Earthquake source Earthquake source modelling by modelling by second degree second degree moment tensors moment tensors Petra Adamo Petra Adamo vá vá Jan Šílený Jan Šílený Geophysical Institute, Academy of Sciences, Prague, Czech Republic e-mail: [email protected], fax: +420-272761549
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Earthquake source modelling by second degree moment tensors
Earthquake source modelling by second degree moment tensors . Petra Adamo vá Jan Šílený. Geophysical Institute, Academy of Sciences, Prague, Czech Republic e-mail: [email protected], fax: +420-272761549. Introduction, motivation. Finite source parameters from point source approximation. - PowerPoint PPT Presentation
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Earthquake source Earthquake source modelling by modelling by
second degree second degree moment tensors moment tensors Petra AdamoPetra Adamovává
Jan ŠílenýJan ŠílenýGeophysical Institute, Academy of Sciences, Prague, Czech Republice-mail: [email protected], fax: +420-272761549
Introduction, motivationIntroduction, motivation• Finite source parameters from point Finite source parameters from point source approximationsource approximation
• traditional modeling of slip on fault plane is more complicated
• 2nd degree moments are adventageous alternative
size of the source, duration of the source process, average slip on the fault, etc.
TheoryTheory: second degree moment : second degree moment tensorstensors
First degree moment tensor representation:
Second degree moment tensor representation (Taylor expansion up to degree two):
Second degree moments, Second degree moments, Doornbos (1982)Doornbos (1982)
1. Time derivative of the response function (1 parameter): temporal centroid – origin time of the finite extent source estimate
Standard MT
2. Spatial derivative (3 parameters): spatial centroid position 3. Combination of temporal and spatial derivative (3 parameters) 4. Second time derivative (1 parameter): source duration
From 3 and 4: rupture propagation along the fault
5. Second spatial derivative (6 parameters): geometrical characteristics of the source (source ellipsoid)
Application for better Application for better estimate of mechanismestimate of mechanism
• High non-DC component is reported for some strong events by seismological agencies (Harvard, USGS, SED)
• This component is often questionable (large events, tectonic origin) it can be false due to unmodeled source finiteness (strong event is modeled as point source)
• the scalar moment underestimation in the agency solution we will try to verify this hypothesis using synthetic test
Example of high non-DC Example of high non-DC componentcomponent
Left: the mechanism obtained by inverting data filtered outside 0.02 -0.08 Hz Right: mechanism from data corrected for the contribution of the 2nd degree moments
frequency used in the inversion of 2nd degree moments
0.02-0.08 Hz
0.02-0.08 Hz
0.02-0.08 Hz
0.02-0.08 Hz
Test of robustnessTest of robustness
a)a) source mislocation (1 km E, 1 km S, 2 km Z) source mislocation (1 km E, 1 km S, 2 km Z) larger error in depth than in the horizontal coordinates larger error in depth than in the horizontal coordinates
Bold line – exact dataA - mislocation of the hypocenter when evaluating Green’s function B - mismodeling of the velocity profile: the true 1-D model used to synthesize the data, simplified when evaluating Green’s function C - noisy data
Second spatial derivative, 6 parameters
Propagation vectorsPropagation vectors
Background: vertical projection of the source model: the moment density distribution of the unilaterally propagating rupture together with the 1 s, 2 s and 3 s isochrones.
exact data (black) (a) hypocenter mislocation
(b) the seismic velocity profile mismodeling
(c) noisy data
Reconstructed Reconstructed mechanismsmechanisms
Left: the mechanism obtained by inverting data filtered outside 0.02 - 0.08 Hz Right: mechanism from data corrected for the contribution of the 2nd degree moments
Synthetic data vs. synthetic Synthetic data vs. synthetic seismograms seismograms
Black: synthetic dataUpper gray: synthetic seismogramsLower gray: 2nd degree termsstation SDL: direction perpendicular to the fault strike. station HER: ‘reverse’ directionstation BAL: ‘forward’ direction
Frequency range 0.02 -0.2 Hz
ConclusionsConclusions• We removed false non-DC component from the data• Scalar seismic moment is higher with 2nd term than with only 1st degree term• Method of the second degree moments is perspective for applications