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Bulletin of the Seismological Society of America
Investigating the characteristics of near-source ground motions using pseudo-dynamicsource models derived with 1-point and 2-point statistics of earthquake source
parameters--Manuscript Draft--
Manuscript Number:
Article Type: Article
Section/Category: Regular Issue
Full Title: Investigating the characteristics of near-source ground motions using pseudo-dynamicsource models derived with 1-point and 2-point statistics of earthquake sourceparameters
Corresponding Author: Seok Goo Song, Ph.D.Korea Institute of Geoscience and Mineral ResourcesDaejeon, KOREA, REPUBLIC OF
Corresponding Author's Institution: Korea Institute of Geoscience and Mineral Resources
Corresponding Author E-Mail: [email protected]
Order of Authors: Donghee Park
Seok Goo Song
Junkee Rhie
Abstract: Ground motion prediction is an important element in seismic hazard analysis.However, the availability of recorded strong ground motion data is limited, particularlyfor large events in near-source regions. Recently, several physics-based groundmotion simulation approaches have been developed, which may be useful forunderstanding the effect of earthquake source on near-source ground motioncharacteristics. In this study we investigated the characteristics of near-source groundmotions controlled by finite-source processes, utilizing pseudo-dynamic sourcemodeling, based on 1-point and 2-point statistics of earthquake source parameters. Wesimulated ground motions for Mw 6.6 and 7.0 vertical strike-slip events using pseudo-dynamic source models derived from multiple sets of input source statistics, andinvestigated the characteristics of near-source ground motions relative to the inputsource statistics. Our results show that the effect of earthquake source on near-sourceground motions can vary depending on the locations of near-source stations. Thevariability of ground motion intensities derived from multiple sets of input sourcestatistics is more dominant in the forward directivity region. The pseudo-dynamicsource modeling method with 1-point and 2-point statistics seems to be an efficientframework for understanding the effect of earthquake source on near-source groundmotion characteristics.
Author Comments: This paper is submitted for the first author (Ms. Donghee Park) to obtain Ph.D degree.It would be grateful if the manuscript is reviewed in a timely manner.
Suggested Reviewers: Mathieu [email protected] Causse
Jorge [email protected]
Asako [email protected]
Opposed Reviewers:
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Submitted to Bull. Seism. Soc. Am.
1
Investigating the characteristics of near-source ground motions using 1
pseudo-dynamic source models derived with 1-point and 2-point 2
statistics of earthquake source parameters 3
4
Donghee Park 5
School of Earth and Environmental Sciences, Seoul National University 1, Gwanak-ro, Gwanak-6
gu, Seoul, 08826, Republic of Korea 7
9
Seok Goo Song 10
Earthquake Research Center, Korea Institute of Geoscience and Mineral Resources, 124, Gwahak- 11
ro, Yuseong-gu, Daejeon, 34132, Republic of Korea 12
14
Junkee Rhie 15
School of Earth and Environmental Sciences, Seoul National University 1, Gwanak-ro, Gwanak-16
gu, Seoul, 08826, Republic of Korea 17
19
Manuscript Click here to access/download;Manuscript;BSSA-manuscript.docx
Pseudo-Dynamic Source Modeling
2
Abstract 20
Ground motion prediction is an important element in seismic hazard analysis. However, the 21
availability of recorded strong ground motion data is limited, particularly for large events in near-22
source regions. Recently, several physics-based ground motion simulation approaches have been 23
developed, which may be useful for understanding the effect of earthquake source on near-source 24
ground motion characteristics. In this study we investigated the characteristics of near-source 25
ground motions controlled by finite-source processes, utilizing pseudo-dynamic source modeling, 26
based on 1-point and 2-point statistics of earthquake source parameters. We simulated ground 27
motions for Mw 6.6 and 7.0 vertical strike-slip events using pseudo-dynamic source models derived 28
from multiple sets of input source statistics, and investigated the characteristics of near-source 29
ground motions relative to the input source statistics. Our results show that the effect of earthquake 30
source on near-source ground motions can vary depending on the locations of near-source stations. 31
The variability of ground motion intensities derived from multiple sets of input source statistics is 32
more dominant in the forward directivity region. The pseudo-dynamic source modeling method 33
with 1-point and 2-point statistics seems to be an efficient framework for understanding the effect 34
of earthquake source on near-source ground motion characteristics. 35
Submitted to Bull. Seism. Soc. Am.
3
Introduction 36
It has been noted that the Korean Peninsula belongs to a stable seismic zone in comparison with 37
active seismic zones, such as the western United States and neighboring Japan. However, 38
according to historical earthquake data that covers approximately 2,000 years, it is known that 39
there was a time period in which many large earthquakes (Modified Mercalli Intensity, MMI > 40
VII) occurred in the southeastern region of the Korean Peninsula (Lee and Yang, 2006). As 41
instrumental earthquake data have been accumulated since 1905, it is also known that moderate 42
earthquakes (ML=5.0) took place several times, and caused damaged more than more than 5 times 43
(e.g., the Ssanggyesa earthquake (ML=5.0) on June 4, 1936, the Hongsung earthquake (ML=5.0) on 44
October 7, 1978, the Gyeongju earthquakes (ML=5.1, ML=5.8) on September 12, 2016, and the 45
Pohang earthquake (ML=5.4) on November 15, 2017. Even though an earthquake of ML 6.0 or 46
greater, which might cause serious damages, have not taken place in the last century, predicting 47
potential seismic hazards has become a more important issue after the occurrence of the Gyeongju 48
earthquake (ML=5.8) on September 12 2016, which is considered to be the largest earthquake in 49
South Korea since the initiation of instrumental recordings (i.e., since 1905). 50
Empirical ground motion prediction equations (GMPEs) have been widely used for probabilistic 51
seismic hazard analysis (PSHA) because they are directly constrained by the observed data 52
(Abrahamson et al., 2008). Boommer and Abrahamson (2006) noted that GMPE controls the 53
shapes of the seismic hazard curves and has a significant impact on PSHA. However, the 54
availability of recorded strong ground motion data is limited, particularly in near-source regions, 55
Pseudo-Dynamic Source Modeling
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even in very active seismic regions. Strasser et al. (2009) illustrated the problem and challenges that 56
arise when we constrain GMPEs for various spectral frequencies with a lack of near-source strong 57
motion recordings. 58
In Korea, there have been few strong ground motion records produced, and it is difficult to 59
develop GMPEs based on the observed data. Therefore, most of the previous GMPE studies (Park 60
et al., 2001; Jo and Baag, 2003; Yun et al., 2005; Korea Hydro and Nuclear Power Co., Ltd 61
(KHNP), 2015) have constrained a few physical parameters, such as stress drop and attenuation 62
(Q) for a small range of earthquake magnitudes, and simulated ground motions for a wide range 63
of earthquake magnitude using the stochastic point-source ground motion model developed by 64
Boore (1996, 2005). Park et al. (2001) used 26 events with local magnitude ranges from 1.4 and 65
4.3, which occurred from 1997 to 1999. Jo and Baag (2003) used 16 events that occurred from 66
1999 to 2001. The only empirical GMPE based on observed data in Korea was presented by Emolo 67
et al. (2015). They analyzed data from 222 earthquakes recorded at 132 three-component stations 68
of the South Korea Seismic Network, from 2007 to 2012, with local magnitudes ranging between 69
2.0 and 4.9. They noted that because of the characteristics of the adopted database, their GMPEs 70
can be confidently applied up to a maximum local magnitude of 5.0. However, there are still many 71
limitations in our understanding of the physical characteristics of near-source ground motions and 72
their attenuation with distance in Korea. 73
Physics-based ground motion simulation methods have received much attention as the effect of 74
finite-source processes on near-source ground motion characteristics can be efficiently taken into 75
Submitted to Bull. Seism. Soc. Am.
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account and understood. Dynamic rupture modeling has been successfully used in physics-based 76
modeling for decades (Olsen et al., 1997; Dalguer et al., 2008; Ripperger et al., 2008; Shi and Day, 77
2013). The finite-faulting process in dynamic modeling is governed by stress and frictional 78
behavior. This approach enables us to generate the physically self-consistent spatio-temporal 79
evolution of a finite-source model. However, dynamic modeling requires high-cost computing 80
resources and time to generate synthetic waveforms of large earthquakes. As an alternative method, 81
pseudo-dynamic source modeling has been introduced to improve computational efficiency. The 82
framework of pseudo-dynamic source modeling is still that of a kinematic source model, while it 83
simultaneously emulated the source physics inferred from rupture dynamics and observations 84
(Guatteri et al., 2004; Song and Somerville, 2010; Mena et al., 2012; Schmedes et al., 2013; Song 85
et al., 2014). 86
Song et al. (2014) developed a pseudo-dynamic source modeling method based on the 1-point 87
and 2-point statistics of earthquake source parameters. They demonstrated that the effect of 88
earthquake source processes on near-source ground motions could be investigated efficiently in 89
the framework of 1-point and 2-point statistics. Song (2016) developed a generalized pseudo-90
dynamic source statistics model for Mw 6.5–7.0 earthquakes by analyzing a number of dynamic 91
rupture models, and validated the synthetic broadband ground motions derived from the pseudo-92
dynamic source models against empirical GMPEs. 93
In recent studies, near-source ground motion characteristics have been studied through finite-94
source modeling approaches. Vyas et al. (2016) analyzed ground motion datasets simulated from 95
Pseudo-Dynamic Source Modeling
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the kinematic source parameters of the Mw 7.3 Landers earthquake of 1992 in terms of the distance 96
and azimuth-dependence of the peak ground velocity. Their simulations revealed that intra-event 97
ground motion variability is higher closer to the fault and decreases with increasing distance. The 98
physical explanation of high near-source ground motion variability is the presence of strong 99
directivity and rupture complexity. Crempien and Archuleta (2017) simulated kinematic rupture 100
scenarios on several vertical strike-slip faults and computed ground motions using a representation 101
theorem. They demonstrated that both intra-event and inter-event ground motion variabilities 102
increase when the slip correlation length on the fault increases. Imitiaz et al. (2015) studied the 103
distance dependency of ground motion variability, especially in near-source regions, using ground 104
motions for strike-slip events, which were generated from finite rupture models of past earthquakes. 105
They showed that the standard deviation of ground motions depends significantly on the rupture 106
type. For bilateral ruptures, variability tends to increase with distance. On the contrary, the 107
variability of unilateral events decreases with distance. They also noted that unilateral rupture 108
models would strengthen directivity effects. 109
This study builds upon previous work by Song et al. (2014), who illustrated the efficiency of 110
pseudo-dynamic source models based on 1-point and 2-point statistics of kinematic source 111
parameters. Here, we extend this previous work by investigating how the input 1-point and 2-point 112
statistics affect near-source ground motion characteristics, especially with respect to the specific 113
locations of near-source stations, such as a forward rupture directivity zone. We simulated ground 114
motions for Mw 6.6 and 7.0 vertical strike-slip events using pseudo-dynamic source models derived 115
from multiple sets of input source statistics, and investigated the characteristics of near-source 116
Submitted to Bull. Seism. Soc. Am.
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ground motions relative to the input source statistics. 117
Source Modeling 118
Pseudo-dynamic source modeling 119
To simulate ground motions for a target event, many source parameters are needed to 120
characterize a finite-fault rupture model, such as rupture dimension (length and width) and 121
kinematic rupture parameters (slip, rupture velocity, and peak slip velocity). If we assume that 122
future earthquakes share the finite-source characteristics of past earthquakes, at least in a statistical 123
sense, we may constrain earthquake parameters for future events by studying the characteristics of 124
past earthquakes (Mai and Beroza, 2000; Mai and Beroza, 2002; Song et al., 2009). However, we 125
are often limited to resolving the details of a kinematic rupture model, especially the temporal 126
source parameters such as rupture velocity and peak slip velocity, by inverting geophysical data 127
observed on the ground for past events (Beresnev, 2003; Mai et al., 2016). Researchers often rely 128
on spontaneous, dynamic rupture models to extract physics-based correlation structures between 129
earthquake slips and temporal source parameters, which have been categorized as pseudo-dynamic 130
source modeling (Guatteri et al., 2004; Schmedes et al., 2010; Song et al., 2010; Mena et al., 2012). 131
In other words, pseudo-dynamic source modeling is still kinematic modeling, but it utilizes the 132
physical correlation structures of kinematic source parameters derived from spontaneous, dynamic 133
rupture modeling. 134
Song et al. (2014) proposed characterizing earthquake rupture processes within a framework of 135
Pseudo-Dynamic Source Modeling
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the 1-point and 2-point statistics of key kinematic source parameters. In brief, their approach 136
involved assigning a set of random spatial fields to a finite-fault plane to model the spatial 137
distribution of several key kinematic source parameters, such as slip, rupture velocity (Vr), and 138
peak slip velocity (Vmax). In other words, one random field was assigned to each source parameter, 139
and one random variable (i.e., one element of the random field was assigned to every subfault 140
patch on the fault). If there are three source parameters, there are also three random fields. The 141
number of random variables for each random field is equal to the number of subfault patches on 142
the finite fault. The 1-point statistics is a marginal probability density function at a given point on 143
the fault. If a Gaussian distribution is assumed, the mean and standard deviation are the two main 144
representative parameters that control the possible range of values for each source parameter. The 145
2-point statistics is composed of both auto and cross correlation. Autocorrelation controls the 146
heterogeneity of each source parameter, while cross-correlation controls the coupling between 147
source parameters. Once the 1-point and 2-point statistics are modeled for a certain event, finite-148
source rupture scenarios can be generated by stochastic modeling. 149
Song (2016) developed a source statistics model by analyzing a number of spontaneous, dynamic 150
rupture models ranging in magnitude from Mw 6.5–7.0. He assumed a multivariate Gaussian 151
distribution for a random field model and developed an input source statistics model for both 1-152
point (mean and standard deviation of source parameters) and 2-point statistics (correlation length 153
and correlation coefficient). For 2-point statistics, a simple exponential function was adopted, as 154
given in equation (1), for a functional form of correlation: 155
Submitted to Bull. Seism. Soc. Am.
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𝜌(ℎ) = 𝜌𝑚𝑎𝑥 ∙ 𝑒𝑥𝑝(−√((ℎ𝑥 − 𝑅𝐷𝑥)/𝑎𝑥)2 + ((ℎ𝑧 − 𝑅𝐷𝑧)/𝑎𝑧)2 )); ℎ = (ℎ𝑥, ℎ𝑧), (1) 156
where h is the separation vector between two locations on the fault. The remaining parameters are 157
as follows: 𝑎𝑥 and 𝑎𝑧 are correlation lengths in the along-strike and along-dip directions, 158
respectively (six parameters: slip versus slip, slip versus Vr, slip versus Vmax, Vr versus Vr, Vr 159
versus Vmax, Vmax versus Vmax). The maximum correlation coefficient is denoted as 𝜌𝑚𝑎𝑥 160
(three parameters: slip versus Vr, slip versus Vmax, Vr versus Vmax); 𝑅𝐷𝑥 and 𝑅𝐷𝑧 are the 161
response distances in the along-strike and along-dip directions (three parameters: slip versus Vr, 162
slip versus Vmax, Vr versus Vmax). 163
The complete form of input parameters for the source statistics model is defined in Table 1 of 164
Song (2016). We set both response distances (i.e., 𝑅𝐷𝑥 and 𝑅𝐷𝑧) to zero in this study because 165
most models used by Song (2016) exhibited near-zero values for these parameters. However, due 166
to rupture propagation effects, particularly in long strike-slip events, the response distance could 167
be relatively large (Song et al., 2009; Song and Sommerville, 2010). The response distance may 168
play an important role in controlling the directivity effects in future studies. Since we considered 169
3 kinematic source parameters (i.e., slip, rupture velocity, and peak slip velocity) for pseudo-170
dynamic source modeling, there were 6 input parameters for 1-point statistics and 15 input 171
parameters for 2-point statistics. 172
In this study, we simulated 4 sets of pseudo-dynamic source models for both Mw 6.6 and 7.0 173
vertical strike-slip target events. The geometry of both target events is summarized in Table 1. 174
Input models were extracted from the source statistics model developed by Song (2016), and are 175
Pseudo-Dynamic Source Modeling
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summarized in Tables 2 and 3. For each set of input source statistics model, 30 earthquake scenario 176
models were developed to allow for statistical stability when we investigated near-source ground 177
motion characteristics. Figure 1 shows an example of four different pseudo-dynamic source 178
models for the Mw 7.0 target event, and we present examples of four different pseudo-dynamic 179
source models for the Mw 6.6 in Figure S1. 180
Perturbation of 1-point and 2-point statistics 181
In this study we aimed to investigate the characteristics of near-source ground motions controlled 182
by the 1-point and 2-point statistics of pseudo-dynamic source models. We adopted the same 183
strategy of perturbing 1-point and 2-point statistics as that used by Song et al. (2014). Thus, we 184
can systematically investigate the effect of input source statistics models on near-source ground 185
motion characteristics. Pseudo-dynamic source models are presented in Figure 2 and Figure S2 186
after perturbing their 1-point statistics. The 1-point statistics of Vr and Vmax (i.e., their standard 187
deviations), were reduced by half or expanded by a factor of two, respectively. 188
For 2-point statistics, the cross-correlations of slip-Vr, slip-Vmax, and Vr-Vmax were 189
sequentially perturbed. Finally, 6 sets of pseudo-dynamic source models were constructed, which 190
were linked to the perturbation of 1-point statistic, and 7 sets of models were constructed that were 191
linked to the perturbation of 2-point statistics. Given an input source statistics model, 420 (= (1 + 192
6 + 7) 30) pseudo-dynamically generated source models were produced for each target 193
magnitude, including both the original and perturbed pseudo-dynamic source models. We then 194
compared ground motions generated from all 6 sets of pseudo-dynamic source models for 1-point 195
Submitted to Bull. Seism. Soc. Am.
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statistics and 7 sets of pseudo-dynamic source models for 2-point statistics with those generated 196
from the original pseudo-dynamic modeling a statistical sense. 197
Figures 3 and S3 show how the simulated source parameters were affected by perturbing the 198
input 2-point statistics. The pseudo-dynamic source model in Figure 3(a) includes the full 199
correlation of 2-point statistics, and it can be seen that high slip patches are correlated with high 200
rupture and peak slip velocities. However, in Figure 3(h), no coupling is observed between the 201
source parameters since the correlation coefficients of the off-diagonal components were set to 202
zero. Figure 3(b–g) shows additional sets of perturbed pseudo-dynamic source models for 2-point 203
statistics. Since there were three off-diagonal cross-correlation structures, 7 different sets of 204
perturbation for 2-point statistics, as in Figure 3, were constructed. The corresponding 205
autocorrelation matrices and 1-point statistics were retained while perturbing the cross-correlation 206
matrices. 207
Characteristics of near-source ground motions 208
Ground motion modeling 209
We initially generated 30 scenario earthquakes via stochastic modeling for each input source 210
statistics model shown in Tables 2 and 3. The slip velocity function (SVF) proposed by Tinti et al. 211
(2005) was adopted to compute the spatio-temporal evolution of earthquake-generated rupturing 212
along the fault. The pseudo-dynamically generated finite-source models were combined with 213
Green's functions computed by the FK method (Zhu and Rivera, 2002). Then, we generated three-214
Pseudo-Dynamic Source Modeling
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component (fault-normal, fault-parallel, and vertical) synthetic seismograms that were effective 215
up to 3 Hz. Figure 4 shows the locations of 168 stations along with the surface trace of the rupture 216
dimension for the Mw 6.6 event. The circle size of each station indicates the mean Peak Ground 217
Velocity (PGV) (normal fault) of 30 earthquake scenarios for the first source statistics model (SSM) 218
in Table 2. Two colored areas show both the forward and backward directivity regions, which were 219
analyzed with the perturbation of 1-point and 2-point statistics in this study. Synthetic waveforms 220
at a few selected stations shown in Figure 4 are displayed in Figure 5. Figure 6 shows the locations 221
of 400 stations, with the surface trace of the rupture dimension for the Mw 7.0 event, and Figure 7 222
shows waveforms at the stations selected in Figure 6. We observed the forward directivity effect 223
especially clearly in the normal fault component. 224
Directivity effects of 1-point and 2-point statistics 225
Directivity effects indicate that earthquake ground motions, especially fault normal components, 226
are more severe in the direction of rupture propagation than in other directions. Sommerville et al. 227
(1997) showed that rupture directivity effects cause spatial variations in ground motion amplitudes 228
and durations around faults, and cause differences between the fault-normal and fault-parallel 229
components of horizontal ground motion amplitudes, which also have spatial variation around the 230
fault. They also found that for strike-slip faulting, the directivity effect on amplitudes is weak at 231
sites close to the epicenter, but grows large at sites located near the fault rupture zone but away 232
from the epicenter. Finally, they have developed the directivity term that accounts for the spatial 233
variations of ground-motion amplitudes and durations, which may be used in GMPEs. Bray and 234
Submitted to Bull. Seism. Soc. Am.
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Adrian (2004) developed empirical relationship between the PGV and period of the velocity pulse 235
of forward directivity motions. Spudich et al. (2008) introduced a new and physically-based 236
isochrone directivity predictor and models of directivity effect based on this predictor. The 237
directivity effect is an important element in understanding the near-source ground motion 238
characteristics, in particular in finite-source modeling. 239
As was discussed in the section "Pseudo-dynamic source modeling” above, 6 sets of pseudo-240
dynamic source models were constructed that are linked to the perturbation of 1-point statistics 241
and 7 sets of pseudo-dynamic source models that are linked to the perturbation of 2-point statistic. 242
We computed the PGV ratios with the waveforms obtained from the original and perturbed pseudo-243
dynamic source models in the selected forward and backward directivity zones as well as in the 244
total area in Figure 4 and Figure 6, and compared the maximum difference of the mean and 245
standard deviation of the PGV ratios. Figures 8 and 9 show the changes of the pseudo dynamically 246
generated ground motions after the perturbation of 1-point and 2-point statistics for both Mw 6.6 and 247
Mw 7.0 target events, respectively. 248
The mean and standard deviation of the PGV ratios were computed following the equations (2) 249
and (3), given below. 250
mean(𝑃𝐺𝑉𝑟𝑎𝑡𝑖𝑜) = 1
𝑛𝑚∑ ∑ 𝑙𝑜𝑔2((𝑃𝐺𝑉𝑝𝑒𝑟𝑡𝑢𝑏𝑎𝑡𝑒𝑑)𝑖𝑗 (𝑃𝐺𝑉𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙)𝑖𝑗⁄ )𝑚
𝑗=1𝑛𝑖=1 , (2) 251
sigma(𝑃𝐺𝑉𝑟𝑎𝑡𝑖𝑜) 252
=√1
𝑛𝑚−1∑ ∑ (𝑙𝑜𝑔2((𝑃𝐺𝑉𝑝𝑒𝑟𝑡𝑢𝑏𝑎𝑡𝑒𝑑)𝑖𝑗 (𝑃𝐺𝑉𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙)𝑖𝑗⁄ ) − 𝑚𝑒𝑎𝑛(𝑃𝐺𝑉𝑟𝑎𝑡𝑖𝑜))
2𝑚𝑗=1
𝑛𝑖=1 . (3) 253
Pseudo-Dynamic Source Modeling
14
where n is the number of selected stations for directivity analysis and m is the number of scenario 254
earthquake models (m = 30) 255
As was observed in Figures 8(a), 9(a), S4, and S6, the PGVs increased if the standard deviation 256
of either rupture velocity (Vr) or peak slip velocity (Vmax) increased. These results are consistent 257
with the findings of Song et al. (2014). Regarding the perturbation of 2-point statistics shown in 258
Figures 8(b), 9(b), S5, and S7, the PGVs were reduced once certain components of the off-diagonal 259
elements, shown in Figure 3, were removed. More interestingly, the PGVs are compatible with 260
those of the original pseudo-dynamic source models if the correlations between Vr and Vmax are 261
included (e.g., corr_23 in Figure 9). The right panels of Figures 8 and 9 show the standard 262
deviations of the PGV ratios computed by equation (3). We also found that the variations in ground 263
motions, as measured by the standard deviation, were generally greater in the forward directivity 264
region. 265
Figures 10 and 11 show the maximum differences of the PGV ratios for the Mw 6.6 and 7.0 target 266
event, respectively, after the perturbation of 1-point and 2-point statistics for all 4 input source 267
statistics models. The results clearly show that the ground motion intensity in the forward 268
directivity region is affected more significantly by the perturbation of source statistics in pseudo-269
dynamic source modeling. However, we also found that this pattern is not dominant for the 270
perturbation of 2-point statistics for the Mw 6.6 target event, which may imply that there is a 271
magnitude dependency for the forward directivity effect relative to the input source statistics 272
models. In other words, the greater the magnitude of the earthquake, the greater the influence of 273
Submitted to Bull. Seism. Soc. Am.
15
forward directivity. 274
Azimuthal dependency of 1-point and 2-point statistics 275
We also analyzed the dependency of the PGV ratios on azimuth. Figure 12 shows the 9 different 276
regions used in this analysis; each region had a 30º range. Figure 13 shows the azimuthal 277
dependency of the PGV ratios after the perturbation of 1-point and 2-point statistics for all 4 input 278
source statistics models for the Mw 7.0 target event. It can be clearly observed that the perturbation 279
effect of 1-point and 2-point statistics is more dominant in the forward directivity regions, such as 280
A1 and A2, and the effect is slightly greater in the backward directivity regions, such as A8 and 281
A9, than in regions A4–A7. This pattern may be affected by the near-source forward and backward 282
directivity effects since the difference is relatively low in the direction perpendicular to the fault 283
plane (A5). 284
Discussion 285
Our investigation of the sensitivity of near-source ground motions to pseudo-dynamic source 286
models was primarily focused on discerning the maximum difference, which can be observed from 287
the perturbation of 1-point and 2-point statistics, as shown in Figures 10 and 11. However, it would 288
also be interesting to examine the perturbation details between the maximum and minimum PGVs. 289
As shown in Figures 8(a),9(a), S4, and S6, the greater standard deviations of both rupture velocity 290
(Vr) and peak slip velocity (Vmax) produce stronger ground motions, although their means are not 291
perturbed The standard deviation of temporal source parameters such as Vr and Vmax was well 292
Pseudo-Dynamic Source Modeling
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constrained by neither kinematic source inversion nor pseudo-dynamic source modeling. Song 293
(2016) explicitly constructed probability density functions (PDFs) for these parameters, but they 294
were based on synthetic dynamic rupture models. Therefore, one must be careful when 295
determining the reasonable range of the standard deviations of these source parameters for physics-296
based ground motion modeling. Minimally, it may be desirable to test a wide range of possible 297
values. 298
Regarding the effect of 2-point perturbation, we also found interesting patterns. For example, if 299
the correlation structure contained a non-zero cross-correlation between Vr and Vmax (e.g., corr-300
23), it produced stronger ground motions, which were compatible with the ground motions derived 301
from the original pseudo-dynamic source model, as shown in Figure 9(b). Song et al. (2014) found 302
that the non-zero cross-correlation between slip and Vr (e.g., corr-12) shows the same effect. It 303
seems that it is not yet clear whether or not a certain correlation pair between source parameters 304
plays a dominant role in determining ground motion intensities. However, since the original 305
pseudo-dynamic source models always produce stronger ground motions when compared to the 306
pseudo-dynamic source models with no cross-correlation, it is important to determine an 307
appropriate level of cross-correlation between source parameters for physics-based ground motion 308
simulations. 309
The greater variation of near-source ground motions in the forward directivity zone may indicate 310
the potential utility of physics-based ground motion modeling for seismic hazards assessment of 311
specific sites. In advanced probabilistic seismic hazard analysis, the directivity effect, which 312
Submitted to Bull. Seism. Soc. Am.
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affects both the intensity and variability of ground motions in the directivity zones, may need to 313
be considered carefully, depending upon the direction and characteristics of nearby fault structures. 314
Even in Korea, major industrial facilities, such as nuclear power plants, are located adjacent to 315
fault lines, which need to be considered as line sources. The type of pseudo-dynamic source 316
modeling performed in this study may help to develop our understanding of a wide range of 317
potential variations in ground motions, which may be expected in the forward directivity zone. 318
Conclusions 319
In this study, we investigated the detailed characteristics of near-source ground motions 320
controlled by finite-source processes, utilizing pseudo-dynamic source modeling that were based 321
on the 1-point and 2-point statistics of earthquake source parameters. We simulated a large number 322
of near-source ground motions using vertical strike-slip pseudo-dynamic models of Mw 6.6 and 323
7.0, derived from multiple sets of input source statistics. We found that near-source ground motions 324
are more significantly affected by input source statistics models in the forward directivity zone, 325
and this effect is more dominant for larger events (Mw 7.0). It is important to understand the 326
characteristics of near-source ground motions in advanced seismic hazard analysis. The pseudo-327
dynamic source modeling method, with 1-point and 2-point statistics of kinematic source 328
parameters, seems to be an efficient framework for understanding the effect of earthquake source 329
processes on near-source ground motion characteristics systematically. 330
331
Pseudo-Dynamic Source Modeling
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Acknowledgments 332
This work was supported by the National Research Foundation of Korea (NRF) grant funded by 333
the Korean government (MSIT : Ministry of Science and ICT ) (No. NRF-2017M2A8A4015042) 334
and Basic Research Project of KIGAM (Korea Institute of Geology and Mining) funded by Korean 335
government (MSIT : Ministry of Science and ICT ).336
Submitted to Bull. Seism. Soc. Am.
19
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Song, S. G., L. A. Dalguer and P. M. Mai (2014). Pseudo-dynamic source modelling with 1-point
and 2-point statistics of earthquake source parameters, Geophys. J. Int., 196, 1770–1786,
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25
Full mailing address for each author
Donghee Park
School of Earth and Environmental Sciences, Seoul National University 1, Gwanak-ro, Gwanak-
gu, Seoul, 08826, Republic of Korea
(D. Park)
Seok Goo Song
Earthquake Research Center, Korea Institute of Geoscience and Mineral Resources, 124,
Gwahak-ro, Yuseong-gu, Daejeon, 34132, Korea
(S. G. Song)
Junkee Rhie
School of Earth and Environmental Sciences, Seoul National University 1, Gwanak-ro, Gwanak-
gu, Seoul, 08826, Republic of Korea
(J. Rhie)
Pseudo-Dynamic Source Modeling
26
Tables
Table 1. Source geometry of the simulated events.
Mw 6.6 Mw 7.0
Rupture dimension*
(length / width)
30 km /12 km 54 km /14 km
Depth to top of fault 2 km 0 km
Dip angle 90 degree (strike-slip)
Source statistics
model
Source statistics model
1, 2-1, 2-2, 3
(3 different input source
statistics models for Mw 6.6)
Source statistics model
1, 2-1, 2-2, 3
(3 different input source
statistics models for Mw 7.0)
Rupture dimension was determined, based on Wells and Coppersmith (1994).
Submitted to Bull. Seism. Soc. Am.
27
Table 2. Input 1-point and 2-point statistics models for Mw 6.6.
Model &
parameter Description
Source Statistics
Model 1
(SSM 1)
Source Statistics
Model 2-1, 2-2*
(SSM 2-1, SSM 2-2)
Source Statistics
Model 3
(SSM 3)
𝜇𝑠𝑙𝑖𝑝
𝜇𝑉𝑟
𝜇𝑉𝑚𝑎𝑥
Mean slip (cm)
Mean rupture velocity (km/s)
Mean peak slip velocity (cm/s)
73.02
2.18
113.14
75.02
1.61
98.66
75.02
1.79
99.77
𝜎𝑠𝑙𝑖𝑝
𝜎𝑉𝑟
𝜎𝑉𝑚𝑎𝑥
Standard deviation of slip (cm)
Standard deviation of rupture velocity (km/s)
Standard deviation of peak slip velocity (cm/s)
43.25
0.71
87.48
32.41
0.56
69.14
33.77
0.58
72.98
𝑎𝑥
Correlation length in the along-strike direction (km)
(slip vs. slip, slip vs. Vr, slip vs. Vmax,
Vr vs. Vr, Vr vs. Vmax, and Vmax vs. Vmax)
(3.9 2.6 2.4
1.3 5.6
6.3
) (5.1 5.7 12.1
3.6 12.8
9.5
) (6.2 7.9 7.5
4.6 15.9
16.4
)
𝑎𝑧
Correlation length in the along-dip direction (km)
(slip vs. slip, slip vs. Vr, slip vs. Vmax,
Vr vs. Vr, Vr vs. Vmax, and Vmax vs. Vmax)
(5.4 1.9 1.5
3.6 1.4
1.9
) (1.4 1.5 0.8
1.3 1.8
2.1
) (0.9 0.3 1.0
2.7 1.2
1.6
)
𝜌𝑚𝑎𝑥 Maximum correlation coefficient
(slip vs. Vr, slip vs. Vmax and Vr vs. Vmax) (
1 0.71 0.94
1 0.64
1.00
) (1 0.62 0.71
1 0.77
1.00
) (1 0.43 0.65
1 0.70
1
)
Two source statistics models (SSM 2-1 and SSM 2-2) share the same input values, but used different seed numbers in stochastic modeling.
1-p
oin
t st
atist
ics
2-p
oin
t st
atist
ics
Pseudo-Dynamic Source Modeling
28
Table 3. Input 1-point and 2-point statistics models for Mw 7.0.
Model &
parameter Description
Source Statistics
Model 1
(SSM 1)
Source Statistics
Model 2-1, 2-2*
(SSM 2-1, SSM 2-2)
Source Statistics
Model 3
(SSM 3)
𝜇𝑠𝑙𝑖𝑝
𝜇𝑉𝑟
𝜇𝑉𝑚𝑎𝑥
Mean slip (cm)
Mean rupture velocity (km/s)
Mean peak slip velocity (cm/s)
142.23
2.19
149.19
142.22
1.63
134.71
142.22
1.81
135.81
𝜎𝑠𝑙𝑖𝑝
𝜎𝑉𝑟
𝜎𝑉𝑚𝑎𝑥
Standard deviation of slip (cm)
Standard deviation of rupture velocity (km/s)
Standard deviation of peak slip velocity (cm/s)
81.29
0.76
117.98
70.44
0.62
99.64
71.81
0.63
103.48
𝑎𝑥
Correlation length in the along-strike direction (km)
(slip vs. slip, slip vs. Vr, slip vs. Vmax,
Vr vs. Vr, Vr vs. Vmax, and Vmax vs. Vmax) (
3.5 2.6 1.8
1.2 5.1
4.9
) (4.7 5.6 9.1
5.1 11.5
7.5
) (5.6 7.8 5.7
4.6 14.2
12.8
)
𝑎𝑧
Correlation length in the along-dip direction (km)
(slip vs. slip, slip vs. Vr, slip vs. Vmax,
Vr vs. Vr, Vr vs. Vmax, and Vmax vs. Vmax) (
11.1 3.5 3.2
4.4 1.8
2.2
) (3.1 2.8 1.8
1.4 2.4
2.5
) (1.8 0.6 2.1
3.1 1.5
1.9
)
𝜌𝑚𝑎𝑥 Maximum correlation coefficient
(slip vs. Vr, slip vs. Vmax and Vr vs. Vmax) (1 0.78 0.90
1 0.68
1
) (1 0.70 0.67
1 0.82
1
) (1 0.51 0.61
1 0.74
1
)
Two source statistics models (SSM 2-1 and SSM 2-2) share the same input values, but used different seed numbers in stochastic modeling.
1-p
oin
t st
atist
ics
2-p
oin
t st
atist
ics
Submitted to Bull. Seism. Soc. Am.
29
List of Figure Captions
Figure 1. Source modeling examples for the Mw 7.0 target event. One example of pseudo-dynamic
source model from each source statistics models in Table 3 is presented although 30 scenario
earthquakes were simulated by stochastic modeling for each input source statistics model.
Figure 2. Pseudo-dynamic source models after the perturbation of 1-point statistics for Mw 7.0
target event using source statistics model 1 (SSM 1) in Table 3. The standard deviation of the
rupture velocity (Vr) and peak slip velocity (Vmax) was reduced by half, or increased by a factor
of two.
Figure 3. Pseudo-dynamic source models after the perturbation of 2-point statistics for Mw 7.0
target event using source statistics model 1 (SSM 1) in Table 3. Three off-diagonal blocks were
perturbed sequentially. The perturbed correlation structures are also given on the right-hand side.
Figure 4. The locations of 168 stations with the surface trace of the rupture dimension of the target
Mw 6.6 event. The circle size of each station indicates the mean PGV (Peak Ground Velocity) of
the fault normal component of 30 scenario earthquakes using source statistics model 1 in Table 2.
The initial nucleation point is marked with a yellow star. The red numbers in the black box indicate
7 selected stations, whose waveforms are shown in Figure 5. Both forward and backward
directivity zones used in the analysis are also colored.
Pseudo-Dynamic Source Modeling
30
Figure 5. Comparison of the waveforms simulated by pseudo-dynamic modeling at the 7 selected
stations in Figure 4. The forward directivity effect is well observed especially in the fault normal
component.
Figure 6. The locations of 400 stations with the surface trace of the rupture dimension of the target
Mw 7.0 event. The circle size of each station indicates the mean PGV (Peak Ground Velocity) of
the fault normal component of 30 scenario earthquakes using source statistics model 1 in Table 3.
The initial nucleation point is marked with a yellow star. The red numbers in the black box indicate
7 selected stations, whose waveforms are shown in Figure 7. Both forward and backward
directivity zones used in the analysis are also colored.
Figure 7. Comparison of the waveforms simulated by pseudo-dynamic modeling at the selected
stations in Figure 6. The forward directivity effect is well observed especially in the fault normal
component.
Figure 8. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point (top) and 2-point (bottom) statistics for the Mw 6.6 target event using source statistics
model 1 in Table 2. The y-axes of the left and right panels indicate the mean and standard deviation
of the log-scale of the PGV ratios, respectively. The PGV ratios were computed with the
waveforms obtained from the original and perturbed pseudo-dynamic source models in the
Submitted to Bull. Seism. Soc. Am.
31
selected forward and backward directivity zones as well as in the total area. The black dashed
arrows represent the maximum difference of the mean and sigma of the PGV ratios, shown in
Figure 10.
Figure 9. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point (top) and 2-point (bottom) statistics for the Mw 7.0 target event using source statistics
model 1 in Table 3. The y-axes of the left and right panels indicate the mean and standard deviation
of the log-scale of the PGV ratios, respectively. The PGV ratios were computed with the
waveforms obtained from the original and perturbed pseudo-dynamic source models in the
selected forward and backward directivity zones as well as in the total area. The black dashed
arrows represent the maximum difference of the mean and sigma of the PGV ratios, shown in
Figure 11.
Figure 10. Comparison of the maximum difference of the mean and standard deviation of the PGV
ratios for the Mw 6.6 target event in Figure 8, but for all 4 models.
Figure 11. Comparison of the maximum difference of the mean and standard deviation of the PGV
ratios for the Mw 7.0 target event in Figure 9, but for all 4 models.
Figure 12. The 9 different azimuthal zones used for the analysis of the azimuthal dependency for
the stations in Figure 6. The analysis of the azimuthal dependency was performed with each 30-
Pseudo-Dynamic Source Modeling
32
degree interval.
Figure 13. Azimuthal dependency of the difference of the mean PGV ratios after the perturbation
of 1-point (top) and 2-point (bottom) statistics for the 4 source models of Mw 7.0 target event.
Submitted to Bull. Seism. Soc. Am.
33
Figures
Figure 1. Source modeling examples for the Mw 7.0 target event. One example of pseudo-dynamic
source model from each source statistics models in Table 3 is presented although 30 scenario
earthquakes were simulated by stochastic modeling for each input source statistics model.
Pseudo-Dynamic Source Modeling
34
Figure 2. Pseudo-dynamic source models after the perturbation of 1-point statistics for Mw 7.0
target event using source statistics model 1 (SSM 1) in Table 3. The standard deviation of the
rupture velocity (Vr) and peak slip velocity (Vmax) was reduced by half, or increased by a factor
of two.
Submitted to Bull. Seism. Soc. Am.
35
Figure 3. Pseudo-dynamic source models after the perturbation of 2-point statistics for Mw 7.0
target event using source statistics model 1 (SSM 1) in Table 3. Three off-diagonal blocks were
perturbed sequentially. The perturbed correlation structures are also given on the right-hand side.
Pseudo-Dynamic Source Modeling
36
Figure 3. (continued)
Submitted to Bull. Seism. Soc. Am.
37
Figure 4. The locations of 168 stations with the surface trace of the rupture dimension of the target
Mw 6.6 event. The circle size of each station indicates the mean PGV (Peak Ground Velocity) of
the fault normal component of 30 scenario earthquakes using source statistics model 1 in Table 2.
The initial nucleation point is marked with a yellow star. The red numbers in the black box indicate
7 selected stations, whose waveforms are shown in Figure 5. Both forward and backward
directivity zones used in the analysis are also colored.
Pseudo-Dynamic Source Modeling
38
Figure 5. Comparison of the waveforms simulated by pseudo-dynamic modeling at the 7 selected
stations in Figure 4. The forward directivity effect is well observed especially in the fault normal
component.
Submitted to Bull. Seism. Soc. Am.
39
Figure 6. The locations of 400 stations with the surface trace of the rupture dimension of the target
Mw 7.0 event. The circle size of each station indicates the mean PGV (Peak Ground Velocity) of
the fault normal component of 30 scenario earthquakes using source statistics model 1 in Table 3.
The initial nucleation point is marked with a yellow star. The red numbers in the black box indicate
7 selected stations, whose waveforms are shown in Figure 7. Both forward and backward
directivity zones used in the analysis are also colored.
Pseudo-Dynamic Source Modeling
40
Figure 7. Comparison of the waveforms simulated by pseudo-dynamic modeling at the selected
stations in Figure 6. The forward directivity effect is well observed especially in the fault normal
component.
Submitted to Bull. Seism. Soc. Am.
41
Figure 8. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point (top) and 2-point (bottom) statistics for the Mw 6.6 target event using source statistics
model 1 in Table 2. The y-axes of the left and right panels indicate the mean and standard deviation
of the log-scale of the PGV ratios, respectively. The PGV ratios were computed with the
waveforms obtained from the original and perturbed pseudo-dynamic source models in the
selected forward and backward directivity zones as well as in the total area. The black dashed
arrows represent the maximum difference of the mean and sigma of the PGV ratios, shown in
Figure 10.
Pseudo-Dynamic Source Modeling
42
Figure 9. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point (top) and 2-point (bottom) statistics for the Mw 7.0 target event using source statistics
model 1 in Table 3. The y-axes of the left and right panels indicate the mean and standard deviation
of the log-scale of the PGV ratios, respectively. The PGV ratios were computed with the
waveforms obtained from the original and perturbed pseudo-dynamic source models in the
selected forward and backward directivity zones as well as in the total area. The black dashed
arrows represent the maximum difference of the mean and sigma of the PGV ratios, shown in
Figure 11.
Submitted to Bull. Seism. Soc. Am.
43
Figure 10. Comparison of the maximum difference of the mean and standard deviation of the PGV
ratios for the Mw 6.6 target event in Figure 8, but for all 4 models.
Pseudo-Dynamic Source Modeling
44
Figure 11. Comparison of the maximum difference of the mean and standard deviation of the PGV
ratios for the Mw 7.0 target event in Figure 9, but for all 4 models.
Submitted to Bull. Seism. Soc. Am.
45
Figure 12. The 9 different azimuthal zones used for the analysis of the azimuthal dependency for
the stations in Figure 6. The analysis of the azimuthal dependency was performed with each 30-
degree interval.
Pseudo-Dynamic Source Modeling
46
Figure 13. Azimuthal dependency of the difference of the mean PGV ratios after the perturbation
of 1-point (top) and 2-point (bottom) statistics for the 4 source models of Mw 7.0 target event.
Submitted to Bull. Seism. Soc. Am.
1
Supplemental Material
List of Figure Captions for Supplemental Material
Figure S1. Source modeling examples for Mw 6.6 target event. One example of pseudo-dynamic
source model from each source statistics models in Table 2 is presented although 30 scenario
earthquakes were simulated by stochastic modeling for each input source statistics model.
Figure S2. Pseudo-dynamic source models after the perturbation of 1-point statistics for Mw 6.6
target event using source statistics model 1 in Table 2. The standard deviation of the rupture
velocity (Vr) and peak slip velocity (Vmax) was reduced by half, or increased by a factor of two.
Figure S3. Pseudo-dynamic source models after the perturbation of 2-point statistics for Mw 6.6
target event using source statistics model 1 in Table 2. Three off-diagonal blocks were perturbed
sequentially
Figure S4. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point statistics for the Mw 6.6 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
Source model 3
(Mw=7.0)
Supplemental Material (Main Page, Tables, Figures) Click here to access/download;Supplemental Material (MainPage, Tables, Figures);BSSA-supplemental material.docx
Pseudo-Dynamic Source Modeling
2
Figure S5. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 2-point statistics for the Mw 6.6 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
Figure S6. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point statistics for the Mw 7.0 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
Figure S7. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 2-point statistics for the Mw 7.0 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area
Submitted to Bull. Seism. Soc. Am.
3
Figures
Figure S1. Source modeling examples for Mw 6.6 target event. One example of pseudo-dynamic
source model from each source statistics models in Table 2 is presented although 30 scenario
earthquakes were simulated by stochastic modeling for each input source statistics model.
Source model 3
(Mw=7.0)
Pseudo-Dynamic Source Modeling
4
Figure S2. Pseudo-dynamic source models after the perturbation of 1-point statistics for Mw 6.6
target event using source statistics model 1 in Table 2. The standard deviation of the rupture
velocity (Vr) and peak slip velocity (Vmax) was reduced by half, or increased by a factor of two.
Submitted to Bull. Seism. Soc. Am.
5
Figure S3. Pseudo-dynamic source models after the perturbation of 2-point statistics for Mw 6.6
target event using source statistics model 1 in Table 2. Three off-diagonal blocks were perturbed
sequentially.
Pseudo-Dynamic Source Modeling
6
Figure S4. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point statistics for the Mw 6.6 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
Submitted to Bull. Seism. Soc. Am.
7
Figure S5. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 2-point statistics for the Mw 6.6 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
Pseudo-Dynamic Source Modeling
8
Figure S6. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 1-point statistics for the Mw 7.0 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
Submitted to Bull. Seism. Soc. Am.
9
Figure S7. Comparison of the pseudo dynamically generated ground motions after the perturbation
of 2-point statistics for the Mw 7.0 target event using source statistics models 2-1, 2-2, and 3. The
y-axes of the left and right panels indicate the mean and standard deviation of the log-scale of the
PGV ratios, respectively. The PGV ratios were computed with the waveforms obtained from the
original and perturbed pseudo-dynamic source models in the selected forward and backward
directivity zones as well as in the total area.
