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: adamova@ig.cas.cz, 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

Izmit earthquake: agency solution (ETH)

N

PT

Strike = 90Dip = 72Rake = -164DC = 59 %CLVD = 41 %ISO = 0 %

Date/Time: 99/ 8/17 0: 1:38 Latitude 40.640 Longitude 29.830 Mw= 7.52

Very high non-DC component

Synthetic test: Synthetic test: configurationconfiguration

• Green’s functions are computed by DWN method• crustal model is identical for data and synthetics (Bulut et al., 2007)• noise-free data

Rupture model (Rupture model (J. J. BurjánekBurjánek))

Unilateral ruptureFault size: 20 km x 10 kmScalar seismic moment: 1e18 Nmf = 0 - 2 HzRupture velocity 2.8 km/sec

Inversion schemeInversion scheme

Additional constraint: the volume of the focus is non-negative (McGuire et al., 2001, 2002)

Synthetic dataSynthetic dataunfiltered synthetic data demonstrating the source directivity:

station SDL: direction perpendicular to the fault strike.

station HER: ‘reverse’ direction

station BAL: ‘forward’ direction

Results: exact dataResults: exact dataCommon Common MTMT, , f f = 0.02 - 0.08 Hz= 0.02 - 0.08 Hz

(3(3rdrd order Butterworth filter) order Butterworth filter)

Strike = 93Dip = 73Rake = -178DC = 78 %CLVD = 12 %V = 10 %

Theoretical mechanism

Strike = 90Dip = 72Rake = 180DC = 100 %CLVD = 0 %V = 0 %

P T

N

Frequency testFrequency test• low-pass filtering as much as possible: low-pass 3rd order Butterworth filter with a low-cut off at 0.02 Hz

• high-pass filter as much as possible but to keep the 2nd

degree effects high-pass 3rd order Butterworth filter with a cut off at 0.1, 0.2, 0.3 and 0.4 Hz

Geometrical Geometrical characteristicscharacteristics

A – 0.1 Hz B – 0.2 Hz C – 0.3 Hz D – 0.4 Hz

frequencies used in the inversion of 2nd degree moments

Optimum frequency range is up to 0.2 Hz

Second spatial derivative, 6 parameters

MT refinement: exclusion MT refinement: exclusion of of 2nd degree terms2nd degree terms

Refined MT: common MT without second degree terms

Strike =93Dip = 73Rake =2DC = 94 %CLVD = 4%V = 2 %

Theoretical mechanism

P T

N

P T

N

Strike = 90Dip = 72Rake = 180DC = 100 %CLVD = 0 %V = 0 %

Strike =93Dip = 73Rake =2DC = 78 %CLVD = 12 %V = 10 %

Reconstructed Reconstructed mechanismsmechanisms0.02- 0.1

Hz0.02-0.2 Hz

0.02-0.3 Hz 0.02-0.4

Hz

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

simulates smaller location precisionsimulates smaller location precision

b)b) inaccurate GF inaccurate GF ((less layers + deviation 10% in each less layers + deviation 10% in each layerlayer))

dashed line – simplified dashed line – simplified modelmodel

c) noise in data noise in data (15 - 30% from the maximal amplitude)(15 - 30% from the maximal amplitude)

Experiments simulating inconsistencies duringduring the data inversion

Geometrical Geometrical characteristicscharacteristics

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