Post on 02-Jan-2016
Physical interpretation of DC and non-DC components
of moment tensors
Václav Vavryčuk
Institute of Geophysics, Prague
Explosive (implosive) source
Force equivalent Moment tensorSource process
1
1
1
00
00
00
M
M
M
M
0Tr M
0Tr M
explosion
implosion
three lineardipoles
Shear faulting
Force equivalent Moment tensorSource process
00
000
00
0
0
M
M
M
double-couple (quadrupole)
fault
no torque
Pure tensile faulting
Force equivalent Moment tensorSource process
faultfault
fault opening
2
1
1
00
00
00
M
M
M
M
0Tr M
0Tr M
opening
closing
Shear-tensile faulting
Force equivalent Moment tensorSource process
fault
fault opening
fault DC +
20
1
01
0
00
0
MM
M
MM
M
0Tr M
0Tr M
opening
closing
Double-couple component of the moment tensor
DC part(shear faulting)
00
000
00
0
0
M
M
M
0
0
00
000
00
M
M
M
Force equivalent Seismic moment tensor
double couple (DC)
rotated double-couple (DC)
Non-double couple components: ISO and CLVD
ISO part
CLVD part
1
1
1
00
00
00
M
M
M
M
2
2
2
200
00
00
M
M
M
M
Force equivalent Seismic moment tensor
(explosion)
(tensile crack)
compensated linear vector dipole
Decomposition of the moment tensor
DCCLVDISO MMMM
*M
M – moment tensor
MISO – trace of M
M* – deviatoric part of M
%100
Tr
3
1
MAXMISO
M ISOM
MCLVD
MAX
MIN %1002
*
*
CLVDISODC %100
Percentage of ISO, CLVD and DC : |ISO|+|CLVD|+DC = 100%
DC componentsDC components
Parameters of shear faulting
• orientation of active faults, fault mapping • type of fracturing (strike-slip, normal/reverse faulting)
Determination of present-day tectonic stress
• orientation of principal stress axes• ratio between principal stresses
Numerical errors of the MT inversionNumerical errors of the MT inversion
• insufficient number of stations• presence of noise in the data• unfavourable station coverage of the focal sphere• inaccurate knowledge of the structure model
• approximate location and Green’s functions
• approximate moment tensor
Presence of single forces
no dipole forces
Examples: impact of meteorites, landslides, volcanic eruptions, fluid flow in volcanic channels
surface
the process is not described by the moment tensor!
Complex shear faulting
Sum of two DCs of different orientations produces DC and CLVD
DC + CLVD
ISO = 0fault
DC1 DC2
DC + CLVD + ISO
Example: hydrofracturing High pore pressure can cause opening faults during the rupture process (CLVD and ISO are then positive).
][u
fluid pressure
fault
Combined shear-tensile faulting I
Combined shear-tensile faulting II
20 .
0 3 0 6 0 9 0
0
2 0
4 0
6 0
8 0
1 0 0
DC
,CLV
D,I
SO
[%] DC
C LVD
ISO
01 .
0 3 0 6 0 9 0
0
2 0
4 0
6 0
8 0
1 0 0
DC
ISO
C LVD
CLVD and ISO are correlated! ISO/CLVD -> vP/vS
Correlation between ISO and CLVD
CLVD [%]
ISO [%]
shear-tensile faulting
linear dependence
different vP/vS ratios
Shear faulting in anisotropic media
The relation between fracture geometry and acting forces is more complicated in anisotropic media than in isotropic media.
fault
u S
n
332313
232212
131211
MMM
MMM
MMM
M kl
DC + CLVD + ISO
Moment tensors in isotropyMoment tensors in isotropy
Shear earthquakes in isotropy (Aki & Richards 2002, Eq. 3.22):
u – slipS – fault area – shear modulus – slip directionn – fault normal cijkl – elastic parameters
u S
n
001
000
100
0MM kl
double-couple (DC) mechanism
kllkkl nnuSM
Moment tensors in anisotropyMoment tensors in anisotropy
Shear earthquakes in anisotropy (Aki & Richards 2002, Eq. 3.19):
lkijklkl nuScM
u – slipS – fault area – shear modulus – slip directionn – fault normal cijkl – elastic parameters
u S
n
332313
232212
131211
MMM
MMM
MMM
M kl
general (non-DC) mechanism
Example: seismicity in West BohemiaExample: seismicity in West Bohemia
• active tectonics• geothermal area
• mineral springs• emanations of CO2
earthquake swarms:• 1985/86• 1994• 1997• 2000• 2008
P wave S wave
1 s
Z
E
N• Duration: 2 weeks
• Number of earthquakes: 1800
• Strongest event: M=3.0
• Depth of events: 8.5-9.5 km
• Focal area: 700x700x1000 m
• Faults activated: 2 different faults
Swarm 97: Basic characteristics
39B e v e n t s
307A e v e n t s
1 km
1 km
N
D C events
non-D C events
A
B
39
307
Swarm 97: epicentres and mechanisms
Nový Kostel focal area
Fischer & Horálek (2000) Horálek et al. (2000)
0 20 40 60 80 100
DC [% ]
0
2
4
6
8
10
12
NA events
0 20 40 60 80 100
D C [% ]
0
2
4
6
8
10
12
NB events
DC & non-DC mechanisms
Type A Type B
Correlation between ISO and CLVD
-20 0 20 40C LVD [% ]
-10
0
10
20
ISO
[%]
corr. coeff = 0.91
vP/vS = 1.48
strong indication for tensile faulting!
+
Shear & tensile faulting
– fault , u – slip, – deviation of the slip from the fault
Slip is along the fault
Shear faulting Tensile faulting
Slip is not along the fault
u
u
Moment tensor is DC Moment tensor is non-DC(DC+CLVD+ISO)
A events B events
-15 -10 -5 0 5 10 15
[º]
0
2
4
6
N
A events
0 5 10 15 20 25 300
2
4
6
8
N
B events
[º]
Deviation of the slip from the fault
A events: -5 < < 5 B events: 10 < <20
P wave S wave
1 s
Z
E
N• location: northern Bavaria, Germany
• holes: pilot hole - 4 km, main borehole - 9.1 km (October 1994), distance – 185 m
• geology: crystalline unit, steeply inclined layers of gneisses, amphibolites
• borehole geometry: vertical to 7.5 km, then inclined
• bottom hole temperature: 265ºC
KTB superdeep drilling hole
P wave S wave
1 s
Z
E
N• experiment: 60 days
• amount of fluid: 4000 m3 of fresh water
• entire 9.1 km borehole was pressurized
• well head pressure was between 20 to 30 MPa
• flow rate ranged between 30 to 70 l/min
• several sharp pressure drops during shut-in phases
Injection experiment 2000
-40 -20 0 20 40
ISO [% ]
0
2
4
6
Num
ber
of e
arth
quak
es
-80 -60 -40 -20 0 20 40 60 80
CLVD [% ]
0
2
4
6
Num
ber
of e
arth
quak
es
Mean value of ISO = 1.5% Mean value of CLVD = -5.7%
ISO percentage CLVD percentage
Positive values - tensile components, negative values - compressive components
Non-DC components
Correlation between ISO and CLVD
corr. coeff. = 0.01
strong indication for other origins than tensile faulting!
-80 -40 0 40 80CLVD [% ]
-40
-20
0
20
40
ISO
[%] no correlation!
0 30 60 90angle [degrees]
4.8
5.6
6.4
pha
se v
eloc
ity [k
m/s
]
P w ave
0 30 60 90angle [degrees]
3
3.4
3.8
4.2
pha
se v
eloc
ity [k
m/s
]
S w aves
P anisotropy: 2 - 18%, S1 anisotropy: 3 - 18%, S2 anisotropy: 8 - 26%anisotropic models of gneiss inferred from: VSP, sonic logs, lab measurements
References: Jahns et al. (1996), Rabbel (1994), Rabbel et al. (2004)
P-wave velocity
S-wave velocity
Anisotropy models at KTB
Inversion for anisotropy: method
The misfit function: misfit between the theoretical and observed non-DC components
Output: • fault normals and slip directions• theoretical DC, CLVD and ISO components
Input: • moment tensors of 37 events• anisotropy at the focal area
Result: optimum orientation of anisotropy
Misfit for TI Misfit for ORT
Inversion for anisotropy: results
o
a
oo
o
b
The misfit function is normalized so it equals 1 for an isotropic medium.
Optimum anisotropy orientation
Triangles: optimum orientation from moment tensorsSquares: orientation from MSPRabbel et al. (2004)
Anisotropy axes (plunge/azimuth): Axis 1: 5º/65º, Axis 2: 50º/160º, Axis 3: 40º/330º
Significance of the DC componentsSignificance of the DC components
Parameters of shear faulting
• orientation of active faults, fault mapping • type of fracturing (strike-slip, normal/reverse faulting)
Determination of present-day tectonic stress
• orientation of principal stress axes• ratio between principal stresses
Significance of the non-DC componentsSignificance of the non-DC components
Discrimination explosions versus earthquakes
Analysis of tensile faulting
• detection of overpressure regime • temporal variation of pore pressure• the vP/vS ratio in a focal area
Estimation of anisotropy in a focal area
• orientation of anisotropy axes• anisotropy strength