZEP
3
#
$ % &
' (
+Mxy ZSS sin(2az)[ ]
+Mxz ZDS cos(az)[ ]
+Myz ZDS sin(az)[ ]
!
ur = Mxx
RSS
2cos(2az) "
RDD
6+REP
3
#
$ % &
' (
+Myy "RSS
2cos(2az) "
RDD
6+REP
3
#
$ % &
' (
+Mzz
RDD
3+REP
3
#
$ % &
' (
+Mxy RSS sin(2az)[ ]
+Mxz RDS cos(az)[ ]
+Myz RDS sin(az)[ ]
!
ut = Mxx
TSS
2sin(2az)
"
# $ %
& '
+Myy (TSS
2sin(2az)
"
# $ %
& '
+Mxy (TSS cos(2az)[ ]
+Mxz TDS sin(az)[ ]
+Myz (TDS cos(az)[ ]
Full waveform moment tensor inversion
d = Gm
Green’s functionscomputed for a 1-Dmodel
Data and synthetics arefiltered between 10 and 50 s MW < 4 20 and 50 s 4 < MW < 5
BDSN regional MT solutions (1997-1998)
The Long Valley Caldera(CA - NV border)
To Las VegasSan Francisco
Bay Area
If you ever…In my opinion,visually the mostspectacular partof California(east of HW395, goingsouth fromMono Laketo DeathValley)
I determinedmost of the“beach balls”shown hereas a graduatestudent at UCBerkeley(some of themin the middleof the night,immediatelyafterearthquakesoccurred)
Anomalous Non-Double CoupleEarthquakes in the Long Valley Caldera
!
M1
0 0
0 M2
0
0 0 M3
"
#
$ $ $
%
&
' ' '
=1
3
tr(M) 0 0
0 tr(M) 0
0 0 tr(M)
"
#
$ $ $
%
&
' ' '
+ (1( 2))
0 0 0
0 (M3
0
0 0 M3
"
#
$ $ $
%
&
' ' '
+ )
(M3
0 0
0 (M3
0
0 0 2M3
"
#
$ $ $
%
&
' ' '
Percentagesof DC, CLVD, ISO (ISO isSet to 0“restrained”)
significantISO, when MT is fullydecomposed
Thepresenceof significantvolumetriccomponentIndicatesA directinvolvementof magmaticprocesses(e.g.pressurisedliquidopeningCracks)
Dreger et al., Science, 2000
The puzzle of the Bárðarbungaearthquake: constraints from
kinematic modelling
?
An example of a research project in volcano seismology -similar problems can be tackled at RSES, ANU
Bárðarbunga
Photo taken by Oddur Sigurdsson, Iceland Geological Survey
Gjalp Subglacial Eruption (3 October 1996)
Gjalp Fissure (October 1996)
Photo taken by Oddur Sigurdsson, Iceland Geological Survey
The Earthquake and Stations Location
Azimuthal coverage excellent!
Time Domain MT Inversion Results
Tkalčić et al., 2007
Insignificant volumetric component!!!(unexpected)
Solution Stability
The importance of having enough stations in the inversion is illustrated here
Faulting mechanism hypothesis
Nettles and Ekström, 1998
Finite source simulationsusing finite differences method
to produce “synthetic” data
Tkalčić et al., 2007
Constraints on geometry of the caldera
Constraints on geometry of the caldera
Tkalčić et al., 2007
Finite Source: Full-Circumference
Not a good solution (opposite sense of CLVD from the observed)
Finite Source: Instantaneous Caldera Drop
Not a good solution; tangential component of displacement very smallin comparison to the observed
Finite Source: Quarter-Circumference
Not a good solution, DC dominates the moment tensor (CLVD too small)in comparison to the observed
Finite Source: Half-Circumference
This is a good solution, similar to the observed focal mechanism
Finite Source: Bilateral Rupture
This is also a good solution, similar to the observed focal mechanism
Possible Rupture Speed
Cone sheets and ring dikes
From “Mull and Iona” by David Stephenson
Under which circumstances can these sheets rejuvenateto produce conical walls Observed, but with steep angles of dipping
not exactly at 45 degrees, as in our models
Mass-exchange mechanism?
Modelling: Horizontal tension crack at 2 km depthand compensating isotropic source at 3 km depth (below the crack)(this is done to simulate two magmachambers exchanging some volume of magma, which would be an alternativemechanism to the tectonic one)
⇒ Retrieves a similar focal mechanism, but in most cases a large isotropic component, that was not observed(however, this can not be excluded as a plausible physical mechanism responsiblefor the puzzling focal mechanism)
Mass-exchange mechanism?
Conclusions
• Although our models are simplified in the sense of fault geometry, slip distribution(assumed uniform) and rupture velocity (assumed constant), they bracket the rangeof possible parameters in the finite-source process.
• An alternative model with two offset sources with similar but opposite volumechanges cannot be ruled out, however our modeling indicates that such scenariosoften produce isotropic components.
• A range of rupture speeds results in the observed mechanism, however theobserved H/V ratio is better fit with super-shear rupture velocity.
• The mechanism for the Bárðarbunga earthquake appears to be strongly NDCwithout a large isotropic component.
• We were able to simulate the observed mechanism using a finite rupture on aconical surface.
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