Spatial Distribution of Simulated Response for Earthquakes, Part I Ground Motion

Spatial Distribution of Simulated Response for Earthquakes, Part I: Ground Motion Jacobo Bielak, Antonio Fernández, Gregory L Fenves, Jaesung Park, and Bozidar Stojadinovic Corresponding author: Gregory L Fenves Mailing address: Department of Civil and Environmental Engineering University of California, Berkeley Berkeley, CA 94720-1710 Phone: 510-643-8543 Fax: 510-643-5264 Email: fenves@ce.berkeley.edu Submission date for review copies: February July 301, 2004 Submission date for camera-ready copies: Bielak Bielak Spatial Distribution of Simulated Response for Earthquakes, Part I: Ground Motion Jacobo Bielak,a)a) M.EERI, Antonio Fernández,b)b) M.EERI, Gregory L Fenves,c) c) M.EERI, Jaesung Park,d)d) and Bozidar Stojadinovice),,e) M.EERI The objective of this study is to examine, by computer computational simulation, the spatial and temporal distribution of the earthquake response of idealized structures to near-source ground motionground motion near a causative fault In this paper we model theAn ground motion of idealized 20 km by 20 km region is modeled as a layer on an elastic halfspace with dense spatial sampling for frequencies up to Hz Two scenario events are considered, a a strike-slip fault and a thrust fault, in a layer on a halfspace, by the use of finite dislocation models These idealized models are representative of two common types of earthquakes, in which the directivity of the rupture generates large, short-duration, velocity pulses in the forward direction, and large spatial variation of the freesurface motion throughout the epicentral region We obtain a dense spatial sampling of ground motion over a large region for frequencies up to Hz in order to elucidate the effects of the source and path on the near-field ground motion For the strike-slip fault event, the fault normal component exhibits a very strong forward directivity effect with a strong pulse-type motion approximately twice the amplitude of the motion in the fault parallel direction The dynamic effect in the fault parallel direction produces a pulse-type motion near the epicenter For the thrust fault event the greatest concentration of ground displacement occurs near the corners of the fault opposite the hypocenter, in the rake direction In contrast with the strike-slip fault, the ground displacement in the direction of the slip is greater by a factor of two than in the direction normal to the slip In a companion paper, we examine how the free-field ground motion from the two scenario earthquakes influences the spatial and temporal distribution of structural response of a family of simple single -degree-of-freedom elastoplastic systems A companion paper then uses the synthetic records to examine how the freefield ground motion for the two scenario earthquakes influences the spatial distribution of structural response of a family of SDF elastoplastic systems in a region close to the causative fault a) Professor, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 b) Formerly, Graduate Student Researcher, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213; currently, Manager of International Projects, Paul C Rizzo Assoc., 520 Exposition Mall, Monroeville, PA, 15245 c) Professor, Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720 d) Graduate Student Researcher, Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720 e) Associate Professor, Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720 Bielak INTRODUCTION Large earthquakes in urban regions cause a highly variable spatial distribution of damage to the built-infrastructure because of source effects, path effects, large-scale geological structures such as sedimentary basins, site response effects, and the structural characteristics of the buildings and other infrastructure components The distribution of damage in the 1994 Northridge Mw=6.5 earthquake (Somerville, 1995) and the 1995 Hyogoken-Nanbu, Japan, Mw=6.9 earthquake (Akai et al., 1995) raised profound questions about these effects, with particular concern about the large velocity pulses at sites near the faults Additional data obtained from the 1999 Kocaeli, Turkey, Mw=7.4 earthquake (Rathje et al., 2000) and the 1999 Chi-Chi, Taiwan, Mw=7.6 earthquake (Li and Shin, 2001) provided further evidence that the spatial distribution of ground motion in a region is related to the fault mechanism and path effects The large number of ground motion data recorded in these earthquakes confirmed that near-fault pulse-type ground motion can be very damaging to buildings, as first identified in the 1971 San Fernando earthquake (Bertero et al., 1978) Researchers have examined the spatial distribution of ground motion based on the extensive records obtained in the 1994 Northridge earthquake and its aftershocks Aftershock records obtained by Meremonte et al (1996) and Hartzell et al (1997) showed that the amplitude of peak ground velocity varied by a factor of two or greater at different sites with the same general geological structure but separated by distances of only 200 m Boatwright et al (2001) developed correlations between ground motion parameters and effects on structural response, as measured by an intensity measure based on building tags The correlations show that peak ground acceleration (PGA) is a poor predictor of damage, peak ground velocity (PGV) is much better, and that an averaged pseudo-velocity (between 0.3 and 3.0 seconds period), which is linearly related to PGV, is a good predictor Contours of PGV and averaged pseudo-velocity correspond to the spatial distribution of damage based on a tagging intensity In another study using 1994 Northridge earthquake strong motion data, Bozorgnia and Bertero (2002) examined various responsethe spatial distribution of structural response parameters associated with damage quantities associated with structural damage as the spatial distribution of damage parameters The spatial distribution of ductility demand for single- degree-of-freedom (SDF) systems of 1- and 3-sec vibration periods using a codespecified strength are qualitatively similar to the PGV contours of peak ground velocity Their analysis shows that 1-sec and 3-sec period SDF systems reach a ductility demand of and 5, respectively The large ductility demands are concentrated in the updip region direction of slip of the buried thrust fault for the 1-sec case and the updip direction and epicentral area for the 3-sec case Additional results are presented for spatial distributions of structural damage measures that include the effect of ductility and hysteretic energy demands and capacities An important feature of large-magnitude earthquakes in the near field is the large amount of seismic energy from the rupture that is concentrated in the forward directivity zone of near a the fault This energy is generally manifested as a single large pulse of ground motion (e.g., Somerville et al., 1997) Somerville (1998) defines the forward directivity effects occurring at sites where the fault rupture propagates towards the site and the direction of fault slip is aligned in the direction of the site These conditions are met with strike-slip faults and dipslip rupture in thrust faults Forward directivity effects in the fault normal direction occur in all locations along a strike-slip fault For thrust faults, however, forward directivity effects occur mostly in the surface projection of the fault, updip from the hypocenter Backward Bielak directivity and neutral directivity effects generally produce longer period, but lower amplitude, motion in the fault-normalfault normal and fault-parallelfault parallel directions Somerville et al (1997) have developed a procedure for taking into considerationconsidering the effects of near-fault motion on the ground motion from strike-slip faults by modifying the elastic response spectra The In this approach, the spatial effect of directivity depends on geometric parameters related toon the direction of fault rupture, and the location of the site with respect to the epicenter, and also the fraction of fault rupture between the epicenter and site To account for near-fault effects in seismic design of buildings, the 1997 Uniform Building Code (ICBO, 1997) incorporated near-fault amplification factors for the acceleration-sensitive and velocity-sensitive period region bands of the elastic design response spectrum The factors depend on the distance to the fault and the fault mechanism and magnitude, and also the The near-fault factors depend on the bands of distance to the fault (less thanwithin 15 km) and the type and magnitude of the anticipated fault rupture The 1997 UBC provisions near-fault factors are compatible comparable with the mean values for spectrum fault-normalmodification factors and fault-parallel values from Somerville et al (1997), but they not distinguish between fault-normalfault normal and fault-parallelfault parallel ground motion, for which the former is substantially larger greater in the forward directivity zone Although recent large earthquakes have produced extensive ground motion records as a result of increased instrumentation in urban areas, their coverage is still far from complete, and theirthe spatial resolution is not high enough to describe fully the distribution of ground motion with sufficient fidelity Thus, there is an important need for developingfor highresolution, realistic simulations of ground motions in a region to study the seismological, geotechnical, and structural effects of urban earthquakes in detail A number of studies have been devoted recently to modeling earthquake ground motion in realistic basins (e.g., Frankel, 1993; Graves, 1993; Olsen et al, 1995; Olsen and Archuleta, 1996; Pitarka et al, 1998; Hisada et al., 1998; and Stidham et al., 1999) These simulations, however, are were usually generally limited to low frequencies ( ≤ 0.5 Hz) Motivated by the 1994 Northridge earthquake, Hall et al (1995) and Hall (1998) simulated the ground motion produced by an earthquake on a thrust fault to examine the effect of near-fault ground motions on 20-story steel frame buildings and long-period based isolated buildings The fault rupture parameters were calibrated to correspond to a scenario Mw=7.0 event on the Elysian Park buried thrust fault in Los Angeles Ground motions were simulated on an 11 by 11 grid with 5-km spacing The peak ground velocity was 1.8 m/s and large areas had velocities greater than m/s The simulations of the 20-story buildings located at the grid points showed that peak story drift ratios reached 0.064 in the forward directivity zone because of the large velocity pulses Standard design procedures for a base-isolated three-story building resulted in large bearing displacements and story drifts Hall (1998) then investigated the earthquake response of six-story and two-story steel frame buildings designed according to U.S and Japanese codes using Elysian Park thrust fault simulation and a simulation based on the 1994 Northridge earthquake The near-source velocity pulses produced large drifts in buildings located at grid points in the forward-directivity zones, and fracture of the moment-resisting connections has a detrimental effect on drifts The pioneering work of Aki (1968) and Haskell (1969), followed by the comprehensive parametric studies of Boore et al (1971), Archuleta and Hartzell (1981), Anderson and Luco (1983a, 1983b), and Luco and Anderson (1983), among others, in which a kinematic model of an extended fault was used to simulate the earthquake source, , These methods, provided Bielak new means to obtain qualitative and quantitative descriptions of thesimulate ground motion in a region, including near-field fault ground motioneffects This was followed by comprehensive parametric studies by Boore et al (1971), Archuleta and Hartzell (1981), Anderson and Luco (1983a, 1983b), and Luco and Anderson (1983), among others, In the past 10 ten years numerical modeling methods for anelastic wave propagation that takes into consideration the earthquake source, propagation path, and local site effects in realistic models of basins have become increasingly available There are using several types of such methods Boundary element and discrete wavenumber methods have been popular for moderate-sized problems with simple geometry and geological conditions (e.g., Mossessian and Dravinski, 1987; Kawase and Aki, 1990; Bielak et al., 1991; Hisada et al., 1993; Sánchez-Sesma and Luzón, 1995; Bouchon and Barker, 1996) Finite differences methods are common (e.g., Frankel and Vidale, 1992; Frankel, 1993; Graves, 1993, 1996; Olsen et al., 1995; Pitarka, 1999; Stidham et al., 1999; Sato et al., 1999), and) and fFfinite elements (e.g., Lysmer and Drake, 1971; Toshinawa and Ohmachi, 1992; Bao et al., 1998; Aagard et al., 2001) are better suited for largerlarge-sized problems that involve realistic basin models with highly heterogeneous materials, because of their flexibility and simplicity Bao et al (1998) developed one of the first scalable, parallel, finite element tools for large-scale ground motion simulation in sedimentary basins with heterogeneous materials Aagaard et al (2001) used parallel finite element simulations to investigate the sensitivity of long-period ground motion to different seismic source parameters, on strike-slip fault and thrust fault mechanisms, with particular emphasis on the large velocity pulses in the forward directivity zones Their simulations show that the peak ground motion occurs within the bands zones for the near-fault factors in thewhich the 1997 UBC for faults with surface rupturespecifies near-fault factors A buried thrust fault simulation, however, shows peak ground motions occurring in the up-dip direction over a larger area than defined for the nearfault factor The previous researchPrevious research using recorded ground motion data and early simulations has examined on the spatial distribution of ground motion and its effects on structural response has s veidentified many important trends Due to the limited relatively few number of ground motion records and earlier limitations in computational capabilitescapabilities, there remain additional questions concerning the characterization of the spatial effects, the systematic interpretation of such effects using structural dynamic concepts, and the evaluation of building code approaches for accounting for the effects Thus, the objective of this paper is to use the ground motion simulation of two representative scenario earthquake events with frequencies up to Hz to obtain a dense spatial sampling of ground motion over a large region in order to elucidate the effects of the source and path on the near-fieldnear-fault ground motions AA companion paper (Fenves et al., 2004) then uses the dense sampling of ground motion to examine the distribution of structural response in a region close tonear the causative faults in the two scenarios The use of an idealized simplified two-layer model of a region and single degree-of-freedom inelastic systems to represent structural response allows the papers to focus on fundamental trends DESCRIPTION OF MODEL AND SCENARIO EARTHQUAKE EVENTS The model considered in this study consists of an elastic layer on an elastic halfspace, as shown in Fig The density,ρ, shear-wave velocity, β, and P-wave velocity, α, of the layer are 2.6 g/cm3, 2.0 km/s, 4.0 km/s, respectively, and the corresponding values for the halfspace Bielak are 2.7 g/cm3, 3.464 km/s, 6.0 km/s These values were chosen to model the region as being made up of rock material and material attenuation is not considered.The model considered in this study consists of an elastic layer on an elastic halfspace, as shown in Figure 1, to represent a 20 km by 20 km region of rock material We consider a buried strike-slip fault (Figure 1a) and a buried thrust fault (Figure 1b) in order to model represent two of the most common types of earthquakes The top edge of the vertical fault is km beneath the interface between the layer and the halfspace, whereas the top edge of the inclined fault touches the interface Red circles in Figure denote The the hypocenters of the two earthquakes are denoted by red circles on the respective faultsearthquakes The dip angle (40º) of the thrust fault is be similar to that of the fault that caused the 1994 Northridge earthquake source The density,  , shear-wave velocity, vs , and P-wave velocity, v p , of the layer are 2.6 g/cm3, 2.0 km/s, 4.0 km/s, respectively, and the corresponding values for the halfspace are 2.7 g/cm3, 3.46 km/s, 6.0 km/s Material attenuation is not considered in the simulations We assume kinematic rupture of the fault by imposing a, that is, a dislocation is imposed across the fault (jump in the tangential displacement and continuous normal displacement) The rupture propagates radiallradiallyy from the hypocenter at a constant speed of 0.8 km/s until it reaches the edges of the fault The slip direction of rake, is 0º and 90º for the vertical and the inclined faults, respectively;, that is, the particle motion across the fault is along the length of the fault in both cases For the vertical fault the motion is right lateral strike- slip, and for the inclined fault the motion of the hanging wall is upward and that of the footwall is downward (thrust slip) The variation of the dislocation with time is defined by the slip function u(t) Df (t) , u(t) = ū f(t), where D ū is the (uniform) amplitude of the dislocationuniform slip, and,  f (t)  1     t  t  1 exp    T   H (t) T0    0 f(t) = [1 – (1 +t/T 0)exp(-t/ T0)]H(t) where T0 T0 definesis the slip rise time There is a delay time at each location with respect to the onset time at the hypocenter of r / vrupt r/Vrupt, where r is the hypocentral distance from the particular location, and vrupt Vrupt is the rupture velocity In the simulations, we assumeWe take vrupt =Vrupt = 3.0 km/s and , T0 T0 = 0.1 sec, and modelwhich allows modeling seismic waves up to 5.0 Hz The model for the strike-slip event is the same that has been used by a group of modelers, including some of this paper’s authors, in verifying several finite difference and finite element codes for simulating earthquake ground motion in large regions (Day et al, 2002) The seismic moment, M M0, of the an earthquake can be expressed as (Aki, 1966),: M   AD , M0 = μAū, in whichwhere  μ is the shear modulus of the crustal volume that contains the fault, and (μ = β2ρ), and A is the area of the causative fault The seismic moment and the moment magnitude, M w Mw, a quantity often used to measure the strength of the earthquake is related Bielak to the seismic moment in dyne-cm, are related by (Kanamori, 1977): M w 0.67 log 10 M  10.7   Mw = ⅔log(10M0, in dyne-cm) – 10.7 For our the scenario simulationsevents, we set Mw = 6.0 and 5.8 is selected for the strike-slip fault and the thrust fault earthquakes, respectively These magnitudes correspond to slip D ofū = 0.112.5 cm m and 0.05.42 cmm, respectively, for the two events Despite their simplicity, models of this type have been shown to capture the essential nature of earthquake ground motion in the near-fault region For example, in a recent simulation of the 1992 Landers earthquake in southern California, Hisada and Bielak (2004) modeled the crustal region in the vicinity of the epicenter as a single layer on a halfspace and the causative fault by piecewise strike-slip planar surfaces, and calculated the ground motion at the Lucerne Valley station using an integral representation technique (Hisada and Bielak, 2003), with satisfactory results Similarly, results for the spatial distribution of ground motion to be presented later for the thrust-fault event are qualitatively similar to those observed during the 1994 Northridge earthquake COMPUTATIONAL METHOD FOR GROUND MOTION SIMULATION To simulate slip on the fault and the resulting ground motion within the domain, we use an elastic wave propagation, finite element code developed for modeling earthquake ground motion in large sedimentary basins (Bao et al., 1998) The wave propagation code is built using Archimedes, a software environment for solving unstructured-mesh finite element problems on parallel computers (Bao et al., 1998) Archimedes includes two- and threedimensional mesh generators, a mesh partitioner, a parceler, and a parallel code generator We use standard, Galerkin linear tetrahedral elements for the spatial discretization of the governing Navier equations of elastodynamics over the tetrahedral mesh The element sizes are tailored to the local wavelengths of the propagating waves, and the mesh generation strictly controls the aspect ratio of every element such that it does not exceed a prescribed value The spatial discretization leads to a standard system of second-order ordinary differential equations with constant coefficients These equations are solved using the central difference method, an explicit, conditionally stable, step-by-step algorithm in the time domain To avoid the need of solving a system of algebraic equations at each time step, a lumped mass matrix is used As a result, the only significant operation at a time step is a matrix-vector multiplication Two important issues must be considered for solving earthquake wave propagation problems in infinite domains by the finite element method One is the requirement for a finite domain of computation and the need to limit spurious reflections at the artificial absorbing boundaries This is accomplished by a sponge layer of viscous material near the artificial boundaries (Israeli and Orszag, 1981) and by placing a set of nodal viscous dampers directly on the artificial boundaries, along the lines described in Lysmer and Kuhlemeyer (1969) The second issue is the need to represent the slip on the fault in the finite element formulation We this, following Aki and Richards (1980), by expressing the slip in terms of a set of double couples, which in turn are expressed as body forces The body forces are reduced to equivalent nodal forces through the Galerkin process for spatial discretization (Bao, 1988) To determine the amplitude of each double couple, the fault is divided into a number of subfaults For the case of uniform slip, the double couple within each element intersected by the fault is proportional to the seismic moment, based on the area of the fault Bielak contained within the element divided by the total area of the fault The finite element code has been verified with several finite differences codes for idealized and realistic earthquakes (Day, 2002), including the strike-slip event considered here, with satisfactory results (a) Strike-slip fault scenario Bielak (b) Thrust fault scenario Figure Model of faults in a homogeneous elastic layer on a homogeneous elastic halfspace Despite their simplicity, models of this type have been shown to capture the essential nature of the earthquake ground motion in the near-fieldnear- region For example, in a recent simulation of the 1992 Landers earthquake in southern California (Fig.Figure 2a), Hisada and Bielak (2004) modeled the crustal region in the vicinity of the epicenter as a single layer on a halfspace and the causative fault by piecewise strike-slip planar surfaces, and calculated the ground motion at the Lucerne Valley station using an integral representation technique (Hisada and Bielak, 2003), with satisfactory results Figures 2b and 2c show the corresponding velocities and displacements in the fault -normal (FN) and fault -parallel (FP) directions The agreement between the synthetic motion (solid lines) and the recorded motion (dashed lines) is satisfactory Notice that at theThe Lucerne Valley station, the peak amplitudes of the FN and FP velocities are comparable, but the permanent offset displacement is much greater in the FP than in the FN directions As an example of a thrust- Bielak As a manifestation of the increase of the dominant periods observed directly in the seismograms with increased distance to the fault, the periods at which the pseudo-velocity attain their peak value also increases with distance from the fault, e.g., the peak for station S15 occurs at 2.2 s The response spectra for the FP component of the ground motion exhibit, in a sense, the trends that are the reverse of reverse behavior of thatthe of the FN component That is, by By comparing the spectra at stations S12, S5, and S6, with those at S3, S4, S7, and S8 in Figuress 11 and 128, the FP component of the former look like the FN compoents components of the latter;; and, vice versa, the FN components S12, S5, and S6 look like the FP components of S3, S4, S7, and S8 Interestingly, theThe peak spectral ordinate of the FP response at S5 is almost the same, around m/s, and the shape of the spectrum is quite similar, to that at S4 in the FN direction Moving away from the fault, the FP and FN components begin to look more similar One important distinction is that whereas the spectra for the FN components differ significantly from the corresponding peak ground motion parameters exhibit because they exhibit a clear dynamic effect in that they differ significantly from the corresponding peak ground motion parameters In contrast, , the spectra for the FP components tend to conform are similar more closely to the corresponding peak values of the ground motion, denoting little effective dynamic action of the structural response This is not true for stations S9, S10, and S11, which exhibit significant amplification within the velocitysensitive period regionband THRUST FAULT In this section we present results of the simulation for the thrust-fault scenario earthquake As forConsideringSimilarly to the idealized strike-slip earthquakeevent, the synthetics for the thrust fault scenario exhibit a strong spatial and temporal dependence with the location of the observer with respect to the fault Figure 13 shows the absolute values of the EW and NS components of the free-surface peak displacements and velocities throughout the epicentralat the ground surface throughout the region The white circle denotes the epicenter and the white rectangle is the projection of the causative fault plane onto the free surface Slip occurs in the direction of the hanging wall relative to the foot wall The rake of the slip is such that the thrust of the hanging wall on the free surface points in the west direction Thus, for this inclined fault we denote the particle motion in the EW east-west direction as slip fault parallel (SPFP) since it is normal to the extended intersection of the fault plane and free surface; and in the NS north-south direction asis slip fault normal (FSN) The simulations show a clear forward directivity effect instead of FP and FN (As a side comment, looking at the results for the two faults considered here, it appears that the nomenclature SP and SN for the ground motion in the directions parallel and normal to the projection of the rake vector onto the horizontal plane might be more appropriate than FP and FN, since the former applies equally well to the strike-slip and the thrust faults, while the latter is ambiguous for thrust faults ) The most salient feature in Figs.Figure 13a , and b for the ground displacement is the concentration of motion that occurs around the upper corners for the SP FP component and along the entire edge in the SN FN direction, directly above locations where the there are stress concentrations There is a clear forward directivity effect, as in the strike-slip fault In contrast with the strike-slip event, however, the displacement in the SP FP direction is greater than that in the SN FN direction, Bielak 24 24 by a factor of about two for the thrust fault Both components show significant displacement beyond the intersection of the extended fault with the free free surface Backward directivity, although present, is small compared with the forward directivity The behavior distribution of the peak velocity is similar to that of the displacement, except that the decay is faster with distance from the fault In addition, the SP FP component of the peak velocity is significantly smaller than that of the corresponding SN FN component The synthetic seismoscope records depicted in Figure 10 show that, in addition to its amplitude, the direction of particle motion varies considerably depending on station, and that for this shallow thrust fault there is a noticeable permanent offset within large portions of the epicentral region The seismograms for velocity and displacement are shown in Figure 11 They, too, show large velocity pulses in the direction of forward directivity, and a decay and increased complexity with distance from the fault Consistent with the distribution of peak values in Figure 9, and contrary to the results for the strike-slip fault, the stronger pulses occur in the FP direction As observed already, the displacements show some permanent offset, but much smaller than for the strike-slip fault Bielak 25 25 Displacement Fault Normal Fault Parallel Velocity Bielak 26 26 Envelope Figure 139 Thrust fault earthquake Spatial distribution of the absolute values of the fault parallel and fault normal components of the peak velocity and displacement at free surface White dot denotes the location of the epicenter and white rectangle the projection of the causative fault on the horizontal plane The response spectra for five percent critical damping are shown in Figures 12 and 13 for the same stations (S1-S15) as in the preceding figures for the thrust fault scenario The shapes of the response spectra not show the same degree of variability with location with respect to the fault as those for the strike-slip scenario The main features are: (a) the FP components exhibit distinct acceleration-sensitive, velocity-sensitive, and displacementsensitive bands, except for stations in the forward directivity direction that lie outside the fault region (S1, S2, S3); and for these, the velocity-sensitive band is very narrow or almost nonexistent; (b) the velocity-sensitive band for the FN components is generally narrower than for the FP region; (c) the displacement spectral ordinates at long periods, both for FP and FN components, are generally smaller than the PGD The synthetic seismoscope records depicted in Fig 14 10 show that, in addition to its amplitude, the direction of particle motion varies considerably depending on location, and that for this shallow thrust fault there is a noticeable permanent offset within large portions of the epicentral region The seismograms for acceleration, velocity, and displacement are shown in Figs 11s 15, 16, and 17 respectively They, too, show large velocity pulses in the direction of forward directivity, and a decay and increased complexity with distance from the fault Consistent with the distribution of peak values in Fig 139, and contrary to the results for the strike-slip fault, the stronger pulses occur in the SP direction In addition, as mentioned already, the displacements show some permanent offset, but much smaller than for the strike-slip fault Bielak 27 27 Figure 1410 Thrust fault earthquake Synthetic seismoscope records of the horizontal displacement path at a number of locations on a regular grid on the free surface CONCLUSIONS The spatial and temporal distribution of ground motion near the causative faults for two scenario earthquake events have been examined using detailed computational simulation Although the models of the crustal structure, causative fault, and the slip are idealized, the synthetic ground motion exhibits many of the significant characteristics of ground motion recorded during actual earthquakes Moreover, the high spatial resolution that can be achieved through simulation provides information that cannot be gleaned from recorded ground motion data alone In particular, the results of this study show that for the strike-slip fault event:      The fault normal (FN) component of velocity exhibits a very strong forward directivity effect, but the dynamic effect in the fault parallel (FP) direction occurs in the neighborhood of the epicenter The peak value of the FN components of velocity and displacement are twice those of the corresponding FP components In contrast with the velocity, both the FP and FN components of displacement show a strong forward directivity effect Displacement seismograms exhibit permanent offsets, or fling, as a consequence of the permanent tectonic deformation at the site The decay of the velocity with distance from the fault plane is much faster than that of the displacement The ground motion also varies in duration and frequency content depending on location The FN component of velocity exhibits a strong pulse-like behavior at stations located in the forward directivity direction On the other hand, at stations located directly north of the epicenter, it is the FP component of the velocity that has a strong pulse-like behavior Bielak 28 28 Fig ure 15 Thrust fault earthquake Seismograms of acceleration (g) in two orthogonal directions at selected locations on the free surface Open circles indicate the locations of the observation points, and the direction of motion is denoted by the orientation of the seismograms The direction of particle motion at each location is perpendicular to the time axes of the corresponding seismogram (a) Velocity Figure 16 Thrust fault earthquake Seismograms of velocity (m/sec) in two orthogonal directions at selected locations on the free surface Location and seismogram identification as in Figure 15 Bielak 29 29 (b) Displacement Figure 1711 Thrust fault earthquake Seismograms of (a) velocity (m/s) and displacement (m) in two orthogonal directions at selected locations on the free surface Location and seismogram identification as in Figure 15.Open circles indicate the locations of the observation points, and the direction of motion is denoted by the orientation of the seismograms The direction of particle motion at each location is perpendicular to the time axes of the corresponding seismogram Response spectra for percent critical damping are shown in Figs 18 12 and 19 13 for the same locations (S1-S15) as in the preceding figures, for the thrust fault scenario The shapes of the response spectra not show the same degree of variability with location with respect to the fault as those for the strike-slip scenario The main features are: (a) FSP components exhibit distinct acceleration-sensitive, velocity-sensitive, and displacement-sensitive regions, except for stations in the forward directivity direction that lie outside the fault region (S1, S2, S3); for these, the velocity-sensitive region is very narrow or almost nonexistent; (b) the velocity-sensitive region for the SFN components is generally narrower than for the SFP region; (c) the displacement spectral ordinates at long periods, both for SFP and SFN Bielak 30 30 components, are generally smaller than the PGD Figure 1812 Thrust fault earthquake Response spectra for percent critical damping for ground motion in the SN direction, calculated from the corresponding free-field accelerogramsseismograms in Figure 15 The spectra are plotted in the usual tripartite logarithmic representation, with pseudovelocity on the vertical axis and period on the horizontal axis The periods considered range from 0.5s to 8.0s Figure 1913 Thrust fault earthquake Same as Figure 1812 for ground motion in the fault parallel direction Bielak 31 31 CONCLUSIONS In this study we have examined in some detail the spatial and temporal distribution of near-source ground motion for two scenario earthquakes Although the models of the crustal structure, causative fault, and of the slip are highly idealized, the synthetic ground motion exhibits many of the significant characteristics of ground motion recorded during actual earthquakes Moreover, the high resolution that can be achieved through simulation provides information that cannot be gleaned from data alone In particular, for the strike-slip fault:  While, the fault-normal (FN) component of velocity exhibits a very strong forward directivity effect, most of the dynamic effect in the fault-parallel (FP) direction occurs in the neighborhood of the epicenter  The peak value of the FN components of velocity and displacement are twice those of the corresponding FP components  In contrast with the velocity, both the FP and FN components of displacement show a strong forward directivity effect Displacement seismograms also exhibit permanent offsets, or fling, as a consequence of the permanent tectonic deformation at the site  The decay of the velocity with distance from the fault plane is much faster than that of the displacement  The ground motion also varies in duration and frequency content depending on location: the FN component of velocity exhibits a strong pulse-like behavior at stations located in the forward directivity direction On the other hand, at stations located directly north of the epicenter, it is the FP component of the velocity the one that exhibits a strong pulselike behavior  The seismograms become more complex in shape and their duration becomes longer farther away from the fault; also the dominant periods become longer with distance from the fault  The seismograms become more complex in shape and their duration becomes longer farther away from the fault; also, the dominant periods become longer with distance from the fault As for with the strike-slip fault earthquakeevent, the simulations of the thrust -fault scenario event earthquake exhibits ashow that the ground motion has strong spatial and temporal dependence with on the location of the observer with respect to the fault The most salient features for the thrust fault event are:   The greatest concentration of ground displacement occurs near the corners of the fault opposite the hypocenter, in the rake direction In contrast to with the strike-slip fault, the displacement in the slipfault -parallel (SP) direction (also in the direction of the slip) is greater than that in the fault slip-normal direction, (normal to the slip) by a factor of about two Both The displacement of both components experience significant displacement beyond the intersection of the extended fault with the free ground surface is significant Bielak 32 32  The peak velocity decays faster than the peak displacement with distance from the fault, as for the strike slipstrike-slip fault The important implications that this behavior of the ground motion has for the response of long- and short-vibration period simple elastoplastic models structures is examined in detail in the companion paper (Fenves et al., 2004) ACKNOWLEDGMENTS The research described in this paper was supported by the National Science Foundation under grant number 0121989 to Mississippi State University The authors appreciate the encouragement of Dr Lynn Preston and Dr Joy Pauschke of the NSF Division of Engineering Education and Centers Drs Michael Stokes and Donald Trotter of MSU were instrumental in establishing the coordinated research program on seismic performance of urban regions, for which the reported research is one component The use of the Pittsburgh Supercomputer Center for the computations is greatly appreciated The strike-slip earthquake simulataionsimulation is based on one conducted as part of a PEER/SCEC project on the validation of numerical methods for ground motion modeling in large basins REFERENCES CITED Aagaard, B.T., Hall, J.F., and Heaton, T.H., 2001 Characterization of 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relations to include amplitude and duration effects of rupture directivity, Seismological Research Letters, 68, 199-222 Stidham, C., Antolik, M., Dreger, D., Larsen, S., and Romanowicz, B., 1999., Three-dimensional structure influences on the strong motion wvaewave-field of the 1989 Loma Prieta earthquake, Bulletin of the Seismological Society of America, 89, 1184-1202 Toshinawa, T., and Ohmachi, T., 1992 , Love wave propagation in a three-dimensional sedimentary basin, Bulletin of the Seismological Society of America, 82, 1661-1667 Bielak 36 36 FIGURE CAPTIONS Figure Model of faults ini a homogeneous elastic layer on a homogeneous elastic halfspace (a) Strike-slip fault; (b) Thrust fault Figure 1992 Landers earthquake (a) Fault model consists of three left-lateral strike-slip faults; (b) and (c) Comparisons between simulations (solid lines) and observations (dashed lines) at the Lucerne Valley station The observed displacement records were corrected by Iwan (1992); (b) Fault-normal (FN) and fault-parallel (FP) components of velocity at Lucerne Valley station; (c) corresponding components of ground displacement Figure Distribution of ground velocity due to thrust fault earthquakes; (a) Peak ground velocity derived from seismograms recorded within the epicentral region during the 1994 Northridge earthquake The causative fault is shown in the lower part of the figure, together with the hypocenter and the distribution of the slip in the fault surface; (b) Peak ground velocity in the direction perpendicular to the strike of the thrust-fault earthquake model (Fig 1b) Figure Strike-slip earthquake Spatial distribution of the peak horizontal displacement in the hypocentral plane in (a) FP and (b) FN directions Figure Strike-slip earthquake Residual (permanent) (a) FP and (b) FN components of displacement in the horizontal hypocentral plane. Figure Strike-slip earthquake Spatial distribution of the absolute values of the FP and FN components of the free surface peak (a) velocity and (b) displacement, as well as the maximum amplitudes of the corresponding resultant velocities and displacements Figure Strike-slip earthquake Synthetic seismoscope records of the horizontal displacement path at a number of locations on a regular grid on the free surface Figure Strike-slip earthquake Seismograms of acceleration in two orthogonal directions at selected locations on the free surface Open circles indicate the locations of the observation points, and the direction of motion is denoted by the orientation of the seismograms The direction of particle motion at each location is perpendicular to the time axes of the corresponding seismogram Figure Strike-slip earthquake Seismograms of velocity in two orthogonal directions at selected locations on the free surface Location and seismogram identification as in Fig Figure 10 Strike-slip earthquake Seismograms of displacement in two orthogonal directions at selected locations on the free surface Location and seismogram identification as in Fig Figure 11 Strike-slip earthquake Response spectra for percent critical damping for ground motion in the FN direction, calculated from the corresponding seismograms in Fig The spectra are plotted in the usual tripartite logarithmic representation, with pseudo-velocity on the vertical axis and period on the horizontal axis The periods considered range from 0.5s to 8.0s Figure 12 Strike-slip earthquake Same as Fig 11 for ground motion in the FP direction Figure 13 Thrust-fault earthquake Spatial distribution of the absolute values of the slip-parallel (SP) and slip-normal (SN) components of the free surface peak (a,b) velocity and displacement (c,d) White dot denotes the location of the epicenter and white rectangle the projection of the causative fault on the horizontal plane Figure 14 Thrust-fault earthquake Synthetic seismoscope records of the horizontal displacement path at a number of locations on a regular grid on the free surface Figure 15 Thrust-fault earthquake Seismograms of acceleration in two orthogonal directions at selected locations on the free surface Open circles indicate the locations of the observation points, and the direction of motion is denoted by the orientation of the seismograms The direction of particle motion at each location is perpendicular to the time axes of the corresponding seismogram Figure 16 Thrust-fault earthquake Seismograms of velocity in two orthogonal directions at selected locations on the free surface Location and seismogram identification as in Fig 15 Bielak 37 37 Figure 17 Thrust-fault earthquake Seismograms of displacement in two orthogonal directions at selected locations on the free surface Location and seismogram identification as in Fig 15 Figure 18 Thrust-fault earthquake Response spectra for percent critical damping for ground motion in the SN direction, calculated from the corresponding seismograms in Fig 15 The spectra are plotted in the usual tripartite logarithmic representation, with pseudo-velocity on the vertical axis and period on the horizontal axis The periods considered range from 0.5s to 8.0s Figure 19 Thrust-fault earthquake Same as Fig 18 for ground motion in the SP direction Bielak 38 38 ... the distribution of ground motion with sufficient fidelity Thus, there is an important need for developingfor highresolution, realistic simulations of ground motions in a region to study the seismological,... Bulletin of the Seismological Society of America, 86, 575-596 Pitarka, A., 1999., 3D elsticelastic finite-difference modeling of seisicseismic motion using staggered grids with non-uniform spacing,... provide insight into the spatial distribution of the dynamic response of elastic SDF systems to the ground motion Figures and show the response spectra for five percent critical damping in the