Physical interpretation of DC and non-DC components

of moment tensors

Václav Vavryčuk

Institute of Geophysics, Prague

MT for simple types of seismic sources

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

Decomposition of MT

Decomposition of MT

CLVDDCISO MMMM

ISO DC CLVD

+ +

MTr

IM

MM3

* Tr

shearnon-shear non-shear

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%

Physical interpretation of MT

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

Examples

1997 West-Bohemian earthquake swarm

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

Induced microseismicity during the 2000 fluid injection experiment

in KTB, Germany

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

Focal mechanisms of 37 events

P

T

Nodal lines P/T axes

Nodal lines and P/T axes are well clustered

-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

Summary

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