A test of a physically-based strong ground motion prediction methodology with the 26 September 1997, Mw = 6.0 Colfiorito (Umbria–Marche sequence), Italy earthquake

Tectonophysics 476 (2009) 145–158

Contents lists available at ScienceDirect

Tectonophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t e c t o

A test of a physically-based strong ground motion prediction methodology with the 26 September 1997, Mw = 6.0 Colfiorito (Umbria–Marche sequence), Italy earthquake Laura Scognamiglio a,⁎, Lawrence Hutchings b a b

Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata, 605, 00143 Roma, Italy Lawrence Berkeley National Laboratory, 1 Cyclotron Road, 94025 Berkeley, California, United States

a r t i c l e

i n f o

Article history: Received 18 January 2008 Received in revised form 29 April 2009 Accepted 28 May 2009 Available online 6 June 2009 Keywords: Empirical Green's functions Strong ground motion prediction 1997, Mw 6.0, Umbria–Marche Earthquake Physically-based ground motion synthesis

a b s t r a c t We test the physically-based ground motion hazard prediction methodology of Hutchings et al. [Hutchings, L., Ioannidou, E., Kalogeras, I., Voulgaris, N., Savy, J., Foxall, W., Scognamiglio, L., and Stavrakakis, G., (2007). A physically-based strong ground motion prediction methodology; Application to PSHA and the 1999 M = 6.0 Athens Earthquake. Geophys. J. Int. 168, 569–680.] through an a posteriori prediction of the 26 September 1997, Mw 6.0 Colfiorito (Umbria–Marche, Italy) earthquake at four stations. By “physically-based” we refer to ground motion synthesized with quasi-dynamic rupture models derived from physics and an understanding of the earthquake process. We test five hypotheses proposed by Hutchings et al. [Hutchings, L., Ioannidou, E., Kalogeras, I., Voulgaris, N., Savy, J., Foxall, W., Scognamiglio, L., and Stavrakakis, G., (2007). A physically-based strong ground motion prediction methodology; Application to PSHA and the 1999 M = 6.0 Athens Earthquake. Geophys. J. Int. 168, 569–680.] that support application of the methodology to physically-based probabilistic seismic hazard or risk analysis. We use two methods to test the hypotheses. First, we test whether observed records fall within the 68% lognormal confidence interval for the distribution of absolute acceleration response (AAR), pseudo velocity response (PSV), and Fourier amplitude spectra (FFT) created by a suite of source models. We also used the godness of fit between synthesized seismograms to verify whether at least one of the source models in the suite generates seismograms that match the observed waveforms, and if good fits to seismograms are due to source models that are close to what is actually known about the Colfiorito earthquake. We tested the hypotheses with a range of source parameters proposed by Hutchings et al. [Hutchings, L., Ioannidou, E., Kalogeras, I., Voulgaris, N., Savy, J., Foxall, W., Scognamiglio, L., and Stavrakakis, G., (2007). A physically-based strong ground motion prediction methodology; Application to PSHA and the 1999 M = 6.0 Athens Earthquake. Geophys. J. Int. 168, 569–680.]. We synthesized records from 100 rupture scenarios that were generated by a Monte Carlo selection of parameters within the range. This range was based upon having some prior knowledge of where the earthquake would occur. Observed values of AAR, PSV and FFT fit within the 68% confidence interval for all four stations, and one of the models generated seismograms that had a good fit compared to the observations. Moreover, a strict test for validating a physically-based ground motion hazard prediction methodology is that as more information is known about the source, the uncertainty of the prediction should narrow, but still include the actual ground motion. Then, we tightened the source parameters to be centered about the known parameters for the Colfiorito earthquake, and allowed for less uncertainty in their values. We found this to be true for this test. While the 68% confidence interval narrowed from a factor of ± about 4 to ± about 2 for the distributions, observed values of AAR, PSV and FFT still fit within the distributions for all four stations. Ultimately, we have calculated peak ground velocity (PGV) and peak ground acceleration (PGA) for all the synthetic seismograms obtained from the computed scenarios, and we have found that they are comparable with the actual and with those from the attenuation relation. We conclude that the methodology of Hutchings et al. [Hutchings, L., Ioannidou, E., Kalogeras, I., Voulgaris, N., Savy, J., Foxall, W., Scognamiglio, L., and Stavrakakis, G., (2007). A physically-based strong ground motion prediction methodology; Application to PSHA and the 1999 M = 6.0 Athens Earthquake. Geophys. J. Int. 168, 569–680.] is promising in giving ground motion hazard prediction estimates. © 2009 Elsevier B.V. All rights reserved.

⁎ Corresponding author. Fax: +39 06 51860507. E-mail address: [email protected] (L. Scognamiglio). 0040-1951/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2009.05.024

146

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

1. Introduction

Table 1 Station locations, and relative site geology.

The purpose of this paper is to test the physically-based ground motion prediction methodology of Hutchings (1991, 1994) and further developed by Hutchings et al. (1996, 2007) through an a posteriori ground motion prediction for the 26 September 1997, 09:40 (GMT), Mw 6.0 Colfiorito earthquake in Italy. This is the largest of the Umbria– Marche (Central Italy) main shock sequence (Ekström et al., 1998). The importance of this validation test is that the source parameters of the Colfiorito earthquake have been very well constrained so that, in addition to testing the ground motion prediction capabilities of the methodology, one can also compare synthetic models' source geometry and rupture parameters to what actually occurred, thereby testing the realism of the rupture models used. This is the second time the methodology has been tested on a normal fault earthquake. We perform the validation at the four stations; these are the only stations that had data available for the methodology used here (Fig. 1, and Table 1). Three of the stations are in the near-source range (within 1–2 fault lengths) and should see significant rupture propagation effects, the fourth station (COLF) is possibly in the near-field range and may have some observed effect. The basis of the methodology is to generate a suite of synthesized seismograms from quasi-dynamic rupture models that use measurable or theoretically determined physical parameters that define fault rupture and control resulting ground motion. The basic hypothesis is that if a particular fault segment is identified as capable of having an earthquake of a particular moment, and if sufficient variations of rupture parameters are sampled, then the suite will encompass all possible seismograms that account for significant engineering responses of structures. Expanding it to all faults or source volumes and all moments (and all sites), then provides the basis of a physicallybased probabilistic seismic hazard analysis (PSHA) or risk analysis (PSRA). The advantages of this methodology, if validated, would be that it is source and site specific, provides actual seismograms rather than single parameters, can include ground motion that has not

Station name

Latitude (°)

Longitude (°)

Site geology

NOCR COLF ASSI GUBP

43.1115 43.0370 43.0800 43.3125

12.7846 12.9210 12.6100 12.5888

Rock Soft soil Rock Soft soil

Fig. 1. 26 September 1997 Umbria–Marche sequence mainshock epicenter (black star), aftershocks used to obtain EGFs (circles), and stations for which we conduct the synthesis (triangles). The stations have the same color of the aftershocks recorded. The black line represents the estimated top of fault rupture. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

previously been recorded, and provides a means to reduce uncertainty in ground motion prediction. 2. Methodology hypotheses Hutchings et al. (2007) stated 5 hypotheses that support the basic hypothesis of the methodology that would ensure its functionality: (1) The rupture characteristics of a fault can be constrained in advance by a range of physical parameters. (2) Accurate synthesis of ground motions for a particular fault rupture scenario, sufficient for engineering purposes, is possible from simple rupture models. (3) The range of possible fault rupture scenarios spans the limits of the earthquake process and effectively constrains the range of predictions. (4) The methodology allows one to identify the specific parameters that contribute most to the epistemic variability in the ground motion predictions; therefore, uncertainty can be reduced by further study. Hutchings et al. (2007) further hypothesized that one of the rupture models should generate synthesized seismograms that match those that are observed, and the rupture parameters of that scenario are close to what actually happened. We call this hypothesis (5) below. The first part of this hypothesis is important because it would ensure that the actual ground motion from a future earthquake would be included in any application of the methodology. For example, performance-based design studies, which require a dynamic analysis of a structure to determine acceptable levels of risk, would include the actual ground motion that occurs. It should be noted that here we refer to “actual ground motion” in an engineering sense. We test this with the “Anderson” score, which measures ten characteristics of strong motion that are important for engineered structures. The second part of this hypothesis would give reliability to the rupture model. This has been satisfied in many validations (Hutchings, 1991, 1994; Foxall et al., 1994; Jarpe and Kasameyer, 1996; Hutchings et al., 1996, 2007). Also, if this hypothesis (5) is supported, it gives rise to the use of this methodology as an inversion tool. Here again, it should be pointed out that general characteristics of earthquake rupture are modeled, but we contend that these are sufficient for synthesizing strong motion that have significant characteristics for engineered structures. A strict test for validating a physically-based ground motion prediction methodology is that as more information is known about the source, the uncertainty of the prediction should narrow, but still include the actual ground motion (Hypothesis 4 and 5). This is one of the key reasons for using a physically-based ground motion prediction methodology over an empirically-based methodology, such as using attenuation relations. Attenuation relations have been shown to have aleatory uncertainty that has not been reduced over the past several decades of adding empirical recordings to regression relations (Bommer and Abrahamson, 2005). In this study we test all five supportive hypotheses to the “basic” hypothesis. We first use fairly broad parameters in the way the methodology has previously been applied, and test hypotheses (1), (2), (3), and (5). This would be the case for most earthquakes, which have source parameters that are constrained by general knowledge of

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

147

Table 2 Column 1, source parameters of the 26 September 1997 Umbria–Marche mainshock determined from several authors: aDeschamps et al. (2000); bEkström et al. (1998); cZollo et al. (1999); dPino and Mazza (2000); and Hernandez et al. (2004). Columns 2 and 3, rupture model parameter ranges used in this study. The rupture velocity, Vr, is a percentage of shear velocity. The healing velocity, Vh, is a percentage of rupture velocity. Models fault rupture parameters

Colfiorito earthquake

100 Scenarios loose constraints

23 Scenarios tight constraint

Strike (deg from N) Dip Hypo latitude (N) Hypo longitude (E) Hypo depth (km) Depth to top of rupture (km) Rupture surface geometry Length rupture surface (km) Width rupture surface (km) Displacement range (cm) Moment (Nm) Rupture velocity, Vr (km/s) Healing velocity (Vh) Slip function Number of asperities Type of asperity Roughness Size of elemental areas Slip amplitude distribution

b

144° ± 10° 42° ± 15° 43.030° ± .014° 12.862° ± .015° 5.7 km ± 2.0 0.65 ± .5 Ellipse 12.0 ± 4.0 7.5 ± 4.0 10–100 1.2 (± 0.4) × 1018 0.5–1.0 × Vs 0.8–1.0 × Vr Kostrov 0–4 Hartzell or Kanamori 0–50% 0.001 km2 All possible

144° ± 5° 42° ± 5° 43.030° ± .002° 12.862° ± .003° 5.7 km ± 0.5 0.65 ± .5 Ellipse 12.0 ± 1.0 7.5 ± 1.0 20–50 1.2 × 1018 2.6 ± 0.2 0.8–1.0 × Vr Kostrov 0–2 Hartzell or Kanamori 0–50% 0.001 km2 Hernandez

144° b 42° a 43.03° a 12.862° a 5.7 c 0.65 Rectangle c 12.0 c 7.5 10–100 b 1.2 × 1018 c,d 2.6 NA NA NA NA NA Hernandez

Table 3 EGFs hypocenter coordinates, and source parameters (seismic moment, corner frequency and moment magnitude) obtained from NetMoment. NOCR

Latitude (°N)

Longitude (°E)

Depth (km)

M0 (N–M)

fc (Hz)a

Mw

9804020530 9803250019 9803250456 9803271218 9804010438 9804010450 9804012251 9804020329 9804021040

43.077 43.1150 43.0850 43.1290 43.0270 43.0190 43.1070 43.0720 43.0420

12.881 12.7910 12.8380 12.8330 12.8250 12.8240 12.7510 12.8100 12.8430

11.0 8.0 1.0 11.0 12.0 12.0 8.0 10.0 11.0

9.86E + 12 2.439E + 12 1.058E + 13 2.822E + 12 1.949E + 12 1.714E + 12 1.181E + 12 1.875E + 12 1.423E + 12

15.6 30.7 11.9 13.6 14.4 13.8 12.1 10.9 13.8

2.6 2.2 2.6 2.3 2.2 2.1 2.0 2.1 2.1

COLF

Latitude

Longitude

Depth

M0

fc

Mw

9802261409 9802271108 9803011603 9803040912 9803051358 9803070923 9803040501 9803070915

43.008 43.015 43.015 43.013 43.024 43.046 43.1420 43.0530

12.825 12.808 12.960 12.831 12.834 12.812 12.8220 12.7890

10.1 8.0 5.5 8.0 10.2 9.8 8.7 8.0

3.38E + 13 5.26E + 12 5.27E + 12 4.34E + 13 1.42E + 13 2.88E + 13 1.461E + 12 3.651E + 12

2.2 3.0 15.1 8.4 8.6 6.2 9.9 16.6

3.0 2.4 2.4 3.1 2.7 2.9 2.1 2.3

ASSI

Latitude

Longitude

Depth

M0

fc

Mw

9804030759 9804030820 9804030823 9804031754 9804171107 9805130041 9806011357 9806022311 9806052153 9806250044 9804170230 9805091236 9806011440 9806101957 9806250032 9804032211 9804051604 9804061119 9805210940

43.194 43.211 43.211 43.180 43.116 43.119 43.189 43.189 43.184 43.009 43.183 43.190 43.185 43.184 43.012 43.186 43.187 43.174 43.189

12.744 12.752 12.755 12.754 12.670 12.670 12.771 12.778 12.787 12.826 12.736 12.758 12.767 12.774 12.817 12.754 12.732 12.737 12.754

9.9 9.9 7.0 8.1 11.3 9.6 5.7 10.0 10.0 8.3 13.1 12.8 9.2 9.7 9.9 10.5 11.8 9.8 10.4

3.8 3.6 3.3 3.1 3.2 2.9 3.7 3.9 3.7 3.5 3.2 3.1 3.3 3.4 3.4 3.0 2.9 2.9 3.2

fc

Mw

GUBP

Latitude

Longitude

9709270808 9709260947 9804051552

43.094 43.114 43.195

12.824 12.813 12.756

a

Corner frequencies for station NOCR not used.

3.1 4.3 4.6 2.7 4.7 2.9 2.1 3.8 2.6 3.5 4.9 4.4 2.8 3.5 4.7 4.4 4.4 5.7 4.4 Depth 8.6 2.0 5.4

5.53E + 14 3.03E + 14 1.01E + 14 5.01E + 13 6.38E + 13 2.59E + 13 4.48E + 14 7.60E + 14 4.12E + 14 2.52E + 14 7.37E + 13 5.20E + 13 8.96E + 13 1.60E + 14 1.48E + 14 3.00E + 13 2.82E + 13 2.82E + 13 7.91E + 13 M0 4.3E + 15 1.4E + 16 6.3E + 15

1.8 2.1 1.1

4.3 4.7 4.5

148

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

with all EGF methods, computations are for linear motion. Hutchings et al. (2007) argue that the former approach is mathematically consistent with the elastodynamic equations of seismology and that it allows for a physically-based methodology. 3.2. Empirical Green's functions

Fig. 2. The figure shows an example of the range of possible geometries chosen by program HAZARD from random variations of source parameters within limits listed in Table 2. (A) Model-052 and Model-070 fault geometries obtained from “broad” constraints, while (B) are Model-012 and Model-023 fault geometries obtained tightening the source parameters constraints. The dotted line is the original location of the top of the fault at 0.65 km depth. The black box is the surface projection of the hazard area within which rupture could occur, and the ellipse is the actual rupture area. Black star is the hypocenter. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

earthquakes and some specific knowledge of the causative fault. If we pass this test and the range is functionally narrow, then it suggests that the methodology has good promise for general application. Then, we use a fairly narrow range of rupture parameters determined by previous studies of the Colfiorito earthquake and an estimated uncertainty in their values. We use this to test hypothesis (2), (4) and (5). We conclude with sensitivity tests on important rupture parameters, and examine the epistemic uncertainty (Hypothesis 4).

Empirical Green's functions are used to capture the effect of the free surface, attenuation, refractions, reflections and scattering due to heterogeneities along the propagation path. The advantage of the EGF approach is that the EGFs contain all the information about the propagation path between the EGF source and the recording site. EGFs inherently include linear site response at the site where they are recorded. In this study, EGFs are distributed along the fault for all stations except ASSI, but are not sufficient to cover the entire fault, meaning that all paths are not sampled. Therefore, we interpolate to fill in the fault with EGFs. However, it is our contention that having been recorded at the site of interest and having passed through the general geology of the area, they are the best Green's functions for modeling ground motion. Station ASSI, in particular, is primarily sampling the site response rather than the entire propagation path. These issues are discussed in Hutchings and Wu (1990), Hutchings (1991), and Hutchings et al. (2007). We used EGFs for frequencies of 0.5 to 20.0 Hz. This is the limit allowed by signal-to-noise ratios. We could have used synthetic Green's functions at lower or higher frequencies because all types of Green's functions can be used by EMPSYN. However we consider the frequency range to be sufficient for the purpose of this work. To solve the representation relation used by EMPSYN, the selected EGFs need to have impulsive point sources. Hutchings and Wu (1990) identified a threshold moment of 1.5 × 1014 Nm for the bandwidth of 0.5 to about 20.0 Hz, below which the seismograms have the characteristics of impulsive point sources. This has been true for other studies (Hanks, 1982; Anderson and Hough, 1984) and we assume it is true for this study. If the events used have moments larger than the threshold identified for a point source earthquake, it is possible to utilize seismic moment and corner frequency estimates of the EGFs to deconvolve the source (Brune, 1976) from the recordings to effectively create impulsive point source recordings (Hutchings, 2002; Hutchings et al., 2007). EMPSYN uses these values, obtained with NetMoment, to deconvolve the Brune source spectrum from each recording before being applied to the synthesis. 3.3. Source model

3. Implementing the methodology We use the set of computer programs described by Hutchings et al. (2007) to implement the methodology: we determine source parameters of EGFs (NetMoment), randomly select rupture parameters (HAZARD), synthesize ground motion with empirical Green's functions (EMPSYN), evaluate results (HazStats), and identify best-fitting models (COMPARE). These are discussed in the text when they are applied. 3.1. Synthetic seismograms Synthetic seismograms are generated using empirical Green's functions (EGFs) in the representation relation as developed by Hutchings and Wu (1990). This EGF method has been applied first by Hartzell (1978) and Wu (1978) and has since been further developed by numerous scientists (Kanamori, 1979; Hutchings 1991, 1994; Wald et al., 1993; Jarpe and Kasameyer, 1996; Hartzell et al., 1999). Another approach consists of using the EGFs as sub-events of the target event to be simulated, and computing seismograms by summing EGFs based on the scaling relation between the small and large events (Irikura, 1983, 1986; Joyner and Boore, 1986; Frankel, 1995). See Wossner et al. (2002) for a more complete explanation of both methodologies. As

Germane to the methodology is the quasi-dynamic source model used by EMPSYN. It is a model for the dynamic processes that occur during an earthquake (Hutchings, 1994). By quasi-dynamic we mean source models that are consistent with the elastodynamic equations of seismology and fracture energy and with a physical understanding of how earthquakes rupture. They also are consistent with results from laboratory experiments, numerical modeling, and field observations of earthquake processes (Hutchings et al., 2007). Our assumption is that the parameters of the model are physical and that: 1) understanding them provides insight into the rupture process of the Colfiorito earthquake, or 2) knowing them allows us to model the earthquake. The source rupture parameters necessary for the synthesis include fault rupture area geometry and location, hypocenter, slip function, roughness of the fault surface, rupture and healing velocity, asperity size and number, slip function, and slip vector. In the quasi-dynamic model, rupture begins at the hypocenter and propagates radially at a percentage of the shear-wave velocity. The elemental areas are small enough to model continuous rupture in the frequency band used here. We constrain rupture areas to be elliptical. Slip at each element follows the Kostrov slip function until a healing phase reaches the element from a fault edge; this results in variable rise times and slip amplitudes on the fault due to the

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

149

Fig. 3. Distribution for the one hundred scenarios obtained by using “broad” constraints, as well as those observed from the actual earthquake (red curves). Top: PVR calculated for all models. Middle and bottom: mean and plus and minus one-standard deviation of the distribution of AAR and FFT for all models that includes epistemic and aleatory uncertainty. Note that PSV axes are logarithmic, while for AAR and FFT we preferred linear scale.

location of the element with respect to the hypocenter and the edge of the fault. The Kostrov slip function is implemented in the time domain by a discretized summation of step functions (Hutchings et al., 2007). Asperities are modeled as circular areas with higher slip amplitudes and high stress drop. They do not overlap, and the added slip grades from the value of background rupture at the edge to greatest at the center. Asperities can rupture along the radially propagating rupture front (Hartzell asperity), or they can rupture from the center to their edge starting at the time the rupture front would have reached the center (Kanamori asperity). Rupture roughness is modeled by delaying an element's rupture time so that it finishes slip (rise time) at the same time as neighboring elements. The delay is randomly chosen to be between 0.1 and 0.9% of the original rise time of the element. Areas of roughness have corresponding high stress drop (i.e. the Scholz, 2002, model of contact asperities). Asperities and background elements have the same percentage of elements with roughness. 3.4. Scenario earthquakes Rupture scenarios are created by selecting rupture parameters using the computer program HAZARD. HAZARD randomly selects values from uniform distributions for rupture geometry, hypocenter location, number

and size of asperities, rupture and healing velocity, and rupture roughness. It selects values for strike, dip, and slip vector from triangular distributions centered about preferred values. Rise times, stress drop and energy are dependent variables. Table 2 lists the parameters and their ranges used to test the hypotheses. No correction was made for focal mechanism solution to the EGFs during the syntheses, so the rake of the slip vector was not listed in the table. Focal mechanism solution corrections are discussed in Hutchings and Wu (1990) and Hutchings (1994). 4. Main shock source parameters The 1997–1998, Umbria–Marche seismic sequence was characterized by six earthquakes with magnitudes larger than 5.0 (Amato et al., 1998; Ekström et al., 1998), and thousands of smaller shocks (Deschamps et al., 2000; Chiaraluce et al., 2003). This sequence has been intensively investigated. Ekström et al. (1998) calculated the CMT fault plane solutions of the 13 largest events, and the results mainly indicate normal-style faulting on NW–SE striking fault planes with tension axes oriented in the range 40°–60°. Pino et al. (1999) and Pino and Mazza (2000) used regional broad-band seismograms to constrain the rupture directivity for the two largest shocks of September 26; they found that the first one (Mw 5.7) occurred at

150

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

Fig. 4. Variability of AAR at 0.2 s and 1.0 s as a function of number of models. We plot the mean and plus/minus one-standard deviation of the mean.

00:33 (GMT) and ruptured toward the SE on a SW dipping normal fault, while the second one (Mw 6.0) occurred at 09:40 (GMT) and broke toward the NW on another SW dipping fault segment. Zollo et al. (1999) modeled strong motion data at near-source distances (within 30 km) to investigate the details of the seismic sources of the two main events. The slip distribution during the three largest shocks was investigated through a forward modeling of GPS measurements (Hunstad et al., 1999), by GPS and DInSAR data (Salvi et al., 2000), and by the inversion of geodetic data (GPS and DInSAR) and strong motion seismograms (Hernandez et al., 2004). The source parameters we used for the a posteriori prediction of the Colfiorito earthquake ground motion are listed in Table 2. The references for each parameter are listed in the table.

5. Data For our test, we used aftershocks that occurred during the Umbria– Marche sequence and were recorded at the locations of four strong motion stations: COLF, NOCR, ASSI, and GUBP (Fig. 1). These

aftershocks are located along or close to the fault associated with the main event, except those for station ASSI, which recorded most of the EGFs from events located about 5 km northwest of the fault (blue circles in Fig. 1). The two data characteristics, being associated with the same fault and recorded at the same location as the main shock, are the basic advantage of empirical Green's functions. When events are not located on the fault of interest, but recorded by the station for the synthesis, one still has the advantage of capturing the site geologic effects. We used the program NetMoment (Hutchings, 2002; Gök et al., 2009) to calculate moments of source events for EGFs recorded at stations COLF, NOCR, and ASSI. We obtained moment values of events recorded at station GUBP from regional studies. Site response has previously been determined for three of the four selected sites: COLF (Di Giulio et al., 2002), NOCR (Cultrera et al., 2003), and ASSI (Bindi et al., 2004.) We deconvolved these responses from the recorded seismograms before calculating moment and the Brune (1971) source spectra at these sites. We did not remove the site response from station GUBP because that was not available. NetMoment carries out a signal-to-noise analysis and it only finds a solution over the frequency band that exceeds the specified signal-to-noise threshold value. We used 10 s of coda following the initial S-wave and required a signal-to-noise ratio (SNR) of 10:1. It resulted in a good SNR from at least 0.5 to 20.0 Hz for the events listed in Table 3. Geometrical spreading is modeled simply as to be equal to 1/r (Malagnini et al., 2000), and whole path Q was solved for in the inversion. Due to the lack of small aftershocks recorded by station GUBP, we used large aftershocks as EGFs. These events had magnitudes 4.3, 4.5, and 4.7. Gök et al. (2009) concluded that finite source effects were present in events with magnitudes greater than 4.2 when recorded nearby. Therefore, there may be some error introduced by deconvolving the source with a Brune (1971) source model to obtain effective EGFs. Table 3 lists locations, moments and source corner frequencies calculated for events used to obtain EGFs. The seismic moment calculated for the events recorded by station NOCR are close to those calculated for the same events by Cultrera et al. (2003). There were no previous analyses available for moments and corner frequencies of the events recorded by stations ASSI and COLF. 6. Testing the methodology We use two methods to test our hypotheses. First, we compare the distribution of absolute acceleration response (AAR), pseudo velocity response (PSV), and Fourier amplitude spectra (FFT) from the scenario earthquakes to those calculated from the recorded strong motion. We plot the plus and minus log-normal one-standard deviation prediction values (68% confidence interval) and observe whether these encompass the actual values from the Colfiorito earthquake. Second, we estimate the quality of the fit between synthesized seismograms from each scenario earthquake and the observed records. We test whether we generate seismograms that match the recorded waveforms, and if

Table 4 (a) Best-fitting models from broadly constrained rupture parameters and (b) best-fitting models from tightly constrained rupture parameters. Model (a) CLF089 CLF101 CLF106 (b) CLF002 CLF032

Anderson score

Asperities and type

Rgh

Hypocenter latitude

longitude

depth

M0

Vr

Vh

Strike

Dip

60 62 60

1 Hartzell 2 Kanamori 1 Hartzell

20 10 0

43.051 43.094 43.050

12.837 12.818 12.847

7.8 3.9 6.3

1.13 0.99 1.30

0.93 0.85 0.82

0.99 0.80 0.86

139° 148° 151°

50° 36° 49°

61 65

2 Kanamori 1 Kanamori

50 20

43.031 43.029

12.864 12.860

5.5 5.4

1.20 1.20

2.62 2.59

0.97 0.91

142° 145°

41° 39°

Rgh states for roughness (%), M0 is the seismic moment (Nm), Vr is the rupture velocity (% of shear-wave velocity) while Vh is the healing velocity (% of Vr).

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

151

Fig. 5. Comparison between Colfiorito earthquake waveforms and the synthetic waveforms resulting from a source model that gives an Anderson score of 60. (A) East–west components of acceleration seismograms from model CLF106 and the mainshock. Data are band-passed between 0.5 and 20.0 Hz. Records are not clipped, but the scale is made small enough to see detail on lower amplitude recordings. (B) Fourier spectra. Those from the observed records are in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

“good” fits to seismograms are due to source models that are close to what is actually known about the Colfiorito earthquake. Following the methodology presented by Anderson (2003), we used the program COMPARE to make this calculation (Appendix A). COMPARE gives a score of up to 100 on comparison between seismograms. Anderson finds that 40 to 60 represents a “fair” fit, 60 to 80 a “good” fit, and 80 to 100 an “excellent” fit. 6.1. Prediction of ground motion for the Colfiorito earthquake with broadly constrained variables In order to examine the possibility of using this methodology as a ground motion prediction tool, we synthesized 100 rupture models that might have been considered prior to the occurrence of the Colfiorito earthquake. Parameters were randomly chosen within ranges that have typically been applied for this methodology (references above). In this case we also allowed the moment to vary

by ±33% to account for uncertainty in calculating the moment of the actual earthquake. These ranges are shown in Table 2. Fig. 2A shows two fault geometries that were randomly chosen. Program HAZARD started with the dotted line as the preferred location of the top of the fault. HAZARD then randomly chose a strike, dip, depth to top of fault and size of the fault (hazard area) within the acceptable range (black box). Then, within this hazard area, the program randomly chose the rupture area (ellipse), hypocenter (star), along with other rupture parameters listed in Table 2. Program EMPSYN was then run to generate the seismograms from one hundred different combinations of parameters. Fig. 3 shows the distribution of PSV, AAR and FFT obtained from the one hundred scenarios as well as those observed from the actual earthquake (red curve). This distribution is considered modeling error in the prediction due to the uncertainty of not knowing which actual event will occur. We also include uncertainties in parameter estimation as part of the calculation for the one-standard deviation

152

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

Fig. 6. Comparison between Colfiorito earthquake waveforms and the synthetic waveforms resulting from a source model that gives an Anderson score of 37. Details are the same as for Fig. 5.

values shown (Hutchings et al., 2007). The plots for the AAR and FFT only show the plus and minus standard deviation values of the computed scenarios. Fig. 4 shows the average values of AAR at 0.2 and 1.0 s and their standard error as a function of the number of models. This demonstrates that the variability of ground motion predictions stabilized after about 50 scenarios. We also computed the distribution from a second set of 100 scenarios and found the same results, furthering our confidence that we have allowed for the full variability of the parameters. We observe that actual records are within or at the limits of the plus and minus log-normal 68% confidence interval from the 100 scenarios at all the stations, and virtually all periods (or frequencies). We call this a success in predicting the range of possible ground motion from this earthquake (Hypothesis 1 and 3), although this test is somewhat subjective. We are only comparing at the 68% confidence level and if we are just below or just above this level it shouldn't mean we pass or fail. If we had designed a structure to withstand a ground motion with 16% chance of exceedence (i.e. greater than the 68% confidence interval), then we would have successfully designed for the Colfiorito earthquake. We note that the shapes of the PSV, AAR and FFT curves of the one hundred scenarios generally match those

observed at all four stations over all periods, except at station NOCR and periods above 0.6 s at ASSI. We also test whether one of these scenarios provides a good match to observed seismograms, Hypothesis (5). We used program COMPARE to find a “family” of scenario earthquakes that give good matches to observed seismograms. Three models had “good” fits to the observed seismograms by the Anderson (2003) score (i.e. values of 60 or better). The parameters for these models are listed in Table 4a while Fig. 5 shows, for model CLF106, the comparison between real and synthetic waveforms (Fig. 5A) and spectra (Fig. 5B). We observe that the shape of the coda and overall amplitudes agree quite well, so that at least one of the family of seismograms synthesized matches what actually occurred. This satisfies the first part of Hypothesis (5). This is important because it allows the use of the methodology for risk-based design using dynamic structure models. Fig. 6A,B shows seismograms and Fourier amplitude spectra for a model that gives the worst fit (CLF083) in order to give an idea of the differences between different Anderson scores. Examining Table 4a there is no apparent distinction among the models that give good fits, and none of these match what actually occurred (Table 2). This demonstrates that the good fits are not unique

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

153

Fig. 7. The distribution for the twenty-three scenarios using “tight” constraints, as well as those observed from the actual earthquake (red curves). Top, PVR calculated for all models. Middle and bottom: mean and plus and minus standard deviation of the distribution of AAR and FFT for all models that includes epistemic and aleatory uncertainty.

and suggest that the synthesis approach may not be ideal as a source inversion application. Perhaps an inversion test should include a more extensive search of parameter space to find a superior family of models that are close to what actually occurred. It should be noted that for engineering purposes our intent is that at least one of the synthesized models produce seismograms consistent with what actually occurred. This has a greater relevance than finding the particular rupture model that actually occurred.

6.2. Calculation of ground motion for the Colfiorito earthquake with “tight” constrained variables In our next test we fixed parameters for the Colfiorito earthquake to be close to those identified by independent researchers, but we let other parameters that have not been identified to vary within a prescribed range. Parameters not constrained by previous studies include rise time (rupture healing), number of asperities, roughness, and slip function. However, we confined the slip distributions to be similar to that found by Hernandez et al. (2004). We calculated 23 scenarios with the parameters randomly chosen within the ranges shown in Table 2. Fig. 2B shows two examples of fault area and hypocenter from “tight” constraints, as described above. The slip

distributions we have chosen allow a wide amount of variation that could account for this uncertainty. As for the loose constraints synthesis we calculate PSV, AAR and FFT from the twenty-three scenarios as described in Table 2 (Fig. 7), and we plot the average AAR at 0.2 and 1.0 Hz as a function of number of scenarios (Fig. 8). The last one shows that the variability has stabilized after about 12 runs. We observe that actual records are within or at the limits of the plus and minus log-normal 68% confidence interval from the 23 scenarios at all the stations, and virtually all periods (or frequencies). We call this a success in predicting the range of possible ground motion from this earthquake with tight constraints. We also note that the shapes of the PSV, AAR and FFT curves of the twenty-three scenarios generally match those of the observed at all four stations over all periods, except at station NOCR and periods above 0.6 s at ASSI. We observe that the distribution of PSV (modeling error) single standard deviation narrowed from a factor of 3.8 when the standard deviation is determined from all stations over all periods (Fig. 3), to 2.3 when the distribution of fault rupture parameters was narrowed, and still the actual records are within distribution. The plus and minus one sigma lines for AAR and FFT, which include the same random errors as described above, encompass the observed values. These observations satisfy Hypothesis (4).

154

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

1.67, 1.37, 1.37, and 1.38, respectively. Since, the rupture model is quasidynamic, changing these parameters also changes some others. For example changing rupture velocity and healing velocity changes the rise times and the slip distribution. Changing the hypocentral location also changes the rise times and slip distribution. Changing the strike, dip, and roughness do not change other parameters. Changing the number of asperities basically allows more moment to be distributed among the reaming asperities and therefore changes the amplitudes, but doesn't change the distribution. We observe that each of the variables examined for parameter sensitivity causes similar variation in ground motions near about a factor of about 1.5 for the modeling error. However, the total sum of the effects is not linear, that is the full distribution (Fig. 3) (about a factor of 4) is not a linear sum of the uncertainty from the individual parameters. Therefore these parameters have an offsetting, nonlinear relationship, when used together for a particular rupture model. 8. Peak ground motion comparison

Fig. 8. Variability of AAR at 0.2 and 1.0 s as a function of number of models. Mean and plus/minus one-standard deviation of the mean is shown.

We have calculated peak ground velocity (PGV) and peak ground acceleration (PGA) for all the synthetic seismograms obtained from the computed scenarios. The resulting peaks have been compared at the four stations with PGV and PGA deriving from the mainshock, and with the attenuation law proposed, for the studied region, by Malagnini et al. (2008). The synthesis of this comparison is displayed in the four panels of Fig. 11, where black triangles are for recorded peaks, solid lines are the attenuation law (average ± σ), while in red and in green the ground motion prediction for loose and tight constrained rupture scenarios respectively (average with 84% confidence interval). For this case, the proposed methodology provides ground motion estimates comparable (PGA at NOCR and ASSI stations) or even more realistic (PGV for all stations) than those from the attenuation relation for the examined region. 9. Discussion and conclusions

We also test whether one of these scenarios provides a good match to observed seismograms (Hypotheses 2 and 5). Hypothesis 2 is tested because presumably we are using rupture models that are close to what actually occurred. We used program COMPARE to find a “family” of scenario earthquakes that gave good matches to observed seismograms. We found two models that attained Anderson scores of 60 or better. The parameters for these models are listed in Table 4b. Fig. 9A,B shows seismograms and Fourier amplitude spectra for the best-fitting model with Anderson score of 65 (CLF032). We observe that the shape of the coda and overall amplitudes agree quite well, and the seismograms have a better fit with respect to those obtained by the “broad” constraints. This suggests that there were no sufficient “broad” constraint models to include the actual model. Moreover, with the rupture parameters centered around what we think actually occurred, we didn't find a fit that had an “excellent” score (80 or more) by the Anderson test. This may also suggest that we did not try enough models, or that the synthesis approach has accuracy limitations due to the models' simplicity (Hypothesis 2). With a score of 65, we argue that we weakly support Hypotheses 2 and both parts of Hypothesis 5. 7. Parameter sensitivity Here we examine the sensitivity of several rupture parameters: rupture and healing velocity, hypocenter location, asperities, strike, dip, and roughness. Fig. 10 shows distributions of AAR when only one of these parameters is allowed to vary, and the computation is for station COLF. The one-standard deviation factor time the average of the scatter for AAR averaged between 0.5 and 20 Hz is ±1.34, 1.69,

We have tested the hypotheses proposed by Hutchings et al. (2007) for prediction of ground motion. The basic premise of the methodology tested is that if a particular fault segment is identified as capable of having an earthquake of a particular moment, and if sufficient variations of rupture parameters are sampled, then the suite of synthesized seismograms would encompass all possible seismograms, in an engineering sense, that could occur from an earthquake of that moment along that fault segment. Expanding it to all faults or source volumes and all moments, then provides the basis of a physically-based probabilistic hazard analysis (PSHA) and probabilistic risk analysis (PSRA). There are five ancillary hypotheses that support this basic hypothesis (numbered 1 through 5 in the Introduction, and referred to here by their number). We used the Colfiorito earthquake to test these hypotheses because it has been extensively studied, and much is known about the earthquake and its rupture process. We first tested hypotheses (3) and (5) with a range of source parameters proposed by Hutchings et al. (2007). We synthesized records from 100 rupture scenarios that were generated by a Monte Carlo selection of parameters within the range. Observed values of AAR, PSV and FFT fit within the 68% confidence interval for all four stations. Therefore, the hypotheses were supported. The shapes of the PSV, AAR and FFT curves of the one hundred scenarios match those of the all four stations over all periods, except at station NOCR, and at station ASSI for periods above 0.6 s. It is not clear why this occurs; NOCR is a rock site so its results are not likely due to non-linearity. The distribution of the prediction is a factor of about 3 and this is essentially that used by empirical attenuation relations, so

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

155

Fig. 9. Example of a good fitting model with Anderson score of 65. (A) East–west components of acceleration seismograms from model CLF106 and the mainshock. Data are bandpassed between 0.5 and 20.0 Hz. Records are not clipped, but the scale is made small enough to see detail on lower amplitude recordings. (B) Fourier spectra. Those from the observed records are in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

we also pass the test that the one-standard deviation values are functionally constrained. Therefore we call this a success in the ability to predict the ground motion at these sites within a one-standard deviation value. We also examined whether the best-fitting models were also similar to those of the actual earthquakes. This would indicate the potential to use the method as a forward calculation in inversion scheme. The best-fitting models were significantly different from each other and not necessarily close to what is thought to have actually occurred. It demonstrates that the good fits are not unique and suggest that the synthesis approach may not be ideal as a source inversion application. Two of the stations could be considered near-source stations (NOCR and COLF), at distances of about 5 and 1 km from the fault, respectively. The syntheses at station COLF were very good and those at station NOCR were the only ones that did not have good matches. This suggests that the methodology works for near-source stations, even if the reason for lack-of-fit at NOCR is not well understood. A strict test for validating a physically-based ground motion hazard prediction methodology is that as more information is known about

the source, the uncertainty of the prediction should narrow, but still include the actual ground motion (fifth hypothesis). So, we tightened the parameters so that they were centered about the known parameters for the Colfiorito earthquake. However, we allowed for some uncertainty in their values. We found true the assumption made. While the 68% confidence interval narrowed from a factor of about 4 to 2 for the distributions, observed values of AAR, PSV and FFT fit within the distributions for all four stations. We conclude that the methodology of Hutchings et al. (2007) is validated with this data set. If we had designed a structure to withstand a ground motion with 16% chance of exceedence (i.e. greater than the 68% confidence interval), then we would have successfully designed for the Colfiorito earthquake.

Acknowledgments We are grateful to two anonymous reviewers who provided a through review and good suggestions. We appreciate the support from the Istituto Nazionale di Geofisica e Vulcanologia,

156

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

Fig. 10. Distributions of AAR when only one parameter is allowed to vary. The parameter varied is labeled on top of each plot.

Fig. 11. Black triangles are peak ground velocity and peak ground acceleration computed for the 26 September 1997, Mw = 6.0, earthquake. Red and green triangles in panels A and B are the ground motion prediction from the loose and tight constrained rupture scenarios respectively (average with 84% confidence interval). Solid lines are the Malagnini et al. (2008) attenuation law (average ± σ). Star and green circles in panels C and D are PGA and PGV for the two models giving the higher Anderson score.

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

Roma, Italy and Lawrence Berkeley National Laboratory, Berkeley, California.

The computer program COMPARE estimates the fit between observed and synthesized seismograms. It utilizes ten ground motion parameters calculated for five frequency bands, and averages the resulting quantities over all the stations. Each scenario earthquake gets a total score of 0 to 100 (a value of 0 to 10 for each parameter calculated) to rate how well it generates seismograms that match the observed records. Due to the complexity of earthquake ground motions, identification of a single parameter that accurately describes all important ground motion characteristics is regarded as impossible (Joyner and Boore, 1986). This procedure follows the approach outlined by Anderson (2003), with some modifications. The chosen parameters are: normalized cross-correlation, peak acceleration, peak velocity, peak displacement, Arias intensity, energy integral, Arias duration, absolute acceleration response (AAR), and Fourier amplitude spectra (FFT). The frequency bands analyzed are: 0.5–2 Hz, 2–5 Hz, 5–15 Hz, 15–20 Hz, and 0.5– 20 Hz, except for AAR and FFT, for which the whole spectra is used for one calculation. With the exception of cross-correlation, the fit between observed and synthesized records is calculated from the function:

A=e

− Z2

;Z =

BO − BS MIN ðBO ; BS Þ

Arias intensity (Arias, 1970) is defined as: Ia =

Appendix A. Anderson COMPARE procedure

ðA1Þ

π 2g

Z

CCOS CC = pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ACO ACS

ðA2Þ

CC and AC are cross-correlation and auto-correlation, respectively, and subscripts o and s refer to observed and synthesized records. CCOS is the absolute value of the cross-correlations, since it can be negative. CC has a value between 0 and 1 for each record pair, but this is normalized to have a total value of between 0 and 10 for all components and stations, for each scenario. Peak acceleration, peak velocity and peak displacement are the absolute maximum values of each component.

2

aðt Þ dt

ðA3Þ

where Ia is the Arias Intensity in units of length per time, a(t) is the acceleration-time history, g is acceleration due to gravity, and the integral is over the complete duration of the accelerogram. R 2 Energy integral : E = vðt Þ dt

ðA4Þ

where, v(t) is the velocity time history, the integral is over the complete duration of the time history, and is proportional to the energy, R Arias duration : Da =

2

aðt Þ dt amax

ðA5Þ

where amax is the maximum value of the integrated signal, and the integral is calculated over the full time history. R Energy duration : Ed =

vðt Þ2 dt vmax

ðA6Þ

where vmax is the maximum value of the integrated signal, and the integral is performed over the full time history.   − Z3 Absolute acceleration response : A = AVG e where, Z =

where, Bo is the observed and Bs is the synthesized value of the parameter to be evaluated. The records to be compared are first aligned by a time lag that maximizes their cross-correlation value, without filtering. This eliminates differences due to unknown origin times. Anderson (2003) points out that Eq. (A1) has several advantageous features. First, it monotonically decreases as the difference between the parameters increases. Second, it is symmetrical, in that it gives the same score regardless of whether the Bo or Bs has the larger value. Third, small differences are not penalized too severely. When the difference is only half the value of the parameter itself, the score is about 8 or larger, out of a peak of 10. On the other hand, it is not sensitive to differences of more than a factor of 2.5; improving the fit from a difference of a factor of 10 to a difference of only a factor of 3 does not yield a significant improvement in the score. This reflects a certain judgment that differences greater than a factor of 2 or 3 should not be considered useful fits for engineering applications. Details on the ground motion parameters calculated are described here: Cross-correlation is performed on velocity waveforms and the normalized cross-correlation is calculated as:

157

ðA7Þ

AARO − AARS MINðAARO ;AARS Þ

and AARo and AARs are the absolute acceleration response of the observed and calculated, respectively for periods from 0.5 to 5.0. Fourier amplitude spectra: The Anderson score for the Fourier amplitude spectra is calculated in the same way as the absolute acceleration response, but then calculation is over the entire spectrum from lowest to the highest frequency of the five frequency bands, i.e. 0.5 to 20.0 Hz. References Amato, A., et al., 1998. The 1997 Umbria–Marche, Italy, earthquake sequence: a first look at the main shocks and aftershocks. Geophys. Res. Lett. 25, 2861–2864. Anderson, J.G., 2003. Quantitative measure of the goodness of fit of synthetic accelerograms, presented at 13th World Conference on Earthquake Engineering, Vancouver, B. C., Canada, August 1–6, 2004, Paper N.243. Anderson, J.G., Hough, S., 1984. A model for the shape of the Fourier amplitude spectra of accelerograms at high frequencies. Bull. Seismol. Soc. Am. 74, 1969–1994. Arias, A., 1970. A measure of earthquake intensity. In: Hansen, R.J. (Ed.), Seismic Design for Nuclear Power Plant. InMIT Press, Cambridge, Massachussets, pp. 438–483. Bindi, D., Castro, R.R., Franceschina, G., Luzi, L., Pacor, F., 2004. The 1997–1998 Umbria– Marche sequence (central Italy): source, path and site effects estimated from strong motion data recorded in the epicentral area. J. Geophys. Res. 109, B04312. doi:10.1029/ 2003JB002857. Bommer, Abrahamson, 2005. Probability and uncertainty in seismic hazard analysis. Earthq. Spectra 21 (2), 603–607. Brune, J.N., 1971. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75, 4997–5010 (Correction, J. Geophys. Res. 76(20), 5002, 1972). Brune, J.N., 1976. The physics of earthquake strong motion. In: Lomnitz, C., Rosenblueth, E. (Eds.), Seismic Risk and Engineering Decisions. Elsevier Sci, Publ. Co., New York, pp. 141–177. Chiaraluce, L., Ellsworth, W.L., Chiarabba, C., Cocco, M., 2003. Imaging the complexity of an active normal fault system: the 1997 Colfiorito (central Italy) case study. J. Geophys. Res. 108. doi:10.1029/2002JB002166. Cultrera, G., Rovelli, A., Mele, G., Azzara, R., Caserta, A., Marra, F., 2003. Azimuthdependent amplification of weak and strong motions within a fault zone (Nocera Umbra, central Italy). J. Geophys. Res. 108 (B3), 2156. doi:10.1029/2002JB0011929. Deschamps, A., Courboulex, F., Gaffet, S., Lomax, A., Virieux, J., Amato, A., Azzara, A., Castello, B., Chiarabba, C., Cimini, G.B., Cocco, M., Di Bona, M., Margheriti, L., Mele, F., Selvaggi, G., Chiaraluce, L., Piccinini, D., Ripete, M., 2000. Spatio-temporal distribution of seismic activity during the Umbria–Marche crisis, 1997. J. Seismol. 4, 377–386. doi:10.1023/ A:1026568419411.

158

L. Scognamiglio, L. Hutchings / Tectonophysics 476 (2009) 145–158

Di Giulio, G., Cara, F., Azzara, R.M., Lenti, L., Rovelli, A., 2002. Seismic hazard increase in intermontane basin: the case study of Colfiorito, central Italy. EOS Trans. AGU 83 (47) (abstract S71B-1076). Ekström, G., Morelli, A., Boschi, E., Dziewonskim, A., 1998. Moment tensor analysis of the central Italy earthquake sequence of September–October 1997. Geophys. Res. Lett. 25, 1971–1974. Foxall, W., Hutchings, L., Kasameyer, P., 1994. Lithological and rheological constraints on fault rupture scenarios for ground motion hazard prediction. IUTM Symp. Mechanic Problems in Geodynamics, September 5–9, 1995, Beijing, China. InLawrence Livermore National Laboratory, Livermore, CA. UCRL-JC-116437. Frankel, A., 1995. Simulating strong motions of large earthquakes using recordings of small earthquakes — the Loma Prieta mainshock as a test-case. Bull. Seismol. Soc. Am. 85 (4), 1144–1160. Gök, R., Hutchings, L., Mayeda, K. and Kalafat, D. (2009). Source parameters for 1999 North Anatolian Fault Zone aftershocks. Accepted, Pure and Applied Geophysics. Hanks, T.C., 1982. fmax. Bull. Seismol. Soc. Am. 72, 1867–1879. Hartzell, S.H., 1978. Earthquake aftershocks as Green's functions. Geophys. Res. Lett. 1, 1–4. Hartzell, Stephen, Harmsen, S., Frankel, A., Larsen, S., 1999. Calculation of broadband time histories of ground motion: comparison of methods and validation using strongground motion from the 1994 Northridge Earthquake. Bull. Seismol. Soc. Am. 89, 1484–1504. Hernandez, B., Cocco, M., Cotton, F., Stramondo, S., Scotti, O., Courboulex, F., Campillo, M., 2004. Rupture history of the 1997 Umbria–Marche (Central Italy) main shocks from the inversion of GPS, DInSar and near field strong motion data. Ann. Geophys. 47 (N 4), 1355–1376. Hunstad, I., Anzidei, M., Cocco, M., Baldi, P., Galvani, A., Pesci, A., 1999. Modeling coseismic displacements during the 1997 Umbria–Marche earthquake. Geophys. J. Int. 139, 283–295. Hutchings, L., 1991. “Prediction” of strong ground motion for the 1989 Loma Prieta earthquake using empirical Green's functions. Bull. Seismol. Soc. Am. 81, 88–121. Hutchings, L., 1994. Kinematic earthquake models and synthesized ground motion using empirical Green's functions. Bull. Seismol. Soc. Am. 84, 1028–1050. Hutchings, L., 2002. Program NetMoment, a simultaneous inversion for moment, source corner frequency, and site specific t*. Lawrence Livermore National Laboratory. UCRL-ID 135693. Hutchings, L., Wu, F., 1990. Empirical Green's functions from small earthquakes' waveform study of locally recorded aftershocks of the San Fernando earthquake. J. Geophys. Res. 95, 1187–1214. Hutchings, L.J., Jarpe, S.P., Kasameyer, P.W., Foxall, W., 1996. Synthetic strong ground motions for engineering design utilizing empirical Green's functions. Proceedings Fourth Caltrans Seismic Research Workshop, pp. 24; Eleventh World Conference of Earthquake Engineering, Acapulco, June 23–28, 1996 (CDROM Elsevier). LLNL, UCRL-JC-123762.

Hutchings, L., Ioannidou, E., Kalogeras, I., Voulgaris, N., Savy, J., Foxall, W., Scognamiglio, L., Stavrakakis, G., 2007. A physically-based strong ground-motion prediction methodology; application to PSHA and the 1999 M = 6.0 Athens earthquake. Geophys. J. Int.168, 569–680. Irikura, K., 1983. Semi-empirical estimation of strong ground motions during large earthquakes. Bull. Disaster Prev. Res. Inst., Kyoto Univ. 33, 63–104. Irikura, K., 1986. Prediction of strong acceleration motions using empirical Green's function. Proc.7th Japan Conf. Earthquake Engineering, pp. 151–156. Jarpe, S.J., Kasameyer, P.K., 1996. Validation of a methodology for predicting broadband strong motion time histories using kinematic rupture models and empirical Green's functions. Bull. Seismol. Soc. Am. 86, 1116–1129. Joyner, W.B., Boore, D.M., 1986. On simulating large earthquakes by Green's function addition of smaller earthquakes. In: Das, S., Boatwright, J., Schultz, C. (Eds.), Proceedings of the Fifth Maurice Ewing Symposium on Earthquake Source Mechanics. American Geophysical Union, pp. 269–274. Kanamori, H., 1979. A semi-empirical approach to prediction of long-period ground motions from great earthquake. Bull. Seismol. Soc. Am. 69, 1645–1670. Malagnini, L., Hermann, R.B., Di Bona, M., 2000. Ground motion scaling in the Apennines (Italy). Bull. Seismol. Soc. Am. 90, 1062–1081. Malagnini, L., Scognamiglio, L., Mercuri, A., Akynci, A., Mayeda, K., 2008. Strong evidence for non-similar earthquake source scaling in central Italy. Geophys. Res. Lett. 35, L17303. doi:10.1029/2008GL034310. Pino, N.A., Mazza, S., 2000. The Umbria–Marche (central Italy) earthquakes: relation between rupture directivity and sequence evolution for the Mw N 5 shocks. J. Seismol. 4, 451–461 (Special Issue). Pino, N.A., Mazza, S., Boschi, E., 1999. Rupture directivity of the major shocks in the 1997 Umbria–Marche (central Italy) sequence from regional broadband waveforms. Geophys. Res. Lett. 26, 2101–2104. Salvi, S., Stramondo, S., Cocco, M., Tesauro, M., Hunstad, I., Anzidei, M., Briole, P., Baldi, P., Sansosti, E., Fornaro, G., Lanari, R., Doumaz, F., Pesci, A., Galvani, A., 2000. Modeling coseismic displacements resulting from SAR interferometry and GPS measurements during the 1997 Umbria–Marche seismic sequence. J. Seismol. 4, 479–499. Scholz, C.H., 2002. The Mechanics of Earthquake and Faulting. InCambridge University Press, New York, NW, p. 471. Wald, D.J., Kanamori, Helmberger, Donald V., Heaton, T.H., 1993. Source study of the 1906 San Francisco earthquake. Bull. Seismol. Soc. Am. 83, 981–1019. Wossner, J., Treml, M., Wenzel, F., 2002. Simulation of M –W = 6.0 earthquakes in the Upper Rhinegraben using empirical Green functions. Geophys. J. Int. 151 (2), 487–500. Wu, F.T., 1978. Prediction of strong ground motion using small earthquakes. Proc. 2nd Int. Microzonation Conf. San Francisco, pp. 701–704. Zollo, A., Mariucci, S., Milana, G., Capuano, P., 1999. The Umbria–Marche 1997 (central Italy) earthquake sequence: insight on the mainshock rupture from near source strong motion records. Geophys. Res. Lett. 26, 3165–3169.