FINITE FAULT MODELING OF STRONG GROUND MOTIONS USING AN EMPIRICAL GREEN’S

FUNCTION APPROACH

Case Study: 26 September 1997, 09:40GMT, Mw= 6.0 Colfiorito Earthquake (Italy)

ISTANBULJANUARY 2005Laura Scognamiglio

OBJECTIVESThe purpose of this study is to test the ground motion synthesis methodology outlined by Hutchings and Wu (1990) and further developed by Hutchings et al. (1991, 1994), and verify its capacity of being used as a predicting tool in strong ground motion seismology as developed by Hutchings (1991) and Hutchings et al. (1996).

The earthquake chosen for this test is the 26 September 1997, 09:40, Mw=6.0 Colfiorito Earthquake (Italy).

METHODThis methodology consists in computing synthetic ground motion solving the discretized representation relation:

iiinNi eiiiiin VtXeMtSAtXu ⎟⎟⎠⎞⎜⎜⎝⎛−′⊗′=∑= χμ ,)(),( 10EGF for the ith element

Rupture surface

Scalar seismic moment of the source event

Radial distance between the Target event hypo. and the elemental source.

Rupture velocity

Slip function

The earthquake is synthesized by discretizing a potential fault rupture surface in N elemental areas Ai small enough to model continuous rupture up to highest frequency of interest, then all available recordings of effectively impulsive point source events are used as EGF for each elemental area, convolved with a slip function and interpolated to model a continuous rupture.

The SECOND STEP consists in constructing the rupture scenarios for the evaluation of the synthetic seismograms. These scenarios consist in a preferred number of faulting model defined by: strike, dip, slip vector, rupture area, rupture and healing velocity (rise times), roughness, hypocenter, and number and location of large asperities. Moment remains fixed. The parameters are varied about a preferred value and selected by a Monte Carlo pick using a triangular distribution.

The FIRST STEP consists in selecting a data-base of small earthquakes to be used as EGF. These events need to be generated by the same fault of the target event and to have same focal mechanism. Seismic moment and corner frequency of the events should be evaluated if not available.

COOK BOOK: how computing synthetic seismograms with EGF

Rupture ParametersSlip function: Kostrov with healing. The slip shape is approximated as a ramp. Slip distribution: varies on the fault following the Kostrov slip function. It has variable rise time and slip amplitude on the fault, but constant stress drop. This results in a different value of slip for each small element due also to the location respect to the hypo and the edges.

Moment: is constrained and depends on the magnitude of the earthquake to synthesize. In the asperities M is randomly selected for obtaining slip at least twice the average slip of background rupture.Hypocenter: at least 0.2km from the edge, and constrained in the lower half of the fault.

Rise time: rupture initiates at the arrival time of the rupture front, and continues until the shortest time for the rupture front to reach a fault edge, and for a healing phase to travel back to the point at the healing velocity.Rupture velocity: from 0.75 to 1.0 times the shear wave velocityHealing velocity: from 0.8 to 1.0 times the rupture velocity.Asperities: small areas of high slip and high stress drop. Circular in shape, diameter between 0.2 and 0.8 times the fault width, area between 10% to 50% of the total fault area. They are not allowed to overlap.Roughness: is the % of the rupture surface for which the rise time is shortened to be between 0.1 to 0.9 times that the original value (delay in the rupture initiation). Areas of roughness have corresponding high stress drop.

COOK BOOK: how computing synthetic seismograms with EGF

THIRD STEP, computing synthetic seismograms.The empirical Green’s function are:• deconvolved from their source function;• normalized by the M0 ;• interpolated to provide the point source contribution to all elemental source areas along a discretized fault surface area (interpolation is performed by correcting for attenuation, 1/R, and P and S-wave arrival times due to differences in source distance);• convolved with analytical slip function;• time delayed to simulate rupture velocity and• summed to compute synthetic seismograms.

DATA ANALYSES AND VALIDATION PROCEDURE

1. I have collected small earthquakes recorded by the same stations that recorded the Colfiorito Earthquake and occurred on the same fault;

2. I have evaluated seismic moment and corner frequency of these events;

3. I have constructed rupure scenarios to simulate the Colfiorito Earthquake rupture and I have calculate synthetic seismograms for each scenarios at each station.

then, I have carried out a validation procedure based on two analyses:

4. a FORWARD MODELING analysis to find whether one of the synthetic seismograms obtained match the Colfiorito observed time histories;

5. a PREDICTION TOOL analysis to develop a range of possible ground motions and see if the actual ground motion recordings fall within the range predicted.

DATA-SET

39 events recorded during the sequence. These events have hypocenter reliable to the main event fault and are recorded in the same location where the main shock was.

Models fault rupture parametersdip (dpp) 40º ± 0.5ºstrike (stkk) 148º ± 5ºRake 270º ± 20ºhypo latitude 43.03ºhypo longitude 12.87ºhypo depth 5.7 kmdepth of hazard surface .65 ± .5 kmwidth hazard surface (dppdis) 11.5 ± .5 kmlength hazard surface (rh11+rh22) rh11=13.0 ± .5 km

rh22=2.0 ± .5 kmrupture surface geometry rectanglewidth rupture surface (rec22) 12.0 ± .001 kmlength rupture surface (rec11) 10.0 ± .001 kmmin and max displacement 10-80 cmseismic moment (M0) 1.2x1025 dyne·cmrupture velocity (Vr) 2.6 km/shealing velocity (Vh) 0.8 Vrslip function Kostrov with healingnumber of asperities 0-7Roughness 0-50%small elements area 0.001 km2

Constructing 30 Rupture Scenarios……..Fault ParametersTime, GMT 970926 09: 40aLatitude (degrees) 43.030aLongitude (degrees) 12.862aDepth (km) 5.7bM0 (N·m) 1.2x1018bMw 6.0bStrike (degrees) 144bDip (degrees) 42bRake (degrees) 280cLength (km) 12cWidth (km) 10cDisplacement (m) 0.37cTop of the rupture surface (km) 0.65c,dRupture Velocity (km/s) 2.6

a, Deschamps et al. 2000; b, Ekström et al., 1998. c, Zollo et al., 1999; d, Pino & Mazza, 2000.

COLF

IORI

TO

EART

HQUA

KE

REPRODUCING THE COLFIORITO EARTHQUAKE

rec22

dppd

is

rh11

rh22

dpp

stkk

rec11

MODEL asperities rgh (%) Mo(x1026dyne·cm) mo1 mo2 mo3 stk dp sv

CLF001 01,02 33 0.044 0.025 0.051 150.9 40.5 263.7CLF002 1 0 0.103 0.017 147 39.5 273.8CLF003 1 10 0.042 0.078 145.9 38.3 265.5CLF004 1 10 0.079 0.041 146.7 40.3 282.3CLF005 1 25 0.089 0.031 145.7 37.6 273.3CLF006 1 0 0.058 0.062 149 39.3 273.9CLF007 1 20 0.064 0.056 147.4 41.8 264.7CLF008 01,02,03 0 0.031 0.029 0.032 0.028 147.4 38.7 273.5CLF009 none 33 0.120 147.9 39.9 256.4CLF010 1 50 0.016 0.104 148.5 36.7 279.3

The scenarios differ essentially for the asperities number and the % of roughness.

rupture scenario CLF001

REPRODUCING THE COLFIORITO EARTHQUAKE

Target event hypocenter

Asperities

Rupturesurface

COMPARISON IN THE SPECTRA RESPONSE DOMAINREPRODUCING THE COLFIORITO EARTHQUAKE

For each model at each station, synthetic seismograms were calculated, then absolute acceleration response spectra (AAR) and the pseudo velocity response spectra (PSV) were evaluated and compared with the Colfiorito Earthquake response spectra.

FITTING PROCEDURE

REPRODUCING THE COLFIORITO EARTHQUAKE

For evaluating if at least one of the 30 rupture scenarios is able to reproduce the Colfiorito Earthquake, the comparison between real and the synthetic seismograms was carried out on 10 different ground motion parameter: Arias duration, energy duration, Arias intensity, energy integral, peak acceleration, peak velocity, peak displacement, absolute acceleration response, Fourier spectra, and cross-correlation (Anderson, 2003).

For each estimate is given a value of 0 to 10, so that the final score is between 0 and 100, with the latter being a perfect fit.

CLF011 CLF021

Waveforms comparisonREPRODUCING THE COLFIORITO EARTHQUAKE

If the source parameters are relatively well known, the ground motion synthesis methodology, here investigated, is reasonably able to reproduce the rupture process and consequently the real seismogram.

The scoring evaluation provides that the most likely scenarios of what likely occurred during the Colfiorito Earthquake are CLF011 and CLF021

MODEL asperitiesrgh(%) Mo(x1026dyne·cm) mo1 mo2 mo3 stk dp sv

CLF011 01,02 0 0.061 0.018 0.041 147.6 41.1 278.8CLF021 01,02 10 0.079 0.026 0.015 146.8 38.2 265

PREDICTING TOOL

I tried to establish the potential of this empirical Green’s function synthesis approach as a prediction tool in strong ground motion seismology.

Strong Ground Motion “Prediction” Analysis

Models rupture fault parametersdip (dpp) 35º ± 15ºstrike (stkk) 150º ± 20ºRake 270º ± 20ºdepth of hazard surface 2 ± 2 kmhypocentral coordinates free to varywidth hazard surface (dppdis) 11.5 ± 2 kmlength hazard surface (rh11+rh22) rh11=13.0 ± 2 km

rh22=2.0 ± 2 kmrupture surface geometry ellipsemajor axis (aa1) 11.0 ± 5.5 kmminor axis (bb1) 9.50 ± 4.25 kmmin and max displacement 10-80 cmseismic moment (M0) 1.2x1025 dyne·cmrupture velocity (Vr) 0.75-1.0 Vs km/shealing velocity (Vh) 0.8-1.0 Vrslip function Kostrov with healingnumber of asperities 0-7Roughness 0-50%small elements area 0.001 km2

No previous information available on the Colfiorito Earthquake was used in calculating the rupture scenarios.I started from:• a normal fault in Apennine direction (NNW-SSE);• with dip coherent with the range showed by Umbria-Marche normal faults (Barchi et al., 2000),• and fault dimension related with the magnitude of the earthquake to reproduce.

Constructing 100 rupture scenarios

THEN I EVALUATED SYNTHETIC SEISMOGRAMS FOR EACH MODEL AT EACH STATION AND I VERIFIED THAT COLFIORITO EARTHQUAKE FALLS IN BETWEEN THE RANGE PREDICTED.

PREDICTING TOOL

COMPARISON IN THE SPECTRA RESPONSE DOMAIN

Almost all the models are comprised between one standard deviation of the mean for the three stations.ASSI: AAR and PSV fit quite well the Colfiorito shape spectra in all the frequency band. Colfiorito earthquake lies close to the average curve.COLF and NOCR spectra show a quite good fit until 0.3-0.4 s, for lower period the predicted ground motion overestimate the real one.

Number of rupture scenarios

PREDICTING TOOL

The average and its uncertainty start to stabilize after 30 models. The 1-bound decreases from 0.2 after 10 scenarios to 0.06 after 100 scenarios, meaning that the uncertainty is reduced to 30 % of its original value. This plot shows that 100 scenarios are sufficient to span the variability in strong ground motion due to the source uncertainties.

MEAN OF “AAR” AT 1 Hz

For verifying the choice of using just 100 scenarios by randomly varying each parameter, that we assume uniformly distributed over its own allowed range and uncorrelated with the others, I plot the evolution of the AAR mean and one standard deviation as the number of scenarios increases.

RESULTS and CONCLUSIONSThe purpose of this study was to test the ground motion synthesis methodology outlined by Hutchings and Wu (1990) for verifying its capability of being used as a predicting tool in strong ground motion seismology. The validation procedure was carried out on the 26 September 1997, Mw 6.0 Colfiorito Earthquake.

1. The “forward modeling” analysis results demonstrate that this strong ground motion synthesis methodology is a technique capable, once the scenarios are well constrained by independent information, to reproduce reasonably well the observed records;

2. comparing the Colfiorito spectra (AAR and PSV) with spectra calculated from 100 rupture scenarios, constructed without including any knowledge of the source characteristics, emerges that it is possible to make reasonable strong ground motion “predictions” even without having a priori knowledge of the fault characteristics, by running enough models.

THE END!!!!

RESULTS……

SPECTRA RESPONSE DOMAIN COMPARISON • Colfiorito response spectra fall inside the 30 AAR’s and PSV’s calculated at ASSI and COLF, showing the same amplitude of the average calculated for these synthetics;• synthetic spectra at NOCR, on average, overestimate the real ground motion. In the range of periods analyzed here, the latter follows the curve defined by the average minus one standard deviation;SCORING PROCEDURE• the quantitative matching evaluation shows that, in the thirty scenarios tried, two combinations of source parameters give a good fit for all the three stations (Models 011 and 021).

Synthesis of Colfiorito Earthquake

Strong Ground Motion “Prediction” AnalysisSPECTRA RESPONSE DOMAIN COMPARISON•The AAR’s and the PSV’s evaluated for the synthetics waveforms at the ASSI station site, fit quite well the shape of the real strong motion spectra, that lies close to the average in all the frequency band;•The AAR’s and the PSV’s obtained from the NOCR and COLF stations’ recordings fall within the range of ground motion response spectra calculated from the synthetics seismograms until the period of 0.3-0.4 s. For period lower than this threshold, the calculated response spectra overestimate the real ones.

COMPARISON IN THE RESPONSE SPECTRA DOMAIN

REPRODUCING THE COLFIORITO EARTHQUAKE

The RESPONSE SPECTRUM describes the maximum response of a single degree-of-freedom (SDOF) system to a particular input motion as a function of the natural frequency (or natural period) and the damping ratio of the SDOF system.

It’s important to remember that:response spectra reflect strong ground motion characteristics indirectly, since they are filtered by the response of the SDOF structure;

amplitude, frequency content and duration of the input motion all influence the spectral values;

response spectra represent only the maximum responses of a number of different structures.

Larry

PREDICTING THE GROUND MOTION:TWO DIFFERENT POINTS OF VIEW

Laura Scognamiglio

ALMA MATER STUDIORUM Dipartimento di Fisica dell’Università

degli Studi di BolognaDottorato in Geofisica, XVI ciclo

OBJECTIVES

The intention of this dissertation is to look into the empirical and semi-empirical approach for estimating strong ground motion.

The two different methods were investigated for understanding their potentials for being used in the evaluation of the earthquake-induced ground motion:

•Regression analyses on background seismicity•Strong ground motion evaluation with empirical Green’s function

EARTHQUAKE GROUND MOTION ESTIMATION TECNIQUES:

1. Theoretical evaluation

2. Semi-Empirical approach

3. Regression Techniques

Score for 100 models