Second degree moments – a tool for the fault plane detection? Petra Adamová Jan Šílený Geophysical Institute, Academy of Sciences, Prague, Czech Republic e-mail: adamova@ig.cas.cz

Introduction to second degree moments Standard moment tensor Point source: couple of planes

Introduction to second degree moments “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

Second degree moments, Doornbos (1982) Theory Zero degree moment tensor (standard MT)   Second degree moments, Doornbos (1982) Temporal centroid Spatial centroid Rupture propagation Source process duration Source ellipsoid

Inverse scheme: full waveform inversion Standard MT Estimation of first and second degree moments exclusion of the non-physical solutions  inversion is faster

Interpretation of second degree moments Centroid Rupture propagation vector Source ellipsoid

Detection of the fault plane Moment tensor (DC part)  couple of planes (fault and auxiliary)  ambiguity 2nd degree moments  source ellipsoid (volume of the focus) Removing of the ambiguity: Plane containing the source ellipsoid (large axis)  fault plane Convenient geometry Inconvenient geometry

Ridgeway Mine, Australia Seismicity in December 2009 (ISS International) Malovichko, D. [2010] Ridgeway. Routine estimation of the source mechanisms: December 2009. ISSI Document Number: ISSREP_RWM_MECHANISMS200912.

Location of selected events 2 5 3 4 2 1 5 3 4 1 Location of 5 events from Ridgeway mine from December 2009

Moment tensor solution 2009 Dec 04 07:35:06, M = 2.1 IMS solution (spectral amplitudes) P and S wave amplitude inversion Full waveform inversion Frequency range 5 - 25 Hz

Second degree moments (1) 2009 Dec 04 07:35:06, M = 2.1 Source ellipsoid 3-D view

Second degree moments (2) 2009 Dec 04 07:35:06, 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 solution 2009 Dec 04 03:19:07 M = 1.3 DC = 32 % CLVD = 23 % ISO = 46 % IMS solution (spectral amplitudes) P wave amplitude inversion DC = 38 % CLVD = 25 % ISO = 37 % Full waveform inversion Frequency range 5 - 30 Hz (Corner frequency ~ 35 Hz)

Second degree moments 2009 Dec 04 03:19:07 M = 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

Jack-knife test, event 3 Removing 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 moments Temporal 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 Source ellipsoid Fault orientation Gray ellipsoid: inversion from all stations Dashed ellipsoids: jack-knife trials with extreme deviations

Standard MT for selected events Fault plane

Source ellipsoids Removal of ambiguity of the two nodal planes Correlation with geological faults

Conclusions a chance to remove ambiguity of the two nodal planes 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 planes