Second degree moments – a tool for the fault plane

detection?

Petra AdamováJan Šílený

Geophysical Institute, Academy of Sciences, Prague, Czech Republice-mail: adamova@ig.cas.cz

Introduction to second degree Introduction to second degree momentsmoments

Standard moment tensorPoint source: couple of planes

Introduction to second degree Introduction to second degree momentsmoments

“Finite source” parameters from point source approximation

• traditional modeling of slip on fault plane is costly and data are not available (no stations near the fault)

• 2nd degree moments are advantageous alternative

geometry of the source

duration of the source process

spatial and temporal centroid

rupture velocity vector

TheoryTheory

Second degree moments, Doornbos (1982)Second degree moments, Doornbos (1982)Temporal centroid

Spatial centroid

Source ellipsoidRupture propagation

Source process duration

Zero degree moment tensor (standard MT)Zero degree moment tensor (standard MT)

Inverse scheme: full waveform inversionInverse scheme: full waveform inversion

exclusion of the non-physical solutions inversion is faster

Standard MT

Estimation of first and second degree moments

Interpretation of second degree Interpretation of second degree moments moments

Centroid Rupture propagation vectorCentroid Rupture propagation vector

Source ellipsoidSource ellipsoid

Detection of the fault plane

Convenient geometryConvenient geometryConvenient geometryConvenient geometry InconvenientInconvenient geometry geometryInconvenientInconvenient geometry geometry

Moment tensor (DC part) couple of planes (fault and auxiliary) ambiguity2nd degree moments source ellipsoid (volume of the focus)

Removing of the ambiguity:Plane containing the source ellipsoid (large axis) fault plane

Moment tensor (DC part) couple of planes (fault and auxiliary) ambiguity2nd degree moments source ellipsoid (volume of the focus)

Removing of the ambiguity:Plane containing the source ellipsoid (large axis) fault plane

Seismicity in December 2009 (ISS International)

Ridgeway Mine, AustraliaRidgeway Mine, Australia

Malovichko, D. [2010] Ridgeway. Routine estimation of the source mechanisms: December 2009.

ISSI Document Number: ISSREP_RWM_MECHANISMS200912.

Location of selected eventsLocation of selected events

Location of 5 events from Ridgeway mine from December 2009

1

32 5

4

5

43

2

1

Moment tensor solutionMoment tensor solution20092009 Dec Dec 0404 0707::3535::0606, M = 2.1, M = 2.1

IMS solution (spectral amplitudes)IMS solution (spectral amplitudes)

P and S wave amplitude inversionP and S wave amplitude inversion

Full waveform inversion

Frequency range 5 - 25 Hz

Second degree momentsSecond degree moments ( (11))20092009 D Decec 0404 0707::3535::0606, M = 2.1, M = 2.1

Source ellipsoid

3-D view

Second degree moments (2)Second degree moments (2)20092009 D Decec 0404 0707::3535::0606, M = 2.1, M = 2.1

Temporal centroid = 0.01 sec

Duration of the source process = 0.1 sec

Average rupture velocity 2.0 km/s

H – hypocenter

C – spatial centroid position

Moment tensor solutionMoment tensor solution2009 Dec 04 03:19:072009 Dec 04 03:19:07 M = 1.3M = 1.3

IMS solution (spectral amplitudes)IMS solution (spectral amplitudes)

P wave amplitude inversionP wave amplitude inversion

Full waveform inversion

Frequency range 5 - 30 Hz

(Corner frequency ~ 35 Hz)

DC = 38 %

CLVD = 25 %

ISO = 37 %

DC = 32 %

CLVD = 23 %

ISO = 46 %

Second degree momentsSecond degree moments2009 Dec 04 03:19:072009 Dec 04 03:19:07 M = 1.3M = 1.3

Temporal centroid = 0.025 sec

Duration of the source process = 0.15 sec

Average rupture velocity 1.8 km/s

Inconvenient geometry for estimation of the remaining parameters: source ellipsoid and rupture velocity vector lie on the intersection of 2 nodal planes

We estimated second degree moments successfully but we cannot recognize which plane is the fault plane

We estimated second degree moments successfully but we cannot recognize which plane is the fault plane

Jack-knife test, event 3Jack-knife test, event 3Removing one or 2 stations from the data set

All jack-knife trials

All jack-knife trials except removal of stations 25 and 39

Jack-knife test, second degree momentsTemporal centroid 0.01 sec For all jack-knife trials Source duration 0.1 sec nearly the same values

Rupture velocity 2.1 km/sec

Spatial centroid 1 m NS, 1 m EW, -10 m Z from the hypocenter

Fault orientation Gray ellipsoidGray ellipsoid: inversion from all

stationsDashed ellipsoidsDashed ellipsoids: jack-knife trials with extreme deviations

Gray ellipsoidGray ellipsoid: inversion from all stationsDashed ellipsoidsDashed ellipsoids: jack-knife trials with extreme deviations

Source ellipsoid

Standard MT for selected eventsStandard MT for selected events

Fault plane

Source ellipsoidsSource ellipsoids

• Removal of ambiguity of the two nodal planes

• Correlation with geological faults

ConclusionsConclusions

• standard moment tensor: dot second degree moments: beyond dot: estimate of source shape, rupture propagation vector, …

• second degree moments bring additional information to standard MT: source ellipsoid, duration of the source process, average rupture velocity

• a chance to remove ambiguity of the two nodal planesa chance to remove ambiguity of the two nodal planes