Earthquake source modelling by second degree moment tensors Petra Adamová Jan Šílený Geophysical Institute, Academy of Sciences, Prague, Czech Republic fax:

Introduction, motivation Finite source parameters from point source approximation Finite source parameters from point source approximation traditional modeling of slip on fault plane is more complicated 2 nd degree moments are adventageous alternative  size of the source, duration of the source process, average slip on the fault, etc.

Theory: second degree moment tensors First degree moment tensor representation: Second degree moment tensor representation (Taylor expansion up to degree two):

Second degree moments, 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 estimate 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 component Izmit earthquake: agency solution (ETH) N P T Strike = 90 Dip = 72 Rake = -164 DC = 59 % CLVD = 41 % ISO = 0 % Date/Time: 99/ 8/17 0: 1:38 Latitude Longitude Mw= 7.52 Very high non-DC component

Synthetic test: configuration 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 (J. Burjánek) Unilateral rupture Fault size: 20 km x 10 km Scalar seismic moment: 1e18 Nm f = Hz Rupture velocity 2.8 km/sec

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

Synthetic data unfiltered synthetic data demonstrating the source directivity: station SDL: direction perpendicular to the fault strike. station HER: ‘reverse’ direction station BAL: ‘forward’ direction

Results: exact data Common MT, f = Hz (3 rd order Butterworth filter) Strike = 93 Dip = 73 Rake = -178 DC = 78 % CLVD = 12 % V = 10 % Theoretical mechanism Strike = 90 Dip = 72 Rake = 180 DC = 100 % CLVD = 0 % V = 0 % P T N

Frequency 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 2 nd degree effects high-pass 3rd order Butterworth filter with a cut off at 0.1, 0.2, 0.3 and 0.4 Hz

Geometrical characteristics A – 0.1 Hz B – 0.2 Hz C – 0.3 Hz D – 0.4 Hz frequencies used in the inversion of 2 nd degree moments Optimum frequency range is up to 0.2 Hz Second spatial derivative, 6 parameters

MT refinement: exclusion of 2nd degree terms Refined MT: common MT without second degree terms Strike =93 Dip = 73 Rake =2 DC = 94 % CLVD = 4% V = 2 % Theoretical mechanism PT N P T N Strike = 90 Dip = 72 Rake = 180 DC = 100 % CLVD = 0 % V = 0 % Strike =93 Dip = 73 Rake =2 DC = 78 % CLVD = 12 % V = 10 %

Reconstructed mechanisms Hz Hz Hz Hz Left: the mechanism obtained by inverting data filtered outside Hz Right: mechanism from data corrected for the contribution of the 2 nd degree moments frequency used in the inversion of 2 nd degree moments Hz

Test of robustness a) source mislocation (1 km E, 1 km S, 2 km Z) larger error in depth than in the horizontal coordinates simulates smaller location precision larger error in depth than in the horizontal coordinates simulates smaller location precision b) inaccurate GF (less layers + deviation 10% in each layer) dashed line – simplified model noise in data ( % from the maximal amplitude) c) noise in data ( % from the maximal amplitude) during Experiments simulating inconsistencies during the data inversion

Geometrical characteristics Bold line – exact data A - 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 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 mechanisms Left: the mechanism obtained by inverting data filtered outside Hz Right: mechanism from data corrected for the contribution of the 2 nd degree moments

Synthetic data vs. synthetic seismograms Black: synthetic data Upper gray: synthetic seismograms Lower gray: 2 nd degree terms station SDL: direction perpendicular to the fault strike. station HER: ‘reverse’ direction station BAL: ‘forward’ direction Frequency range Hz

Conclusions We removed false non-DC component from the data Scalar seismic moment is higher with 2 nd term than with only 1 st degree term Method of the second degree moments is perspective for applications