# V

Authors: Yan Yu; Walter J. Silva; Bob Darragh; Xiaojun Li
Journal: International Journal of Geophysics
 (2016)

---

## Abstract

Several methods were used to estimateV
s
30 from site profiles with borehole depths of about 20 m for the strong-motion stations located in Southwest China. The methods implemented include extrapolation (constant and gradient), Geomatrix Site Classification correlation with shear-wave velocity, and remote sensing (terrain and topography). The gradient extrapolation is the preferred choice of this study for sites with shear-wave velocity profile data. However, it is noted that the coefficients derived from the California data set are not applicable to sites in Southwest China. Due to the scarcity of borehole profiles data with depth of more than 30 m in Southwest China, 73 Kiknet profiles were used to generate new coefficients for gradient extrapolation. Fortunately, these coefficients provide a reasonable estimate of V
s
30 for sites in Southwest China. This study showed V
s
30 could be estimated by the time-average shear-wave velocity (average slowness) of only 10 meters of depth. Furthermore, a median V
s
30 estimate based upon Geomatrix Classification is derived from the results of the gradient extrapolation using a regional calibration of the Geomatrix Classification with V
s
30. The results of this study can be applied to assign V
s
30 to the sites without borehole data in Southwest China.


---

## Body

## 1. Introduction

As ground motion records became more abundant, site amplification had been studied by many researchers. Hayashi et al. [1] proposed the average acceleration response spectra for various subsoil condition in Japan. Seed et al. [2] derived site-dependent spectra from 104 ground motion records obtained from 23 earthquakes, mostly in the western part of US. To meet the application of seismic engineering and measure the site amplification, V
s
30 (time-average shear-wave velocity with depth of 30 meters) was a principal parameter to represent site condition and widely used for site classification. Borcherdt [3] studied the relation between F
a and V
s
30 for NEHRP recommended building code provisions. Hartzell et al. [4] derived a correlation between site amplification and V
s
30 from the aftershock records of the 1989 Loma Prieta earthquake. Five NGA ground motion prediction models [5] all used V
s
30 for site classification. Although V
s
30 cannot, of course, capture all of the physics controlling site amplification [6], V
s
30 is widely accepted by seismic engineers for its simplicity and low cost.The most straightforward way to evaluateV
s
30 for a given site is to measure seismic velocities to a depth of at least 30 meters. For a number of reasons, engineering seismic exploration was always not available for target areas. Then, V
s
30 was estimated from proxies, which may be based on geomorphology [7, 8], geology [9], or geotechnical site categories [10]. Since many seismic explorations would not reach the depth of 30 meters, the empirical relationship between V
s
30 and V
s at shallower depths was derived from borehole data at target areas [11–15]. All these proxies were approximations and had obvious regional limitations. Stewart et al. [16] found the empirical relationship always overestimate V
s
30 for Greece. Boore et al. [12] found that the difference of empirical relationship between Japan and the other places resulted from the difference of site classification of borehole data.On May 12, 2008, an earthquake withM
w 7.9 occurred in Wenchuan county, Sichuan province, China, which resulted in widespread damage and a great number of casualties. During the Wenchuan earthquake, the National Strong-Motion Observation Network System (NSMONS) of China obtained 1,350 components of strong-motion records from the main shock, including records from 437 free-field stations in 17 provinces, municipalities, and autonomous regions, 1 topographic array (8 stations) in Sichuan province, and 2 temporary arrays (10 monitoring sites) for structural response at the Kunming mobile observatory [17–19]. After the main shock, 59 mobile instruments were deployed to record ground motion and structural response from strong aftershocks [20]. 15,903 components of digital strong-motion records were obtained from 949 aftershocks, in which 9750 components were recorded by portable instruments [20–22].In order to use these records from the Wenchuan main shock and aftershocks in the NGA (Next-Generation Attenuation) project of PEER (Pacific Earthquake Engineering Research Center), an estimate ofV
s
30 of the recording sites is needed. V
s
30 is a widely used parameter for classifying site condition regarding its ability to amplify seismic shaking. However, in China, the site classification is based on V
s
20, depth of 20 m, and the thickness of overlying soil over rock according to the Chinese site classification in the seismic design building code. During the construction of strong-motion stations in China, the investigation of the site condition only provides the information on the overlying soil layers of depths less than 20 m, including the thickness and shear-wave velocity of soil layers. In the site investigation, layers with shear-wave velocity greater than 500 m/s are considered bedrock. Therefore, most of the depths of drilling holes are less than 30 m at the strong-motion station sites. As a result, an important issue for the strong-motion stations in China is the use of shear-wave velocity profiles with borehole depth less than 30 m to assign a V
s
30.In this study, 147 shear-wave velocity profiles measured with borehole technique at the strong-motion station in Southwest China (Sichuan and Gansu provinces) were used. These strong-motion stations are located in the heavily damaged region of the Wenchuan earthquake. The locations of these stations are shown in Figure1. The Appendix gives the borehole depth, shear-wave velocity at the bottom of borehole, and whether or not the drilling reached bedrock (defined as V
s
>
500 m/s). There are 6 stations with borehole depth less than 10 m, 32 stations with borehole depth between 10 m and 20 m, and 109 stations with borehole depth larger than 20 m. This study estimates V
s
30 for these 147 stations based on the measured shear-wave velocity profiles to the depth available.Figure 1
Station distribution around the main shock.


## 2. Methodology

### 2.1. Simple Extrapolation

In this method, we assume that the shear-wave velocity from the bottom of the borehole to 30 m is constant atV
s measured at the borehole bottom. The time-average shear-wave velocity (average slowness, [23]), named V
s
30
p
r
o
f
i
l
e, was computed from the equation (1)
V
s
30
=
30
t
t
30
,where the travel time t
t
(
30
) was given by (2)
t
t
30
=
∫
0
30
d
Z
V
s
Z
.V
s
(
Z
) is the shear-wave velocity at depthZ.SinceV
s
30
p
r
o
f
i
l
e is based on the measured velocity profile data, it is taken as the reference value of V
s
30 for comparison with other empirical estimates.V
s
30
p
r
o
f
i
l
e is typically less than the actual V
s
30 in general as V
s generally increase with increasing depth. In cases, where the borehole depth is greater than 20 meters, the difference is generally small.


### 2.2. Geomatrix Classification Assignment

The PEER NGA database [10] includes 561 sites with borehole data. All the sites were assigned with a Geomatrix Classification according to geological and geographic conditions. The NGA Geomatrix Site Classification criteria are given as follows:A, rock: instrument on rock (V
s > 600 m/s) or <5 m of soil over rock.
B, shallow (stiff) soil: instrument on/in soil profile up to 20 m thick overlying rock.
C, deep narrow soil: instrument on/in soil profile at least 20 m thick overlying rock, in a narrow canyon or valley not more than several km wide.
D, deep broad soil: instrument on/in soil profile at least 20 m thick overlying rock, in a broad valley.
E, soft deep soil: instrument on/in deep soil profile with averageV
s < 150 m/s.A median V
s
30 and standard deviation have been obtained for each Geomatrix Classification based upon a global database of measured profiles. Table 1 gives the median V
s
30 and standard deviation.Table 1
MedianV
s
30  and standard deviation for NGA database [10] profiles based on Geomatrix Classification bins.
Geomatrix Classification
MedianV
s  (m/s)
σ (m/s)
N
A
660
324
74
B
424
211
97
C
338
70
44
D
274
110
306
E
191
61
40The Geomatrix Classification for the 147 Southwest China sites is 9 A sites, 52 B sites, 83 C sites, and 3 D sites.Next, we compare the median shear-wave velocity profiles of Southwest China (SWC) with NGA profiles based on Geomatrix Classification. The result is shown in Figure2. In the depth range of 0 to 5 m, the median V
s of SWC is less than that of NGA profiles on average. The near surface soils in SWC are softer than those in NGA. However, at depths below 5 m, the median V
s of SWC profiles is similar to that of NGA profiles, except for site class B. The site class B profile of SWC has a slightly larger median V
s than NGA.Figure 2
Comparison of medianV
s between Southwest China (SWC) profiles and NGA profiles.Since the median shear-wave velocity profiles of SWC sites are similar to those of the NGA sites, we may assign the medianV
s
30 to the sites with the same Geomatrix Classification, (V
s
30
G
e
o
m
a
t
r
i
x), with a small bias on the high side. Also, we can assign V
s
30 to sites without V
s profile but with a Geomatrix Classification, again slightly biased high.


### 2.3. Boore Extrapolation

Boore [11] used a set of 135 borehole profiles with depths greater than or equal to 30 m to estimate a correlation between V
s
30 and V
s
(
d
), which is time-average shear-wave velocity for a profile to depth d. V
s
(
d
) is given by(3)
V
s
d
=
d
t
t
d
,where d is the borehole depth and t
t
(
d
) is given by (2).Boore [11] found that the logarithm of V
s
30 against logarithm of V
s
(
d
) could be fit by a straight line, given by(4)
log
⁡
V
s
30
=
a
+
b
log
⁡
V
s
d
.Table2 gives the regression coefficients and standard deviation for Boore’s correlation equation from 135 California profiles.Table 2
Coefficients of (4) for 135 California profiles [11].
d (m)
a
b
σ
l
n
10
0.0421
1.0292
0.0713
11
0.0221
1.0341
0.0647
12
0.0126
1.0352
0.0594
13
0.0142
1.0318
0.0548
14
0.0123
1.0297
0.0501
15
0.0138
1.0263
0.0459
16
0.0139
1.0237
0.0422
17
0.0196
1.0190
0.0394
18
0.0249
1.0144
0.0364
19
0.0256
1.0117
0.0332
20
0.0254
1.0095
0.0302
21
0.0253
1.0072
0.0270
22
0.0269
1.0044
0.0241
23
0.0222
1.0042
0.0208
24
0.0169
1.0043
0.0177
25
0.0115
1.0045
0.0147
26
0.0066
1.0045
0.0115
27
0.0025
1.0043
0.0084
28
0.0008
1.0031
0.0055
29
0.0004
1.0015
0.0027Since the standard deviation of Boore’s estimate is less than 8 percent for stations with borehole depth larger than 10 m, we apply Boore’s empirical model, which is generated from California data, to the SWC profiles to estimateV
s
30 (V
s
30
Boore
cal), given by(5)
V
s
30
Boore
cal
=
1
0
a
+
b
log
⁡
V
s
d
,where the superscript Cal means that the model is based on California data.A comparison ofV
s
30
Boore
cal to V
s
30
p
r
o
f
i
l
e in the Appendix shows that Boore’s estimate for profiles with borehole depth greater than 20 m is very close to V
s
30
p
r
o
f
i
l
e, which has an average bias of 0.006. However, for the 32 profiles with borehole depth between 10 and 20 m, V
s
30
Boore
cal has an average bias of 0.139 (positive bias reflects an underprediction) relative to V
s
30
p
r
o
f
i
l
e. The result suggests that the coefficients of Boore’s estimate derived from California profiles may not be applicable to SWC profiles.Boore indicates thatV
s of SWC profiles is larger than that of California profiles in the same depth and the velocity gradients of these two regions are different, which results in the underestimate of V
s
30. Similar to Boore, in order to eliminate the difference of velocity gradients between the regions, we want to derive the coefficients from similar profiles.Linear and cubic fit to Kiknet profiles were performed to fitlog
⁡
(
V
s
30
) against log
⁡
(
V
s
(
d
)
). The cubic fit is given by the following equation:(6)
log
⁡
V
s
30
=
C
0
+
C
1
log
⁡
V
s
d
+
C
2
log
2
⁡
V
s
d
+
C
3
log
3
⁡
V
s
d
.According to (6), V
s
30 can be estimated by(7)
V
s
Boore
3
=
1
0
C
0
+
C
1
log
⁡
V
s
d
+
C
2
log
2
⁡
V
s
d
+
C
3
log
3
⁡
V
s
d
.Table3 gives the coefficients and standard deviation of linear and cubic fit based on Boore’s correlation equation applied to 73 Kiknet measured profiles with Geomatrix Classification, and Figure 3 displays the fit.Table 3
Coefficients and natural logarithm of the standard deviation for (4) and (6) from Kiknet profiles.
Depth (m)
a
b
C
0
C
1
C
2
C
3
σ
l
i
n
e
a
r
σ
c
u
b
i
c
5
1.3412
0.5626
1.0320
1.3924
−0.5117
0.0906
0.1174
0.1158
6
1.2498
0.5975
−1.2168
3.8378
−1.3922
0.1955
0.1120
0.1110
7
1.1650
0.6288
−1.1351
3.6074
−1.2640
0.1756
0.1062
0.1055
8
1.1071
0.6492
0.0978
2.1222
−0.6846
0.1022
0.1018
0.1012
9
1.0009
0.6878
−2.0070
4.3394
−1.4621
0.1928
0.0956
0.0952
10
0.9056
0.7223
−3.2943
5.6294
−1.8935
0.2410
0.0896
0.0894
11
0.8111
0.7559
−4.0334
6.2874
−2.0859
0.2595
0.0837
0.0835
12
0.7307
0.7840
−4.0876
6.2020
−2.0116
0.2464
0.0784
0.0782
13
0.6465
0.8132
−4.6981
6.7207
−2.1550
0.2592
0.0732
0.0729
14
0.5709
0.8389
−4.9266
6.8299
−2.1532
0.2550
0.0681
0.0677
15
0.5018
0.8617
−5.3861
7.2075
−2.2547
0.2638
0.0627
0.0622
16
0.4401
0.8816
−5.5568
7.2781
−2.2480
0.2600
0.0579
0.0573
17
0.3824
0.8999
−5.6979
7.3279
−2.2381
0.2563
0.0533
0.0525
18
0.3315
0.9156
−5.6043
7.1366
−2.1460
0.2433
0.0489
0.0480
19
0.2848
0.9296
−4.8807
6.2744
−1.8177
0.2028
0.0445
0.0436
20
0.2440
0.9415
−4.0266
5.2892
−1.4511
0.1583
0.0404
0.0395
21
0.2055
0.9525
−2.9989
4.1264
−1.0243
0.1071
0.0362
0.0353
22
0.1724
0.9616
−1.8671
2.8692
−0.5696
0.0532
0.0323
0.0315
23
0.1424
0.9695
−1.1240
2.0489
−0.2768
0.0191
0.0288
0.0280
24
0.1155
0.9763
−0.5169
1.3890
−0.0458
−0.0073
0.0255
0.0248
25
0.0883
0.9832
−0.1184
0.9585
0.1017
−0.0236
0.0223
0.0217
26
0.0622
0.9897
0.2604
0.5551
0.2377
−0.0383
0.0194
0.0189
27
0.0413
0.9943
0.2788
0.5517
0.2275
−0.0355
0.0163
0.0158
28
0.0216
0.9985
0.2809
0.5694
0.2087
−0.0315
0.0136
0.0133
29
0.0033
1.0023
0.4227
0.4434
0.2391
−0.0331
0.0117
0.0115Figure 3
The linear fit and cubic fit to the Kiknet data in 4 depth bins, 5, 10, 20, and 28 m.Figure3 shows that the goodness of cubic fit is slightly better than linear fit for some stiff sites, especially for depth less than 5 m. When the borehole depth is greater than 10 meters, the difference between these two fits becomes negligible.Next, we assess whether conditioning a Geomatrix category can improve theV
s
30 estimate. We classify 73 Kiknet sites as 60 rock sites with Geomatrix class A or class B and 13 soil sites with Geomatrix C or D. We use both linear and cubic fit to the rock sites and soil sites separately. Table 4 gives the comparison of the bias and standard deviation between the simple extrapolation, normal fit (all site pooled), and Geo fit (rock and soil bins).Table 4
Comparison of bias and standard deviation between the normal fit and Geo fit to Kiknet profiles.
Depth bins
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Simple extrapolate
Simple extrapolate
Linear fit
Linear fit
Geolinear fit
Geolinear fit
Cubic fit
Cubic fit
Geocubic fit
Geocubic fit
5
0.4945
0.3137
0.0074
0.2603
0.0049
0.2428
0.0068
0.2570
0.0028
0.2395
10
0.1670
0.1518
0.0051
0.1998
0.0036
0.1859
0.0068
0.1990
0.0045
0.1855
15
0.0664
0.0790
0.0026
0.1416
0.0014
0.1342
0.0028
0.1411
0.0014
0.1326
20
0.0240
0.0438
0.0015
0.0912
0.0007
0.0868
0.0026
0.0896
−0.0007
0.0827
28
0.0029
0.0249
0.0005
0.0310
0.0003
0.0301
0.0004
0.0303
0.0021
0.0291
Bias =ln
⁡
(
V
s
30
t
r
u
e
/
V
s
30
p
r
e
d
i
c
t
).Table4 shows that the bias and standard deviation decrease with an increase of depth and that of Geo fit, conditioning on Geomatrix categories, provides slightly superior results to that of the normal fit.We use the normal linear fit, which is defined asV
s
30
Boore, to estimate V
s
30 for three reasons. First, it is simple. Second, the bias and standard deviation of the normal linear fit to the 20 m depth bin are only 0.0015 and 0.0912, respectively. The maximum error is just nine percent. At shallow depth, 10 m depth bin, the maximum error is only 20 percent, which is acceptable for many applications. Third, the improvement of Geo fit and cubic fit is not significant and the procedure is more complicated than normal fit due to the large number of coefficients.


### 2.4. Topographic Slop and Terrain-Based Estimate

The USGS earthquake hazards program developed an approach based on the similarity of geology and topography to provide a first-order assessment ofV
s
30 [7]. It is assumed that the slope of topography, or gradient, could be diagnostic of V
s
30, because more competent (high-velocity) materials are more likely to maintain a steep slope whereas deep basin sediments are deposited primarily in environments with low gradients. Correlation between topographic slop data and regional V
s
30 is built to estimate V
s
30. We go to http://earthquake.usgs.gov/hazards/apps/vs30/custom.php and choose a location boundary including all the 147 Southwest China recording sites; V
s
30 estimate on each grid point is generated. V
s
30 at the closest grid point, whose distance to the target station is less than 0.6 km, is assumed as topographic estimate of V
s
30, named V
s
30
W.Yong built a correlation betweenV
s
30 and California terrain-based units, which are derived from 1 km spatial resolution (SRTM30) digital elevation model. Based on California terrain-based units, Yong made an estimate of V
s
30 for Southwest China, named V
s
30
a
r
c. Considering the difference of terrain between California and Southwest China, Yong makes a small change to V
s
30
a
r
c to provide an alternative estimate of V
s
30, named V
s
30
R.


## 2.1. Simple Extrapolation

In this method, we assume that the shear-wave velocity from the bottom of the borehole to 30 m is constant atV
s measured at the borehole bottom. The time-average shear-wave velocity (average slowness, [23]), named V
s
30
p
r
o
f
i
l
e, was computed from the equation (1)
V
s
30
=
30
t
t
30
,where the travel time t
t
(
30
) was given by (2)
t
t
30
=
∫
0
30
d
Z
V
s
Z
.V
s
(
Z
) is the shear-wave velocity at depthZ.SinceV
s
30
p
r
o
f
i
l
e is based on the measured velocity profile data, it is taken as the reference value of V
s
30 for comparison with other empirical estimates.V
s
30
p
r
o
f
i
l
e is typically less than the actual V
s
30 in general as V
s generally increase with increasing depth. In cases, where the borehole depth is greater than 20 meters, the difference is generally small.


## 2.2. Geomatrix Classification Assignment

The PEER NGA database [10] includes 561 sites with borehole data. All the sites were assigned with a Geomatrix Classification according to geological and geographic conditions. The NGA Geomatrix Site Classification criteria are given as follows:A, rock: instrument on rock (V
s > 600 m/s) or <5 m of soil over rock.
B, shallow (stiff) soil: instrument on/in soil profile up to 20 m thick overlying rock.
C, deep narrow soil: instrument on/in soil profile at least 20 m thick overlying rock, in a narrow canyon or valley not more than several km wide.
D, deep broad soil: instrument on/in soil profile at least 20 m thick overlying rock, in a broad valley.
E, soft deep soil: instrument on/in deep soil profile with averageV
s < 150 m/s.A median V
s
30 and standard deviation have been obtained for each Geomatrix Classification based upon a global database of measured profiles. Table 1 gives the median V
s
30 and standard deviation.Table 1
MedianV
s
30  and standard deviation for NGA database [10] profiles based on Geomatrix Classification bins.
Geomatrix Classification
MedianV
s  (m/s)
σ (m/s)
N
A
660
324
74
B
424
211
97
C
338
70
44
D
274
110
306
E
191
61
40The Geomatrix Classification for the 147 Southwest China sites is 9 A sites, 52 B sites, 83 C sites, and 3 D sites.Next, we compare the median shear-wave velocity profiles of Southwest China (SWC) with NGA profiles based on Geomatrix Classification. The result is shown in Figure2. In the depth range of 0 to 5 m, the median V
s of SWC is less than that of NGA profiles on average. The near surface soils in SWC are softer than those in NGA. However, at depths below 5 m, the median V
s of SWC profiles is similar to that of NGA profiles, except for site class B. The site class B profile of SWC has a slightly larger median V
s than NGA.Figure 2
Comparison of medianV
s between Southwest China (SWC) profiles and NGA profiles.Since the median shear-wave velocity profiles of SWC sites are similar to those of the NGA sites, we may assign the medianV
s
30 to the sites with the same Geomatrix Classification, (V
s
30
G
e
o
m
a
t
r
i
x), with a small bias on the high side. Also, we can assign V
s
30 to sites without V
s profile but with a Geomatrix Classification, again slightly biased high.


## 2.3. Boore Extrapolation

Boore [11] used a set of 135 borehole profiles with depths greater than or equal to 30 m to estimate a correlation between V
s
30 and V
s
(
d
), which is time-average shear-wave velocity for a profile to depth d. V
s
(
d
) is given by(3)
V
s
d
=
d
t
t
d
,where d is the borehole depth and t
t
(
d
) is given by (2).Boore [11] found that the logarithm of V
s
30 against logarithm of V
s
(
d
) could be fit by a straight line, given by(4)
log
⁡
V
s
30
=
a
+
b
log
⁡
V
s
d
.Table2 gives the regression coefficients and standard deviation for Boore’s correlation equation from 135 California profiles.Table 2
Coefficients of (4) for 135 California profiles [11].
d (m)
a
b
σ
l
n
10
0.0421
1.0292
0.0713
11
0.0221
1.0341
0.0647
12
0.0126
1.0352
0.0594
13
0.0142
1.0318
0.0548
14
0.0123
1.0297
0.0501
15
0.0138
1.0263
0.0459
16
0.0139
1.0237
0.0422
17
0.0196
1.0190
0.0394
18
0.0249
1.0144
0.0364
19
0.0256
1.0117
0.0332
20
0.0254
1.0095
0.0302
21
0.0253
1.0072
0.0270
22
0.0269
1.0044
0.0241
23
0.0222
1.0042
0.0208
24
0.0169
1.0043
0.0177
25
0.0115
1.0045
0.0147
26
0.0066
1.0045
0.0115
27
0.0025
1.0043
0.0084
28
0.0008
1.0031
0.0055
29
0.0004
1.0015
0.0027Since the standard deviation of Boore’s estimate is less than 8 percent for stations with borehole depth larger than 10 m, we apply Boore’s empirical model, which is generated from California data, to the SWC profiles to estimateV
s
30 (V
s
30
Boore
cal), given by(5)
V
s
30
Boore
cal
=
1
0
a
+
b
log
⁡
V
s
d
,where the superscript Cal means that the model is based on California data.A comparison ofV
s
30
Boore
cal to V
s
30
p
r
o
f
i
l
e in the Appendix shows that Boore’s estimate for profiles with borehole depth greater than 20 m is very close to V
s
30
p
r
o
f
i
l
e, which has an average bias of 0.006. However, for the 32 profiles with borehole depth between 10 and 20 m, V
s
30
Boore
cal has an average bias of 0.139 (positive bias reflects an underprediction) relative to V
s
30
p
r
o
f
i
l
e. The result suggests that the coefficients of Boore’s estimate derived from California profiles may not be applicable to SWC profiles.Boore indicates thatV
s of SWC profiles is larger than that of California profiles in the same depth and the velocity gradients of these two regions are different, which results in the underestimate of V
s
30. Similar to Boore, in order to eliminate the difference of velocity gradients between the regions, we want to derive the coefficients from similar profiles.Linear and cubic fit to Kiknet profiles were performed to fitlog
⁡
(
V
s
30
) against log
⁡
(
V
s
(
d
)
). The cubic fit is given by the following equation:(6)
log
⁡
V
s
30
=
C
0
+
C
1
log
⁡
V
s
d
+
C
2
log
2
⁡
V
s
d
+
C
3
log
3
⁡
V
s
d
.According to (6), V
s
30 can be estimated by(7)
V
s
Boore
3
=
1
0
C
0
+
C
1
log
⁡
V
s
d
+
C
2
log
2
⁡
V
s
d
+
C
3
log
3
⁡
V
s
d
.Table3 gives the coefficients and standard deviation of linear and cubic fit based on Boore’s correlation equation applied to 73 Kiknet measured profiles with Geomatrix Classification, and Figure 3 displays the fit.Table 3
Coefficients and natural logarithm of the standard deviation for (4) and (6) from Kiknet profiles.
Depth (m)
a
b
C
0
C
1
C
2
C
3
σ
l
i
n
e
a
r
σ
c
u
b
i
c
5
1.3412
0.5626
1.0320
1.3924
−0.5117
0.0906
0.1174
0.1158
6
1.2498
0.5975
−1.2168
3.8378
−1.3922
0.1955
0.1120
0.1110
7
1.1650
0.6288
−1.1351
3.6074
−1.2640
0.1756
0.1062
0.1055
8
1.1071
0.6492
0.0978
2.1222
−0.6846
0.1022
0.1018
0.1012
9
1.0009
0.6878
−2.0070
4.3394
−1.4621
0.1928
0.0956
0.0952
10
0.9056
0.7223
−3.2943
5.6294
−1.8935
0.2410
0.0896
0.0894
11
0.8111
0.7559
−4.0334
6.2874
−2.0859
0.2595
0.0837
0.0835
12
0.7307
0.7840
−4.0876
6.2020
−2.0116
0.2464
0.0784
0.0782
13
0.6465
0.8132
−4.6981
6.7207
−2.1550
0.2592
0.0732
0.0729
14
0.5709
0.8389
−4.9266
6.8299
−2.1532
0.2550
0.0681
0.0677
15
0.5018
0.8617
−5.3861
7.2075
−2.2547
0.2638
0.0627
0.0622
16
0.4401
0.8816
−5.5568
7.2781
−2.2480
0.2600
0.0579
0.0573
17
0.3824
0.8999
−5.6979
7.3279
−2.2381
0.2563
0.0533
0.0525
18
0.3315
0.9156
−5.6043
7.1366
−2.1460
0.2433
0.0489
0.0480
19
0.2848
0.9296
−4.8807
6.2744
−1.8177
0.2028
0.0445
0.0436
20
0.2440
0.9415
−4.0266
5.2892
−1.4511
0.1583
0.0404
0.0395
21
0.2055
0.9525
−2.9989
4.1264
−1.0243
0.1071
0.0362
0.0353
22
0.1724
0.9616
−1.8671
2.8692
−0.5696
0.0532
0.0323
0.0315
23
0.1424
0.9695
−1.1240
2.0489
−0.2768
0.0191
0.0288
0.0280
24
0.1155
0.9763
−0.5169
1.3890
−0.0458
−0.0073
0.0255
0.0248
25
0.0883
0.9832
−0.1184
0.9585
0.1017
−0.0236
0.0223
0.0217
26
0.0622
0.9897
0.2604
0.5551
0.2377
−0.0383
0.0194
0.0189
27
0.0413
0.9943
0.2788
0.5517
0.2275
−0.0355
0.0163
0.0158
28
0.0216
0.9985
0.2809
0.5694
0.2087
−0.0315
0.0136
0.0133
29
0.0033
1.0023
0.4227
0.4434
0.2391
−0.0331
0.0117
0.0115Figure 3
The linear fit and cubic fit to the Kiknet data in 4 depth bins, 5, 10, 20, and 28 m.Figure3 shows that the goodness of cubic fit is slightly better than linear fit for some stiff sites, especially for depth less than 5 m. When the borehole depth is greater than 10 meters, the difference between these two fits becomes negligible.Next, we assess whether conditioning a Geomatrix category can improve theV
s
30 estimate. We classify 73 Kiknet sites as 60 rock sites with Geomatrix class A or class B and 13 soil sites with Geomatrix C or D. We use both linear and cubic fit to the rock sites and soil sites separately. Table 4 gives the comparison of the bias and standard deviation between the simple extrapolation, normal fit (all site pooled), and Geo fit (rock and soil bins).Table 4
Comparison of bias and standard deviation between the normal fit and Geo fit to Kiknet profiles.
Depth bins
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Bias ofln
⁡
(
V
s
30
)
Standard deviation
Simple extrapolate
Simple extrapolate
Linear fit
Linear fit
Geolinear fit
Geolinear fit
Cubic fit
Cubic fit
Geocubic fit
Geocubic fit
5
0.4945
0.3137
0.0074
0.2603
0.0049
0.2428
0.0068
0.2570
0.0028
0.2395
10
0.1670
0.1518
0.0051
0.1998
0.0036
0.1859
0.0068
0.1990
0.0045
0.1855
15
0.0664
0.0790
0.0026
0.1416
0.0014
0.1342
0.0028
0.1411
0.0014
0.1326
20
0.0240
0.0438
0.0015
0.0912
0.0007
0.0868
0.0026
0.0896
−0.0007
0.0827
28
0.0029
0.0249
0.0005
0.0310
0.0003
0.0301
0.0004
0.0303
0.0021
0.0291
Bias =ln
⁡
(
V
s
30
t
r
u
e
/
V
s
30
p
r
e
d
i
c
t
).Table4 shows that the bias and standard deviation decrease with an increase of depth and that of Geo fit, conditioning on Geomatrix categories, provides slightly superior results to that of the normal fit.We use the normal linear fit, which is defined asV
s
30
Boore, to estimate V
s
30 for three reasons. First, it is simple. Second, the bias and standard deviation of the normal linear fit to the 20 m depth bin are only 0.0015 and 0.0912, respectively. The maximum error is just nine percent. At shallow depth, 10 m depth bin, the maximum error is only 20 percent, which is acceptable for many applications. Third, the improvement of Geo fit and cubic fit is not significant and the procedure is more complicated than normal fit due to the large number of coefficients.


## 2.4. Topographic Slop and Terrain-Based Estimate

The USGS earthquake hazards program developed an approach based on the similarity of geology and topography to provide a first-order assessment ofV
s
30 [7]. It is assumed that the slope of topography, or gradient, could be diagnostic of V
s
30, because more competent (high-velocity) materials are more likely to maintain a steep slope whereas deep basin sediments are deposited primarily in environments with low gradients. Correlation between topographic slop data and regional V
s
30 is built to estimate V
s
30. We go to http://earthquake.usgs.gov/hazards/apps/vs30/custom.php and choose a location boundary including all the 147 Southwest China recording sites; V
s
30 estimate on each grid point is generated. V
s
30 at the closest grid point, whose distance to the target station is less than 0.6 km, is assumed as topographic estimate of V
s
30, named V
s
30
W.Yong built a correlation betweenV
s
30 and California terrain-based units, which are derived from 1 km spatial resolution (SRTM30) digital elevation model. Based on California terrain-based units, Yong made an estimate of V
s
30 for Southwest China, named V
s
30
a
r
c. Considering the difference of terrain between California and Southwest China, Yong makes a small change to V
s
30
a
r
c to provide an alternative estimate of V
s
30, named V
s
30
R.


## 3. Comparisons and Conclusion

We have six types ofV
s
30 estimates for Southwest China: V
s
30
p
r
o
f
i
l
e, V
s
30
B
o
o
r
e, V
s
30
G
e
o
m
a
t
r
i
x, V
s
30
a
r
c, V
s
30
R, and V
s
30
W. Since V
s
30
p
r
o
f
i
l
e is obtained from the shear-wave velocity profile, we use V
s
30
p
r
o
f
i
l
e as a reference V
s
30 to calculate the bias and standard deviation of the five other types of V
s
30 estimates. Table 5 summarizes the results.Table 5
Bias and standard deviation of the five other types ofV
s
30 estimates relative to V
s
30
p
r
o
f
i
l
e.
V
s
30
B
o
o
r
e
V
s
30
G
e
o
m
a
t
r
i
x
V
s
30
a
r
c
V
s
30
R
V
s
30
W
Bias (ln)
−0.0704
−0.0656
−0.3189
−0.3451
−0.4434
σ
0.0796
0.2003
0.2769
0.2444
0.4062Table5 indicates that two kinds of terrain-based V
s
30 estimates have large bias and standard deviation. We believe this is mainly due to the large difference of terrain slop between Southwest China and California. It is the same with topographic estimate. Because of the difference of geographic and topographic condition between these two regions, the topographic estimate shows more than 40 percent bias and huge standard deviation. The bias of V
s
30
G
e
o
m
a
t
r
i
x is small whereas the standard deviation is about 30 percent. This is because there are only five categories in the Geomatrix Classification scheme and there is considerable within-category variability (Table 1). However, for the sites without profile data, V
s
30
G
e
o
m
a
t
r
i
x provides a largely unbiased estimate of V
s
30.The bias and standard deviation ofV
s
30
B
o
o
r
e are both small, which verify that Boore’s model is a good method to estimate V
s
30
. However, the coefficients must be attained from profiles with similar geological conditions and similar velocity gradient, that is, local or regional calibration. Our results indicate that the geological condition of Sichuan province of China is similar to that of Japan. Hence, we use V
s
30
B
o
o
r
e to estimate site effect for ground motion prediction equation.In addition, Table4 shows that V
s
30 can be estimated by average shear-wave velocity to 10 m depth with a bias of 0.0051 and σ of only 0.1998. Since the NGA models [5] use the natural logarithm of V
s
30 to estimate site effect, 20 percent difference of V
s
30 can make only five percent difference to the site effect, which is suitable for ground motion prediction and engineering applications.Based onV
s
30
B
o
o
r
e for 145 profiles, we get a median V
s
30
G
e
o
m
a
t
r
i
x for the SWC profiles. Table 6 gives V
s
30
G
e
o
m
a
t
r
i
x for Geomatrix Classification A, B, C, and D sites, which can be used to assign V
s
30 to SWC sites without profile data.Table 6
MedianV
s
30
G
e
o
m
a
t
r
i
x  for WCS sites.
Geomatrix Classification
MedianV
s
30  (m/s)
σ
N
A
553.40
79.23
9
B
412.29
69.23
52
C
353.73
63.72
83
D
296.83
72.54
3



---

*Source: 9305095-2016-03-13.xml*