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Prediction of High-Frequency Ground Motion Parameters Based on Weak Motion Data

The study of earthquakes combines science, technology and expertise in infrastructure and engineering in an effort to minimize human and material losses when their occurrence is inevitable. This book is devoted to various aspects of earthquake research and analysis, from theoretical advances to practical applications. Different sections are dedicated to ground motion studies and seismic site characterization, with regard to mitigation of the risk from earthquake and ensuring the safety of the buildings under earthquake loading. The ultimate goal of the book is to encourage discussions and future research to improve hazard assessments, dissemination of earthquake engineering data and, ultimately, the seismic provisions of building codes.


Introduction
Large earthquakes that have occurred in recent years in densely populated areas of the world (e.g. Izmit, Turkey, 17 August 1999;Duzce, Turkey, 12 November 1999;Chi-Chi, Taiwan 20 September 1999, Bhuj, India, 26 January 2001Sumatra 26 December 2004;Wenchuan, China, May 12, 2008;L'Aquila, Italy, April 6, 2009; Haiti, January 2010 Turkey 2011) have dramatically highlighted the inadequacy of a massive portion of the buildings erected in and around the epicentral areas. For example, the Izmit event was particularly destructive because a large number of buildings were unable to withstand even moderate levels of ground shaking, demonstrating poor construction criteria and, more generally, the inadequacy of the application of building codes for the region. During the L'Aquila earthquake (April, 06, 2009;Mw=6.3) about 300 persons were killed and over 65,000 were left homeless . It was the deadliest Italian earthquake since the 1980, Irpinia earthquake, and initial estimates place the total economic loss at over several billion Euros. Many studies have already been carried out describing the rupture process and the characteristics of local site effects for this earthquake (e.g. D' Amico et al., 2010a;Akinci et al., 2010). It has been observed that many houses were unable to withstand the ground shaking. Building earthquake-resistant structures and retrofitting old buildings on a national scale may be extremely costly and may represent an economic challenge even for developed western countries, but it is still a very important issue (Rapolla et al., 2008). Planning and design should be based on available national hazard maps, which, in turn, must be produced after a careful calibration of ground motion predictive relationships (Kramer, 1996) for the region. Consequently, the assessment of seismic hazard is probably the most important contribution of seismology to society. The prediction of the earthquake ground motion has always been of primary interest for seismologists and structural engineers. For engineering purposes it is necessary to describe the ground motion according to certain number of ground motion parameters such as: amplitude, frequency content and duration of the motion. However it is necessary to use more than one of these parameters to adequately characterize a particular ground motion. Updating existing hazard maps represents one of the highest priorities for seismologists, who contribute by recomputing the ground motion and reducing the related uncertainties. The quantitative estimate of the ground motion is usually obtained through the use of the www.intechopen.com so-called predictive relationships (Kramer, 1996), which allow the computation of specific ground-motion parameter as a function of magnitude, distance from the source, and frequency and they should be calibrated in the region of interest. However this is only possible if seismic records of large earthquakes are available for the specific region in order to derive a valid attenuation relationship regressing a large number of strong-motion data (e.g. Campbell and Bozorgnia, 1994;Boore et al., 1993;Pugliese, 1987, 1996;Akkar and Bommer 2010). For the Italian region the most used attenuation relationships are those obtained by Pugliese (1987, 1996) regressing a few data recorded for earthquakes in different tectonic and geological environments. It has been shown in several cases that it is often not adequate to reproduce the ground motion in each region of the country using a single model. Furthermore the different crustal properties from region to region play a key role in this kind of studies. However, the attenuation properties of the crust can be evaluated using the background seismicity as suggested by Chouet et al. (1978) and later demonstrated by Raoff et al. (1999) and Malagnini et al (2000aMalagnini et al ( , 2007. In other words, it becomes possible to develop regionallycalibrated attenuation relationships even where strong-motion data are not available. One of the purposes of this work is to describe quantitatively the regional attenuation and source characteristics for constraining the amplitude of strong motion expected from future earthquakes in the area. In this work we describe how to use the background seismicity to perform the analysis (details in Malagnini et. 2000aMalagnini et. , 2007. In particular, this chapter describes the procedures and techniques to study the ground motion and will focus on describing both strong motion attenuation relationships and the techniques used to derive the ground motion parameters even when strong ground motion data are not available. We will present the results obtained for different regions of the Italian peninsula, showing that the attenuation property of the crust and of the source can significantly influence the ground motion. In addition, we will show that stochastic finite-fault modeling based on a dynamic frequency approach, coupled with field investigations, confirms to be a reliable and practical method to simulate ground motion records of moderate and large earthquakes especially in regions prone to widespread structural damage.

Weak motion data set processing
In general, a large dataset of weak motion data are processed by following the approach described in details by Malagnini et al. (2000aMalagnini et al. ( , 2007. The advantage of the procedure is that no hypothesis on the functional form of the scaling laws needs to be formulated before the analysis. The method takes into account the duration parameter, as a function of frequency and distance, through the statistical tool called Random Vibration Theory (RVT, see Cartwright & Longuet-Higgins 1956). The latter is used to estimate the peak ground motion of a random time history, given the empirical attenuation parameter, source spectrum and its duration in time. A detailed description of the method and data processing technique are provided in Malagnini et al. (2000aMalagnini et al. ( , 2007. Each waveform is visually inspected to eliminate recordings with low signal-to-noise ratios, anomalous glitches, and calibration issues., and seismograms are corrected for the instrument response. The pickings of the P-and S-wave arrivals are also reviewed. Each corrected time series is filtered using bandpass filter at every f 0 constructed as the contribution of two 8-pole Butterworth filters: a low-pass filter and a high-pass filter with corner frequency, respectively, at √2 f 0 and 1/√2 f 0 . A general form for a predictive relationship for observed ground motion is ( Fig. 1): where A ij (f) represents the logarithm of peak amplitude of ground-motion velocity at site "j" for the earthquake "i" on each filtered seismogram recorded at the hypocentral distance r ij, EXC i (r ref , f) is the excitation term; SITE j (f) represents the site term and describes the site modification effects; and D(r ref , r, f) is the crustal propagation term and represents an estimate of the average frequency-dependent crustal response for the region. Usually the value of 40 km is chosen for r ref . A piece-wise linear function defined by fixed-distance nodes was used to model the D(r,r ref ,f) function. The number of nodes of this piece-wise linear function, and the spacing between the nodes are selected according to the distance distribution of our data. Equation (1) is solved in the time domain, from multiple narrow band-passed signals. By using the model equation (1), we can arrange all our observations in a large matrix and then invert to obtain source, path and site terms. According to Malagnini et al. (2000a) the regression requires two constraints for stable inversion: The first constraint defines the distance to which the excitation term is projected. The effect of the second one is that common site effects are mapped on the excitation term. During the inversion the sum of all site terms is forced to zero (relation 2b) for each frequency, so that the source terms represent what would be recorded at the reference hypocentral distance by the average network site. Each individual site term measures the deviation from the mean seismic spectra for each station, which is due to the physical properties of the shallow geology at the recording site or, in some cases, to instrumental calibration. The duration of ground motion is a function of the fault size and of the dispersion of elastic waves along the path between the source and the seismic station. To make specific predictions for large earthquakes, the duration of the event must be added in the form of a constant term equal to the inverse of the corner frequency. Since no unique definition of the effective duration of the ground motion is possible, we define the effective duration for the ground motion as given by Raoof et al. (1999). Then for each seismogram the duration T is determined as the width of the time window that delimits the 5%-75% portion of the seismic energy following the S-wave arrivals. The functional form for the propagation terms expresses the effects of frequency-dependent geometrical spreading and anelastic attenuation (Aki, 1980), depending, for each frequency, on the average velocity structure along the propagation path and rock's physical properties. Therefore, we obtain the results of the regression at a set of sampling frequencies, and model them by using the following functional form: where g(r) is the apparent geometrical spreading, β is the shear-wave velocity, and the frequency-dependent attenuation is defined through the quality factor, Q( f ), which is defined as with the reference frequency f ref chosen at 1 Hz. The parameter η defines the frequency dependence of Q( f ). The term: log 10 (D(r, r ref , f)) is modeled as a piecewise linear function between a number of distance nodes, and assumed to be zero at a reference distance r ref , which defines the excitation term log 10 (EXC i (r ref , f)). The r ref is chosen such that mislocations in source depth would not significantly change the reference hypocentral distance. A body-wave-like geometric attenuation and a surface-wave-like decay is used to model the decay of the Fourier amplitudes as a function of distances (Malagnini et al., 2000a) The source excitation, (1), may be thought of as the average expected level of ground motion at r ref for each earthquake. The observed excitation is related to the actual source spectrum through the expression where s(f,M w ) is the source excitation as a function of moment magnitude, V(f) is a frequency-dependent 'regional' site amplification (the average site term of the stations included in Eq. 2b) and   controls near-surface attenuation at high frequency. The term represents the effect of the propagation at the reference distance due to geometrical spreading and crustal attenuation. The term {V(f)exp(−f   )} avg term controls the average site modification of the signal spectrum. V(f) represents the average site amplification term relative to hard rock (in the manner of Atkinson & Silva, 1997), and can be calculated from the shallow shear-wave velocity structure near the site (Boore, 1996).   describes the depletion of the high-frequency motion at the site, which may be caused by the local Q(z) structure. The form of s(f,M w ) representing the Fourier velocity spectra is, where log M o = 1.5(M w + 6.03) (M 0 in Nm) (from Hanks & Kanamori 1979), K = (0.55·2.0·0.707) is a coefficient composed of the effects of the average radiation pattern, freesurface amplifications for vertically incident S waves and the energy partition of initial shear wave amplitude into two horizontal components, M o is the seismic moment,is the mass density at the source and  is the shear wave velocity at the source (D'Amico et al., 2011b). S(f) is the single-corner source term: where f c = 0.49(/M o ) 1/3 . Here the corner frequency f c is determined from the spectra and is related to the stress drop,  (Pa), seismic moment, M o (N-m) and the shear wave velocity  (m s -1 ). The constant 0.49 depends on the type of model spectra and the geometry of the source. In order to model the excitation term, we use Brune's (1970Brune's ( , 1971)  2 source model, which describes the spectrum of shear radiation in terms of stress drop and moment magnitude. The average stress parameter required to best reproduce the observed propagationcorrected source spectra for the larger earthquakes in the data is adjusted using a trial-anderror procedure. In order to properly calibrate the Δσ, and k 0 the scaling relations must be constrained by using moment magnitudes derived from regional moment tensor inversion, both for small and moderate earthquakes (e.g. D'Amico et al. 2010b, D'Amico et al 2011a). In general, a tradeoff exists between the stress parameter and κ 0 . κ 0 governs the high-frequency decay of the theoretical excitation terms, as well as the Δσ, which affects the radiated spectra beyond their corner frequencies. In the frequency band of our interest, however, the effect of the stress parameter is strongest for the largest earthquakes, while κ 0 completely controls the behavior of the small earthquakes at high frequency. For this reason, it is necessary first to find estimates of the high frequency parameter, k 0 , by examining the spectra of small events, and then, knowing k 0 , of the stress parameter of the larger events. During the inversion the sum of all site terms is forced to zero for each frequency. This constraint represents what would be recorded at the reference hypocentral distance by the average network site. The site term measures the deviation from the mean seismic spectra for each station, which is due to the physical properties of the shallow geology at the recording site. The methodology described above for determining the attenuation properties has been successfully applied in different part of the world: California (Raoof et al. 1999;Malagnini et al. 2007), northwestern United States (Herrmann and Dutt, 1999;Jeon and Herrmann 2004), central United States (Herrmann and Malagnini, 1996), Mexico (Ortega et al., 2003), Greece and Crete , Italy (Malagnini et al., 2000a(Malagnini et al., , 2002Malagnini and Herrmann 2000;Morasca et al. 2006;Scognamiglio et al. 2005), Central Europe (Malagnini et al, 2000b, Bay et al. 2003, Turkey , India (Bodin et al., 2004). For example, comparisons can be done among different Italian regions in which this kind of studies have been conducted. It has been found that the western Alps (Morasca et al., 2006), eastern Alps (Malagnini et al., 2002), Southern Appenines, central Italy (

Prediction of ground motion parameters
The estimation of ground motion for a particular region and also site-specific investigation is essential for the design of engineered structures. Estimates of expected ground motion at a given distance from an earthquake of a given magnitude are fundamental inputs to www.intechopen.com earthquake hazard assessments. The determination of seismic design criteria for engineered structures depends upon reproducible estimates of the expected lifetime of the structures. There are also several site classification schemes used in different papers ranging from qualitative description of the near surface material to very quantitative definitions based on shear wave velocities. In order to predict the expected ground motion parameters (e.g. in terms of peak ground acceleration (PGA) and peak ground velocity (PGV) as a function of distance and magnitude we used a stochastic approach. We performed the task by using two widely used computer codes; for point-source model, SMSIM and for extended-source model, EXSIM that is originally developed by Boore (1996Boore ( , 2003 and Motazedian & Atkinson (2005) & Boore (2009), respectively. During the SMSIM point-source simulations we did not use any information about fault geometry and rupture properties. In general, the simulations are carried out by using the regional propagation parameters derived as described above and, for the EXSIM simulations, having rectangular faults having length and width proportional to the moment magnitude according to the relationship proposed by Wells and Coppersmith (1994). Each fault is assigned with a random slip distribution, if known, otherwise it is reasonable to assume a random slip distribution if we do not have any constraint on the slip distribution. It has been shown that only the gross features of slip distribution on a fault plane that do not diverge significantly from the average value of slip may be reliable; all other complexities could be extremely uncertain (Beresnev and Atkinson, 2002). During each simulation the fault plane is discretized into several subfaults. Site effects at a specific station are very important and may be used for engineering purpose to define the regional predictive law and the seismic hazard. In the simulations in order to consider different site conditions, we will refer to the NEHRP classification (BSSC, 1994). Figures 3, 4, 5, and 6 shows several examples of stochastic simulations (both using SMSIM and EXSIM) carried out in different parts of the globe. Figure 3 shows a ccomparison between observed and simulated (a) PGA and (b) PGV obtained for the large and destructive Chi-Chi (Taiwan) event that occurred on 20 th September 1999. The simulation values are obtained using the EXSIM computer codes. The PGA and PGV simulated values were estimated for an earthquake of M w 7.6 using the parameters derived by D' Amico et al. (2011b), and the proposed fault geometry by Ma et al. (2001). The grey symbols represent the observed data of the Chi-Chi earthquake (http://www.cwb.gov.tw). Predictions obtained using Akkar & Bommer (2010), Boore & Atkinson (2008) and Campbell & Bozorgnia (2008) are also shown. Figure (Boore & Joyner 1997), and from the strongmotion relationships by Sabetta & Pugliese (1996). Predictions are given in terms of medians values ±1σ. Predictions by Akinci et al. (2010), computed using the ground motion model developed by Malagnini et al. (2008), are only slightly different from the ones obtained in this study, and fit quite well the recorded strong motion data up to a distance of 200 km (Malagnini et al. 2011). Figure 5 and 6 report the ground motion simulated parameter in terms of PGA and PGV, for the island of Malta due to the possible activation of two active faults located (i) on the Hyblean-Maltese Escarpment, at an epicentral distance of 140 km and (ii) about 20 km south of Malta (D'amico et al. 2011c). In particular for the fault on the Hyblean-Maltese Escarpment we simulated the possible ground motion parameters for four earthquakes of different moment magnitude. It is worth noting on these figures that peak ground accelerations close to 0.1g would be generated on Class B and C sites from a magnitude 7.6 event on the Malta escarpment. Such an event is comparable to the 1693 and the 1169 events  Ma et al. (2001). The grey symbols represent the observed data of the Chi-Chi earthquake (http://www.cwb.gov.tw). Predictions obtained using Akkar & Bommer (2010), Boore & Atkinson (2008) and Campbell & Bozorgnia (2008) are also shown. on the same fault (Azzaro and Barbano, 2000). Because of the inherent brittleness, lack of ductility and lack of tensile strength of unreinforced masonry buildings (URM), it is expected that even such accelerations could cause significant damage in these buildings (Hess, 2008). It is also observed that a magnitude 5 event on the active fault zone immediately south of Malta would produce similar PGA/PGV values as the above event, albeit the frequency content would be different. Such a magnitude is rare on the Sicily Channel faults but approximate calculations based on radius of perceptibility indicate that they have occurred on at least one occasion (1911) in the past century.

Comparison between simulated ground motions for different moment magnitude events from different regions of the world
Because the technique used here for the investigation of the scaling properties of the highfrequency parts of the ground motion is virtually identical to those used in studies  Bodin et al ., 2004); N-E Alps (blue lines, Malagnini et al ., 2002); Japan (green lines, Malagnini et al ., 2010b); Taiwan (black lines, this study). Predictions obtained using Akkar & Bommer (2010) are also shown by dashed black lines. The thick and thin lines are the prediction of PGA and PGV for moment magnitude of 5.5 and 6.5, respectively conducted in a wide variety of environments (e.g., Bodin et al., 2004;, we can compare our results with those studies to reveal systematic similarities and differences with other areas. Figure 7 shows the predicted ground motions computed for moment magnitude of M w 6.5 and 5.5 from different regions of the world using the generic rock sites by Boore & Joyner (1997), and provide a comparison with the attenuation relationship developed by Akkar and Boommer (2010) (hereafter AB10). For example in Figure 7 it is clear that weak-motion based predictive relationships fit quite well with the observed data from M w 6.5 and 5.5 events in Taiwan. The predictive relationships of AB10 overestimate the PGA and PGV with compare to both our RVTgenerated ground motion predictions and the observed data at lower magnitude, M w 5.5. The predicted decay of PGA and PGV with distance clearly indicates that Taiwanese ground motions may be similar to that observed in tectonically active regions, rather than in stable www.intechopen.com areas like the Indian plate. The differences in the predicted peak amplitudes between regions get larger at lower magnitudes. The stronger attenuation is experienced by the highfrequency part of the spectrum since peak ground motions are carried by a dominant frequency band that is magnitude-dependent. Most of the seismic energy is radiated around the earthquake corner frequency, so that at larger magnitudes, peak ground motions are dominated by lower frequencies and are not very sensitive to crustal attenuation. Therefore, peak ground motions decay faster for the M w 5.5 event than for the M w 6.5 event. Moreover, the level of ground shaking increases as the quality factor Q o increases, and as the slope of the effective geometrical spreading function gets more gentle. The effect gets more severe for distant records. Due to the heterogeneities that are present (mainly vertically) in the crustal structure, different slopes may be presented in the predicted curves. Unfortunately, many of the existing predictive relationships (e.g., Ambraseys, 1995;Sabetta & Pugliese, 1996;Akkar & Bommer, 2010) were obtained by forcing a body-wave geometrical spreading to a distance range where supercritical reflections at the Moho appear to be quite important. Another important parameter is the stress drop, which may cause the differences in the ground motion levels at short distances and must be carefully calibrated in the region of interest. For example,  observed that the absolute levels of the stress drop parameters are region-dependent that results in different estimation of gorund motion paramters. As an example, Figure 8 shows the comparison of simulated PGA and PGV as a function of distance for moment magnitude of 5 and 6 obtained using the SMSIM programs (Boore, 2003; http://www.daveboore.com/software_online.htm). It is clear how the predictions of the ground motion are different in the different areas, therefore the regional calibration of attenuation properties and source scaling is a really important task even considering a quite small area.

Conclusions
Such kind of studies clearly demonstrate that the weak-motion based ground-motion predictive equations successfully predict the ground motions induced by larger events, once the source term is adequately calibrated (D'Amico et al. 2011b;. The results obtained applying the technique described in this chapter could be used for upgrading the most recent hazard map of Italy and for engineering designs as well. The results are also useful to implement tools like Shake Map® (Wald et al. 2005) which use this kind of information to generate a rapid earthquake response. ShakeMap® is a tool used to portray the extent of potentially damaging shaking following an earthquake. It can be used for emergency response, loss estimation, and public information. Shake maps show the distribution of ground shaking in the region, information that can be really critical for emergency management decision making. In fact, it is the distribution of peak ground motion and intensity rather than the magnitude that provides useful information about areas prone to damage. Having this information in real time will result in lives saved and reduction in property damage. After a damaging earthquake, emergency managers must quickly find answers to important questions such as the localization of the most serious damage, and the areas with less; the resources that must be mobilized and in what quantity. Usually government response organizations answer these questions after a preliminary survey of the damaged area. This reconnaissance can require several hours or sometimes some days to be completed. As a result, decisions regarding search and rescue, medical emergency response, care and shelter for the damaged and displaced persons, and other www.intechopen.com critical response needs must often be made while information is still incomplete. In this context a rapid and automatic response for the injured area is really important; hence predictive attenuation relationships play a key and really important role in similar tools.