Implications of NGA for NEHRP Site Coefficients

By Roger D. Borcherdt 

Open-File Report 2012–1269 

U.S. Department of the Interior 

U.S. Geological Survey 

0

1

2

3

4

5

6

100 300 500 700 900 1100 1300

Mid-Period Amplification, Fv

Vs30 (m/s)

Loma Prieta Strong-Motion Data

Fv - 95%

 Fv = (1067 / Vs )^0.64

Fv + 95%

Fv for Site Class Intervals

NGA MP Avg 0.1g

Fv = (1050 / Vs)^0.65 (Borcherdt, 1994)

Site Class E

Site Class D

Site Class C

Site Class B

NGA and Loma Prieta Estimates of Fv at S1=0.1
ii

U.S. Department of the Interior 

KEN SALAZAR, Secretary 

U.S. Geological Survey 

Marcia K. McNutt, Director 

U.S. Geological Survey, Reston, Virginia: 2012 

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Suggested citation: 

Borcherdt, R.D. 2012, Implications of NGA for NEHRP Site Coefficients: Menlo Park, CA 

U. S. Geological Open File Number 2012-1269, 25 p. 

Any use of trade, firm, or product names is for descriptive purposes only and does not imply 

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Although this information product, for the most part, is in the public domain, it also may contain 

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secured from the copyright owner. 
iii

Contents

Abstract................................................................................................................................................. 1

Introduction .......................................................................................................................................... 1

Background for proposals ...................................................................................................................... 1

Proposal I ....................................................................................................................................................3

Proposal II ..................................................................................................................................................4

Proposal III .................................................................................................................................................5

Justification ........................................................................................................................................... 6

NGA Amplification as a Function of Period ..............................................................................................6

Comparison of NGA and NEHRP Amplification Factors .......................................................................11

Agreement between NGA and Observed Spectral Amplification ............................................................11

Reference Site Condition Discussion .......................................................................................................21

Inference of NGA Site Coefficients at Intermediate Values of 

S

v ..........................................................22

Acknowledgements ............................................................................................................................. 22

References ........................................................................................................................................... 24
iv
 1 11/14/12 

Implications of NGA for NEHRP Site Coefficients

Roger D. Borcherdt 

ABSTRACT 

Three proposals are provided to update tables 11.4–1 and 11.4–2 of Minimum Design Loads for 

Buildings and Other Structures (7-10), by the American Society of Civil Engineers (2010) 

(ASCE/SEI 7–10), with site coefficients implied directly by NGA (Next Generation Attenuation) 

ground motion prediction equations (GMPEs). Proposals include a recommendation to use straightline interpolation to infer site coefficients at intermediate values of 

S

v

(average shear velocity). 

Site coefficients are recommended to ensure consistency with ASCE/SEI 7-10 MCER (Maximum 

Considered Earthquake) seismic-design maps and simplified site-specific design spectra procedures 

requiring site classes with associated tabulated site coefficients and a reference site class with unity 

site coefficients. Recommended site coefficients are confirmed by independent observations of 

average site amplification coefficients inferred with respect to an average ground condition 

consistent with that used for the MCER maps. The NGA coefficients recommended for 

consideration are implied directly by the NGA GMPEs and do not require introduction of additional 

models. 

INTRODUCTION 

The proposals provided here are based on NGA (Next Generation Attenuation) site coefficients 

provided by each NGA developer as part of a comprehensive review of the implications of NGA for 

site coefficients as specified in Tables 11.4-1 and 11.4-2 of Minimum Design Loads for Buildings 

and Other Structures (7–10), by the American Society of Civil Engineers (2010) (ASCE/SEI 7–10). 

That review (Task Committee 8, NGA West 2) was coordinated by the Pacific Earthquake 

Engineering Research Center (PEER) as part of a larger initiative to improve the NGA GMPEs 

capabilities for earthquake-resistant design (Bozorgnia, 2010). Analysis and review of the NGA 

data for Task 8 was conducted by Stewart and Seyhan (2012) with review meetings of the Steering 

Committees organized under the auspices of PEER (Pacific Earthquake Engineering Research 

Center). The results reported here were derived from spreadsheets summarizing NGA results as 

reported by each NGA developer and provided by Stewart and Seyhan (written commun, 2011). 

BACKGROUND FOR PROPOSALS 

The current procedure adopted in ASCE/SEI 7-10 for estimation of site-specific design spectra uses 

a simplified procedure to account for site conditions. The simplified procedure is based on the 

concept of six site classes with an associated set of discrete tabulated site coefficients for five of the 

classes (Tables 11.4-1 and 11.4-2). The simplified procedure implies that a reference site class be 

chosen such that the amplification factor for the reference site class is unity and those for the other 

classes specified with respect to that for the reference site class. For consistency, the uniform 
 2 11/14/12 

ground condition chosen to specify the input ground motion level should be the same as that of the 

reference site class. 

In addition, the simplified procedure as implemented with site classes implies that the tabulated set 

of site coefficients represent the average amplification across the entire site class. For consistency 

with the definition of the site classes in terms of 

S

v

 intervals and amplification factors expressed as 

a function of

S

v

, the simplified procedure implies that the short- and mid-period site coefficients,

F

a

and

F

v

, represent the amplification at the mid-point of each site class interval. In addition, the 

simplified procedure uses MCER maps (Maximum Considered Earthquake ground-motion Response 

maps) prepared by the U.S. Geological Survey (2010) to estimate the input ground-motion level for 

a uniform ground condition specified by

760 / Sv m s 

. Sites with 

760 / Sv m s 

are classified as 

site-class B sites, which implies that the reference site class is site class B and the associated site 

coefficients for site class B must be unity in order to maintain consistency with the MCER maps. 

The proposals included herein provide a set of coefficients consistent with the simplified procedure 

adopted in ASCE/SEI 7-10 and consistent with those as initially adopted in the 1994 edition of the 

NEHRP Recommended Seismic Provisions for New Buildings (1994). The proposed coefficients 

provide average amplification factors at the 

S

v

 mid-point for each site class referenced to the 

corresponding 

S

v

midpoint for the reference site class B. This procedure previously reviewed and 

adopted in numerous versions of the codes provides unity amplification factors for the reference site 

class B, and hence unity amplification factors for the uniform ground condition specified in the 

MCER design maps. This procedure provides site coefficients consistent with those inferred from 

strong motion data for the Loma Prieta earthquake (Seed, 1992; Seed et al., 1994; Borcherdt, 1992, 

1994; Joyner et al., 1992, 1994; Dobry et al, 1992, 1994).

The proposals recommend that if site coefficients are desired as a continuous function of site 

conditions (

S

v

) as opposed to discrete values as specified for the five site classes, then the site 

coefficients should be inferred by straight-line interpolation using the site coefficients as specified 

at the mid-point of each site class interval. This procedure yields results that agree with site 

coefficients adopted in Tables 11.4-1 and 11.4-2 and those proposed herein. 

Three proposals for adjustments to Tables 11.4.-1 and 11.4-2 are provided for consideration. The 

first proposal suggests minimal changes based on adjusting only those site coefficients that exceed 

the 95% confidence limits for the NGA predictions. The second proposal replaces each coefficient 

with the corresponding mean NGA value for site classes C and D. The third proposal replaces each 

coefficient with the corresponding mean NGA value for site classes C, D, and E. No changes are 

proposed for the reference site class B or for site class A. 
 3 11/14/12 

PROPOSAL I 

Proposal I provides changes as shown in parenthesis for those 

F

a

and 

F

v

coefficients exceeding 

95% NGA confidence limits with the exception to that for site class E for Ss <0.25 (see Figures 5, 

6, and 7). The proposed changes are the mean NGA value. 

Table 1a) Proposal I changes to Table 11.4-1 ASCE/SEI 7-10.

Table 11.4-1 Site Coefficient, Fa

Mapped Risk-Targeted Maximum Considered Earthquake (MCER) Spectral Response Acceleration 

Parameter at Short Period

Site Class S

s

< 0.25 S

s

= 0.50 S

s

= 0.75 S

s

= 1.00 S

s

> 1.25

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C (1.37) 1.2 (1.33) 1.2 (1.31) 1.1 (1.29) 1.0 (1.27) 1.0

D 1.6 1.4 1.2 1.1 1.0 

E 2.5 1.7 1.2 0.9 0.9

F see Section 

11.4.7

Notes: 1) Use straight-line interpolation for intermediate values of SS. 

2) Use straight-line interpolation for intermediate values of 

S

v

 using site class mid-point value for

S

v from chapter 20. 

Table 1b) Proposal I changes to Table 11.4-2 ASCE/SEI 7-10.

Table 11.4-2 Site Coefficient, Fv

Mapped Risk-Targeted Maximum Considered Earthquake (MCER) Spectral Response Acceleration 

 Parameter at 1-s Period

Site Class S

1

< 0.1 S

l

= 0.20 S

l

= 0.30 S

l

= 0.40 S

l

> 0.50

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C 1.7 1.6 1.5 1.4 (1.48) 1.3

D (2.35) 2.4 (2.25) 2.0 (2.19) 1.8 (2.14) 1.6 (1.97) 1.5

E 3.5 3.2 2.8 2.4 2.4

F see Section 

11.4.7

Notes: 1) Use straight-line interpolation for intermediate values of S1. 

2) Use straight-line interpolation for intermediate values of 

S

v

 using site class mid-point value for

S

v from chapter 20. 
 4 11/14/12 

PROPOSAL II 

Proposal II provides changes for site class C and D coefficients with corresponding mean NGA 

values. A large epistemic uncertainty in the NGA results and a limited amount of data for site class 

E suggests that until these uncertainties are better resolved, changes to only the site coefficients for 

site classes C and D may be warranted. 

Table 2a) Proposal II changes to Table 11.4-1 ASCE/SEI 7-10.

Table 11.4-1 Site Coefficient, Fa

Mapped Risk-Targeted Maximum Considered Earthquake (MCER) Spectral Response Acceleration 

 Parameter at Short Period

Site Class S

s

< 0.25 S

s

= 0.50 S

s

= 0.75 S

s

= 1.00 S

s

> 1.25

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C (1.37) 1.2 (1.33) 1.2 (1.31) 1.1 (1.29) 1.0 (1.27) 1.0

D (1.68) 1.6 (1.47) 1.4 (1.34) 1.2 (1.24) 1.1 (1.16) 1.0 

E 2.5 1.7 1.2 0.9 0.9

F see Section 

11.4.7

Notes: 1) Use straight-line interpolation for intermediate values of SS. 

2) Use straight-line interpolation for intermediate values of 

S

v

 using site class mid-point value for

S

v from chapter 20. 

 

Table 2b) Proposal II changes to Table 11.4-2 ASCE/SEI 7-10.

Table 11.4-2 Site Coefficient, Fv

Mapped Risk-Targeted Maximum Considered Earthquake (MCER) Spectral Response Acceleration 

 Parameter at 1-s Period

Site Class S

1

< 0.1 S

l

= 0.20 S

l

= 0.30 S

l

= 0.40 S

l

> 0.50

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C (1.57) 1.7 (1.56) 1.6 (1.56) 1.5 (1.55) 1.4 (1.48) 1.3

D (2.35) 2.4 (2.25) 2.0 (2.19) 1.8 (2.14) 1.6 (1.97) 1.5

E 3.5 3.2 2.8 2.4 2.4

F see Section 

11.4.7

Notes: 1) Use straight-line interpolation for intermediate values of S1. 

2) Use straight-line interpolation for intermediate values of 

S

v

 using site class mid-point value for

S

v from chapter 20. 
 5 11/14/12 

PROPOSAL III 

This proposal provides options for changes in the site coefficients for site classes C, D, and E with 

corresponding mean NGA values. However, a large epistemic uncertainty in the NGA results and a 

limited amount of data for site class E suggests that until these uncertainties are better resolved, 

revision of only the site coefficients for site classes C and D may be warranted (see Proposal II).. 

Table 3a Potential NGA changes to Table 11.4-1 ASCE/SEI 7-10. 

Table 11.4-1 Site Coefficient, Fa

Mapped Risk-Targeted Maximum Considered Earthquake (MCER) Spectral Response Acceleration 

 Parameter at Short Period

Site Class S

s

< 0.25 S

s

= 0.50 S

s

= 0.75 S

s

= 1.00 S

s

> 1.25

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C (1.37) 1.2 (1.33) 1.2 (1.31) 1.1 (1.29) 1.0 (1.27) 1.0

D (1.68) 1.6 (1.47) 1.4 (1.34) 1.2 (1.24) 1.1 (1.16) 1.0 

E (1.87) 2.5 (1.31) 1.7 (1.02) 1.2 (0.84) 0.9 (0.72) 0.9

F see Section 

11.4.7

Notes: 1) Use straight-line interpolation for intermediate values of SS. 

2) Use straight-line interpolation for intermediate values of 

S

v

 using site class mid-point value for

S

v from chapter 20. 

Table 3b Potential NGA changes to Table 11.4-2 ASCE/SEI 7-10. 

Table 11.4-2 Site Coefficient, Fv

Mapped Risk-Targeted Maximum Considered Earthquake (MCER) Spectral Response Acceleration 

 Parameter at 1-s Period

Site Class S

1

< 0.1 S

l

= 0.20 S

l

= 0.30 S

l

= 0.40 S

l

> 0.50

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C (1.57) 1.7 (1.56) 1.6 (1.56) 1.5 (1.55) 1.4 (1.48) 1.3

D (2.35) 2.4 (2.25) 2.0 (2.19) 1.8 (2.14) 1.6 (1.97) 1.5

E (3.38) 3.5 (2.83) 3.2 (2.52) 2.8 (2.31) 2.4 (2.08) 2.4

F see Section 

11.4.7

Notes: 1) Use straight-line interpolation for intermediate values of S1. 

2) Use straight-line interpolation for intermediate values of 

S

v

 using site class mid-point value for

S

v from chapter 20. 
 6 11/14/12 

JUSTIFICATION 

The results reported herein were derived from spreadsheets summarizing NGA results provided by 

each NGA developer and compiled by Stewart and Seyhan (written commun. 2011). (Most of the 

results presented herein have been previously presented at Task Committee 8 meetings.) 

Amplification values were provided by the four developers, Abrahamson and Silva (2008; referred 

to as AS), Boore and Atkinson (2008; BA), Campbell and Bozorgnia (2008; CB), and Chiou and 

Youngs (2008; CY)) as a function of period and ground motion level as referenced to 1100 m/s 

(AS, CB), 1130 m/s (CY), and 760 m/s (BA). The spreadsheets compiled from these values were 

provided by Stewart and Seyhan (written commun. 2011). In order to maintain consistency with the 

simplified procedure, that requires site classes and an associated discrete set of site coefficients, all 

of the amplification factors were normalized to the mid-point 

S

v

 value for reference site class B.

Average short- and mid-period band site coefficients were computed from the NGA factors using 

equally spaced values of period. (

S

v

 is defined as in ASCE/SEI 7-10 chapter 20 as the average 

shear velocity to a depth of 30 m, which is equivalent to the ratio of 30 m to the travel time for a 

wave to travel from the surface to a depth of 30 m. 

S

v

also is referred to as 

S 30 v

and 

S

v .) 

NGA AMPLIFICATION AS A FUNCTION OF PERIOD 

Plots of the NGA amplification factors inferred as a function of period are shown in Figures 1, 2, 

and 3 for site classes E, D, and C with input ground-motion levels of 0.1g and 0.4g. The plots show 

the dependence of amplification as a function of period as inferred by each developer for each site 

class. They also illustrate the epistemic or model uncertainty associated with the four NGA models. 

They show that the amplification factors for site Class E first decrease with period for periods less 

than about 0.1 s, then show a well-defined increase with period. The rate of this increase with 

period decreases for periods greater than about 0.75 s for site class D and about 0.5 s for site class 

C. The plots show that variation in estimates of amplification for each of the NGA developers 

increase with period with the largest variations occurring for periods greater than about 0.5 s. 

Figures 1, 2, and 3 also show average amplification factors inferred for the short- and mid-period 

bands from amplification values at equally spaced intervals. In addition, Figure 1 shows average 

amplification factors inferred using amplification values derived at equally spaced logarithmic 

periods used by Stewart and Seyhan (2012). Figure 4 shows a comparison of average short- and 

mid-period amplification factors computed using the equal and logarithmic spacing in period for 

site class E as a function of PGA. The comparisons (Figs. 1 and 4) show that the averages computed 

using the two spacings in period differ significantly for the mid-period amplification values. 

The average amplification factors computed with logarithmic spacing are biased to smaller values, 

because more values of amplification at short periods are included in each average than at the 

longer periods. This unequal spacing in period causes the resultant NGA averages to be biased 

toward smaller values. This effect is most pronounced for the averages computed for site class E 

(Fig.4), but also apparent for site classes D and C (not shown). The bias toward smaller values is 

most apparent for the mid-period amplification factor, where it increases with increasing PGA 

values. The bias impacts conclusions regarding the comparison of NEHRP and NGA values (e.g. 

compare Fig 3.3, Stewart and Seyhan, 2012 with Figs. 5-12 herein). The bias incorrectly implies an 

increase in nonlinearity (see Fig. 4b). It biases the comparison between NGA and NEHRP low 
 7 11/14/12 

Figure 1. NGA amplification for site class E with respect to mid-point of site class B 

S

v

 interval versus period 

for 0.1g (Fig. 1a) and 0.4g (Fig. 1b). Short-period (0.1-0.5 s) and mid-period (0.4-2.0 s) averages inferred 

from equally-spaced period values (solid black lines) and logarithm-spaced period values (dashed red lines) 

are shown. The plots show that the logarithm-spaced values (Stewart and Seyhan, 2012) are biased to 

significantly smaller values for the average mid-period amplification for site class E. 

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5

NGA Amplification wrt Site Class B

Period (s)

AS Aa=0.1g; Vs= 150 m/s

BA Aa=0.1g; Vs= 150 m/s

CB Aa=0.1g; Vs= 150 m/s

CY Aa=0.1g; Vs= 150 m/s

NGA SP Avg 0.1g

NGA MP Avg 0.1g

nga sp LN T avg

NGA Amplification versus Period

(Site Class E, 0.1g)

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5

NGA Amplification wrt Site Class B

Period (s)

AS Aa=0.4g; Vs= 150 m/s

BA Aa=0.4g; Vs= 150 m/s

CB Aa=0.4g; Vs= 150 m/s

CY Aa=0.4g; Vs= 150 m/s

NGA SP Avg 0.4g

NGA MP Avg 0.4g

nga sp LN T avg

NGA Amplification versus Period

(Site Class E, 0.4g)
 8 11/14/12 

Figure 2. NGA amplification for site class D with respect to mid-point of site class B 

S

v

 interval versus 

period for 0.1g (Fig. 2a) and 0.4g (Fig. 2b). Short-period (0.1-0.5 s) and mid-period (0.4-2.0 s) averages 

inferred from equally-spaced period values (solid black lines) are shown. 

0

1

2

3

0 0.5 1 1.5 2 2.5

NGA Amplification wrt Site Class B

Period (s)

AS Aa=0.1g; Vs= 290 m/s

BA Aa=0.1g; Vs= 290 m/s

CB Aa=0.1g; Vs= 290 m/s

CY Aa=0.1g; Vs= 290 m/s

NGA SP Avg 0.1g

NGA MP Avg 0.1g

NGA Amplification versus Period

(Site Class D, 0.1g)

0

1

2

3

0 0.5 1 1.5 2 2.5

NGA Amplification wrt Site Class B

Period (s)

AS Aa=0.4g; Vs= 290 m/s

BA Aa=0.4g; Vs= 290 m/s

CB Aa=0.4g; Vs= 290 m/s

CY Aa=0.4g; Vs= 290 m/s

NGA SP Avg 0.4g

NGA MP Avg 0.4g

NGA Amplification versus Period

(Site Class D, 0.4g)
 9 11/14/12 

Figure 3. NGA amplification for site class C with respect to mid-point of site class B 

S

v

 interval versus period 

for 0.1g (Fig. 3a) and 0.4g (Fig. 3b). Short-period (0.1-0.5 s) and mid-period (0.4-2.0 s) averages inferred 

from equally-spaced period values (solid black lines) are shown. 

0

1

2

0 0.5 1 1.5 2 2.5

NGA Amplification wrt Site Class B

Period (s)

AS Aa=0.1g; Vs= 540 m/s

BA Aa=0.1g; Vs= 540 m/s

CB Aa=0.1g; Vs= 540 m/s

CY Aa=0.1g; Vs= 540 m/s

NGA SP Avg 0.1g

NGA MP Avg 0.1g

NGA Amplification versus Period

(Site Class C, 0.1g)

0

1

2

0 0.5 1 1.5 2 2.5

NGA Amplification wrt Site Class B

Period (s)

AS Aa=0.4g; Vs= 540 m/s

BA Aa=0.4g; Vs= 540 m/s

CB Aa=0.4g; Vs= 540 m/s

CY Aa=0.4g; Vs= 540 m/s

NGA SP Avg 0.4g

NGA MP Avg 0.4g

NGA Amplification versus Period

(Site Class C, 0.4g)
 10 11/14/12 

Figure 4. NGA short-period (Fig. 4a) and mid-period average amplification (Fig . 4b) values for site class E 

inferred from equally-spaced period values (solid blue lines) and those inferred from logarithmic spaced 

period values (solid red lines) inferred as a function of PGA. The plots show that the logarithm-spaced 

values (Stewart and Seyhan, 2012) are biased to significantly smaller values, especially for the average midperiod amplification factor. 

0

1

2

3

0 0.2 0.4 0.6 0.8 1

Short-Period Amplification 

PGA (g)

NGA SP Avg

NGA SP LN T avg

Equal ∆ T and Log T Short-Period Avg Amplification versus PGA 

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Mid-Period Amplification 

PGA (g) 

NGA MP Avg

NGA MP LN T Avg

Equal ∆ T and Log T Mid-Period Avg Amplification versus PGA 
 11 11/14/12 

strain coefficients and, in turn, biases recommendations regarding implications of NGA for 

proposed changes in ASCE/SEI 7-10 site coefficients (see Stewart and Seyhan, 2012). 

COMPARISON OF NGA AND NEHRP AMPLIFICATION FACTORS 

Figures 5, 6, and 7 show plots of the short- and mid-period amplification factors as a function of 

PGA for each site class. Superimposed on each plot are mean values and mean + 2 standard 

deviation (S.D.) values inferred from the sample comprised of the four NGA estimates. For 

comparison, the NEHRP site coefficients also are plotted. Comparison of the NGA and NEHRP 

estimates as a function of input ground shaking level (Figs. 5, 6, and 7) show that the majority of 

the NEHRP values are within the 95 % uncertainty limits implied by the NGA estimates with 

exceptions as noted: 

Site Class D: 

F

v

 is less than the NGA mid-period mean – 2 S.D. value at PGA = 0.3g, 0.4g, 

and 0.5g (S1= 0.3, 0.4, and 0.5), 

Site Class C: 

F

a

is less than the NGA mid-period mean – 2 S.D. value at 0.1-0.5g (SS= 0.25-

1.25), 

F

v

is slightly less than the NGA mid-period mean – 2 S.D. value at 0.5g (S1=0.5). 

Proposal I (Tables 1a and 1b) suggests adjustment of Tables 11.4-1 and 11.4-2 of ASCE/SEI 7-10 

to ensure that all coefficients for site classes D and C are within the 95% uncertainty limits implied 

by the NGA GMPEs. 

Comparison of the NGA and NEHRP estimates as a function of 

S

v

 (Figs. 8, 9, 10, 11, and 12) again 

show that the majority of the NEHRP values are within or near the 95% uncertainty limits implied 

by the NGA estimates with exceptions as noted above. The plots in Figures 8-12 further emphasize 

that the uncertainty in the NGA estimates increases with decreasing 

S

v

 with the largest variation 

between NGA model predictions clearly being associated with site class E. The large uncertainty in 

the NGA results for site class E suggests that adjustment of these coefficients may not be warranted 

until additional consensus is achieved regarding GMPE models for nonlinear soil behavior. 

AGREEMENT BETWEEN NGA AND OBSERVED SPECTRAL AMPLIFICATION

Recalling that the NEHRP values for PGA levels near 0.1g were inferred from strong-motion 

recordings of the Loma Prieta earthquake, it is of interest to compare these inferences of spectral 

amplification with those derived from the NGA models based on a larger set of strong motion 

recordings. The Loma Prieta coefficients represent a consensus derived from observed strongmotion data using; response spectra ratios (Joyner, 1992; Joyner et al., 1994; Seed 1992; Seed et al, 

1994), Fourier amplitude spectra ratios (Borcherdt, 1992, 1994), and response spectra parametric 

studies (Dobry et al., 1992, 1994). These coefficients at PGA=0.1g were subsequently adopted in 

the 1994 edition of the NEHRP Recommended Seismic Provisions for New Buildings, with the 

exception of the value for 

F

a

, which was increased from a value of 2.0 to 2.5 in order to better 

account for observed amplification effects of high plasticity clays in Mexico City. The average 

short- and mid-period amplification coefficients as inferred from the Loma Prieta strong-motion 

recordings are shown in Figure 13 (black step function). The amplification coefficients were 

inferred with respect to an average 

795 / Sv m s 

 for rock sites in the San Francisco Bay region 

(Borcherdt, 1992, 1994). The corresponding + 2 S.D. limits derived from the original regression 

analysis also are shown (Borcherdt, 1994). 
 12 11/14/12 

Figure 5. Short-period (Fig. 5a) and mid-period average amplification (Fig. 5b) values for site class E inferred 

from equally-spaced period values for each NGA developer (green lines), mean and 95% NGA limits (blue 

lines), and NEHRP site coefficients (black line) as a function of PGA. The plots show that the NEHRP 

F

a

and 

F

v

 coefficients are within 95% NGA uncertainty limits for all values except for Fa at PGA=0.1g 

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Short-Period Amplification

PGA (g)

NEHRP

NGA SP Avg

NGA SP Avg-2 SD

NGA SP Avg+2 SD

AS SP Avg

BA SP Avg

CB SP Avg

CY SP Avg

Short-Period Avg. Amplification versus PGA 

(Site Class E)

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

Mid-Period Amplification

PGA (g)

NEHRP

NGA MP Avg

NGA MP Avg-2 SD

NGA MP Avg+2 SD

AS MP Avg

BA MP Avg

CB MP Avg

CY MP Avg

Mid-Period Avg. Amplification versus PGA 

(Site Class E)
 13 11/14/12 

Figure 6. Short-period (Fig. 6a) and mid-period average amplification (Fig. 6b) values for site class D inferred 

from equally-spaced period values for each NGA developer (green lines), mean and 95% NGA limits (blue 

lines), and NEHRP site coefficients (black line) as a function of PGA. The plots show that the NEHRP 

F

a

and 

F

v

 coefficients are within 95% NGA uncertainty limits for all values except Fv at PGA > 0.3g. 

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Short-Period Amplification 

PGA (g)

NEHRP

NGA SP Avg

NGA SP Avg-2 SD

NGA SP Avg+2 SD

AS SP Avg

BA SP Avg

CB SP Avg

CY SP Avg

Short-Period Avg. Amplification versus PGA 

(Site Class D)

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

Mid-Period Amplification 

PGA (g)

NEHRP

NGA MP Avg

NGA MP Avg-2 SD

NGA MP Avg+2 SD

AS MP Avg

BA MP Avg

CB MP Avg

Mid-Period Avg. Amplification versus PGA 

(Site Class D)

(NGA values from Stewart and Seyhan, 2011)
 14 11/14/12 

Figure 7. Short-period (Fig. 7a) and mid-period average amplification (Fig. 7b) values for site class C for each 

NGA developer (green lines), mean and 95% NGA limits (blue lines), and NEHRP site coefficients (black line) 

as a function of PGA. The plots show that the NEHRP Fa and Fv coefficients are within 95% NGA uncertainty 

limits for all PGA values except for Fa with PGA > 0.1g and for Fv with PGA= 0.5g. 

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Short-Period Amplification

PGA (g)

NEHRP

NGA SP Avg

NGA SP Avg-2

SD

NGA SP Avg+2

SD

Short-Period Avg. Amplification versus PGA 

(Site Class C)

(NGA values from Stewart and Seyhan, 2011)

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

Mid-Period Amplification

PGA (g)

NEHRP

NGA MP Avg

NGA MP Avg-2 SD

NGA MP Avg+2 SD

AS MP Avg

BA MP Avg

CB MP Avg

CY MP Avg

Mid-Period Avg. Amplification versus PGA 

(Site Class C)

(NGA values from Stewart and Seyhan, 2011)
 15 11/14/12 

Figure 8. Short-period coefficients at SS=0.25 (Fig. 8a) and mid-period coefficients at S1=0.1 (Fig. 8b) as a 

function of 

S

v

for each NGA developer (green lines), mean and 95% NGA values (blue lines), and NEHRP site 

coefficients (black line). The plots show that the NEHRP 

F

a

and 

F

v

 coefficients are within 95% NGA 

uncertainty limits for all 

S

v

values except for 

F

a

 with values just beyond the limits for site class E and at 

indicated ground-motion levels. 

0

1

2

3

4

0 200 400 600 800 1000 1200

Short-Period Amplification 

Vs30 (m/s)

Short-Period Avg. Amplification versus Vs30

(SS = 0.25) 

NEHRP

BA SP Avg

CB SP Avg

AS SP Avg

CY SP Avg

NGA SP Avg

NGA SP Avg - 2 SD

NGA SP Avg + 2 SD

0

1

2

3

4

0 200 400 600 800 1000 1200

Mid-Period Amplification 

Vs30 (m/s)

Mid-Period Avg. Amplification vrsus Vs30

(S1=0.1)

NEHRP

BA MP I Avg

CB MP I Avg

AS MP I Avg

CY MP I Avg

NGA MPI Avg

NGA MP Avg - 2 SD

NGA MP Avg + 2 SD
 16 11/14/12 

Figure 9. Short-period coefficients at SS=0.5 (Fig. 9a) and mid-period coefficients at S1=0.2 (Fig. 9b) as a 

function of 

S

v

 for each NGA developer (green lines), mean and 95% NGA values (blue lines), and NEHRP 

site coefficients (black line). The plots show that the NEHRP 

F

a

and 

F

v

coefficients are within 95% NGA 

uncertainty limits for all 

S

v

 values except for 

F

a

 with values just beyond the limits for site class C at 

indicated ground-motion levels. 

0

1

2

3

4

0 200 400 600 800 1000 1200

Short-Period Amplification

Vs30 (m/s)

Short-Period Avg. Amplification versus Vs30

(SS=0.5)

NEHRP

BA SP Avg

CB SP Avg

AS SP Avg

CY SP Avg

NGA SP Avg

NGA SP Avg - 2 SD

NGA SP Avg + 2 SD

0

1

2

3

4

0 200 400 600 800 1000 1200

Mid-Period Amplification 

Vs30 (m/s)

Mid-Period Avg. Amplification versus Vs30

(S1=0.2)

NEHRP

BA MP I Avg

CB MP I Avg

AS MP I Avg

CY MP I Avg

NGA MPI Avg

NGA MP Avg - 2 SD

NGA MP Avg + 2 SD
 17 11/14/12 

Figure 10. Short-period coefficients at SS=0.75 (Fig. 10a) and mid-period coefficients at S1=0.3 (Fig. 10b) as a 

function of 

S

v

 for each NGA developer (green lines), mean and 95% NGA values (blue lines), and NEHRP 

site coefficients (black line). The plots show that the NEHRP 

F

a

and 

F

v

coefficients are within 95% NGA 

uncertainty limits for all 

S

v

 values except for

F

a

with values just beyond the limits for site class C and Fv 

value for site class D at indicated ground-motion levels. 

0

1

2

3

4

0 200 400 600 800 1000 1200

Short-Period Amplification

Vs30 (m/s)

Short-Period Avg. Amplification versus Vs30

(SS=0.75)

NEHRP

BA SP Avg

CB SP Avg

AS SP Avg

CY SP Avg

NGA SP Avg

NGA SP Avg - 2 SD

NGA SP Avg + 2 SD

0

1

2

3

4

0 200 400 600 800 1000 1200

Mid-Period Amplification

Vs30 (m/s)

Mid-Period Avg. Amplification versus Vs30

(S1=0.3)

NEHRP

BA MP I Avg

CB MP I Avg

AS MP I Avg

CY MP I Avg

NGA MPI Avg

NGA MP Avg - 2 SD

NGA MP Avg + 2 SD
 18 11/14/12 

Figure 11. Short-period coefficients at SS=1.0 (Fig. 11a) and mid-period coefficients at S1=0.4 (Fig. 11b) as a 

function of 

S

v

 for each NGA developer (green lines), mean and 95% NGA values (blue lines), and NEHRP 

site coefficients (black line). The plots show that the NEHRP 

F

a

and 

F

v

 coefficients are within 95% NGA 

uncertainty limits for all 

S

v

 values except for 

F

a

 for site class C and Fv value for site class D at indicated 

ground-motion levels. 

0

1

2

3

4

0 200 400 600 800 1000 1200

Short-Period Amplification 

Vs30 (m/s)

Short-Period Avg. Amplification versus Vs30

(SS= 1.0)

NEHRP

BA SP Avg

CB SP Avg

AS SP Avg

CY SP Avg

NGA SP Avg

NGA SP Avg - 2 SD

NGA SP Avg + 2 SD

0

1

2

3

4

0 200 400 600 800 1000 1200

Mid-Period Amplification

Vs30 (m/s)

Mid-Period Amplification versus Vs30

(S1=0.4g)

NEHRP

BA MP I Avg

CB MP I Avg

AS MP I Avg

CY MP I Avg

NGA MPI Avg

NGA MP Avg - 2 SD

NGA MP Avg + 2 SD
 19 11/14/12 

Figure 12. Short-period coefficients at SS=1.25 (Fig. 12a) and mid-period coefficients at S1=0.5 (Fig. 12b) as a 

function of 

S

v

 for each NGA developer (green lines), mean and 95% NGA values (blue lines), and NEHRP 

site coefficients (black line). The plots show that the NEHRP 

F

a

and 

F

v

coefficients are within 95% NGA 

uncertainty limits for all 

S

v

 values except for 

F

a

for site class C and Fv value for site class D at indicated 

ground-motion levels. 

0

1

2

3

4

0 200 400 600 800 1000 1200

Short-Period Amplification 

Vs30 (m/s)

Short-Period Avg. Amplification versus Vs30

(SS=1.25)

NEHRP

BA SP Avg

CB SP Avg

AS SP Avg

CY SP Avg

NGA SP Avg

NGA SP Avg - 2 SD

NGA SP Avg + 2 SD

0

1

2

3

4

0 200 400 600 800 1000 1200

Mid-Period Amplification

Vs30 m/s

Mid-Period Avg. Amplification versus Vs30

(S1=0.5)

NEHRP

BA MP I Avg

CB MP I Avg

AS MP I Avg

CY MP I Avg

NGA MPI Avg

NGA MP Avg - 2 SD

NGA MP Avg + 2 SD
 20 11/14/12 

Figure 13. Short-period coefficients at SS=0.25 (Fig. 13) and mid-period coefficients at S1=0.1 (Fig. 13) from 

Loma Prieta strong motion data (black site-class step function and continuous curves: Seed, 1992; Seed et 

al., 1994; Borcherdt, 1992, 1994; and Dobry et al., 1992, 1994; and Joyner et al., 1992, 1994) and the NGA 

coefficients proposed herein (brown dots). The figures show that the empirical NGA coefficients are in very 

good agreement with the empirical coefficients inferred from observed Loma Prieta strong-motion data, 

especially for

F

v

. The plots confirm that the proposed NGA coefficients (see Tables 1, 2, and 3) are in good 

agreement with Loma Prieta coefficients inferred with respect to a 

795 / Sv m s 

 and in turn consistent 

with the use of the site coefficients referenced to the mid-point of site class B. 

0

1

2

3

4

5

6

100 300 500 700 900 1100 1300

Short-Period Amplification, Fa 

Vs30 (m/s)

Loma Prieta Strong-Motion Data

Fa - 95%

Fa = (997 / Vs )^0.36

Fa +95%

Fa for Site Class Intervals

NGA SP Avg 0.1g

Site Class E Fa= (1050 / Vs)^0.35 (Borcherdt, 1994)

Site Class D

Site Class C

Site Class B

NGA and Loma Prieta Fa Estimates at Ss=0.25

0

1

2

3

4

5

6

100 300 500 700 900 1100 1300

Mid-Period Amplification, Fv

Vs30 (m/s)

Loma Prieta Strong-Motion Data

Fv - 95%

 Fv = (1067 / Vs )^0.64

Fv + 95%

Fv for Site Class Intervals

NGA MP Avg 0.1g

Fv = (1050 / Vs)^0.65 (Borcherdt, 1994)

Site Class E

Site Class D

Site Class C

Site Class B

NGA and Loma Prieta Estimates of Fv at S1=0.1
 21 11/14/12 

Figure 13 shows that the average spectral amplification values inferred from the NGA data base 

(Ancheta, 2012) agree extremely well with the coefficients derived from the strong-motion 

recordings of the Loma Prieta earthquake, and in turn the adopted NEHRP coefficients at 0.1g with 

the exception of 

F

a

 which was increased from 2.0 to 2.5 to account for observed response of 

Mexico City clays. The plots confirm that the proposed NGA coefficients (see Tables 1, 2, and 3) 

are in good agreement with the Loma Prieta coefficients inferred using various independent 

analyses techniques. The agreement confirms that average spectral amplifications inferred from 

strong-motion recordings at low strain levels are consistent with those derived from GMPEs and the 

NGA data base. The agreement confirms that the Loma Prieta coefficients inferred with respect to 

an average ground condition of 

795 / Sv m s 

with corresponding regression analysis of recorded 

data implying unity amplification near 1050 m/s is consistent with NGA coefficients proposed 

herein and consistent with MCER maps inferred at 

760 / Sv m s  .

REFERENCE SITE CONDITION DISCUSSION 

Further insight into the appropriate 

S

v

 to be used as a reference velocity for the simplified 

procedure with site classes can be gained by considering the results of the application of a linear 

regression model to derive continuous curves to relate the logarithm of short- and mid-period 

empirical amplification coefficients to the logarithm of

S

v

. Application of this model to the Loma 

Prieta coefficients led to a set of functions that allow the site coefficients computed with respect to 

795 / S ref v m s 

to be expressed as a continuous function of 

S

v

by the following functions 

( / )ma F v v a S norm S (1a) 

and 

 ( / )mv F v v v S norm S

 , (1b) 

where the empirical regression fits to the Loma Prieta coefficients imply that 

1050 / S norm v m s 

(Borcherdt, 1994). Application of this model to coefficients computed for the Northridge strong motion 

recordings yields a similar result, namely linear regression models fit to the logarithm of spectral ratios 

computed with respect to an average 

S

v

for the rock sites of

795 / S ref v m s 

indicate in all cases that 

S norm S ref v v 

 and 

S norm S ref v v 

(Borcherdt, 2002). Hence, if continuous curves specified by the 

functions in 1a and 1b are to be used to predict amplifications with respect to

760 / S ref v m s 

, then the 

normalization velocity for the functions implied by the empirical fits is

1050 / S norm v m s  . This model 

specified by 1a and 1b with 

1050 / S norm v m s 

implies that the normalization velocity in the model, 

namely

1050 / S norm v m s  , is at the mid-point of the 

S

v

 interval for site class B. The fact that 

1050 / S norm v m s 

 in the above model is not equal to the 

S

v

for the average rock conditions to which the 

coefficients were computed, namely

795 / S ref v m s 

, has led to considerable confusion in the literature. 
 22 11/14/12 

Nevertheless, within the known approximations implied by average site coefficients applied to a range of 

site conditions in each site class interval, the above considerations show that the NEHRP site 

coefficients computed with respect to an average 

795 / S ref v m s 

for rock sites, which is near 

760 / m s

, the site coefficients predicted by the empirical curves 1a and 1b with 

1050 / S norm v m s  , 

and the reference site condition of

760 / S ref v m s 

 for the MCER design maps are all consistent 

with each yielding an amplification coefficient of unity for 

. 

760 / S ref v m s  . 

Figure 14 shows the NGA mid-period site coefficients at S1=0.1 as proposed herein (Tables 1b and 

2b, red step function) and mid-period coefficients inferred by Stewart and Seyhan (Table 6.2, 2012, 

purple step function) superimposed on mid-period site coefficients at S1=0.1 (Fig . 13b) as inferred 

from Loma Prieta strong motion data (black curves). The plots show that the mid-period 

coefficients proposed in Tables 1b and 2b are in close agreement with those measured from the 

Loma Prieta strong-motion recordings. The coefficients depicted by the purple curves significantly 

under predict the measured coefficients, especially for site class E. Application of the purple 

coefficients using the simplified procedures as currently adopted in ASCE/SEI 7-10 implies a 

significant uniform reduction in maximum considered earthquake design motions as predicted on 

MCER maps. 

INFERENCE OF NGA SITE COEFFICIENTS AT INTERMEDIATE VALUES OF 

S

v

A model such as that represented by equations 1a and 1b could be used to predict NGA coefficients for 

the various site classes. The NGA coefficients as inferred for the short- and mid-period bands at the midpoints of the 

S

v

 intervals (Figs. 8-12 show that a simple model as described by 1a and 1b does not predict 

all of the NGA coefficients as inferred directly from the GMPEs for various levels of input motion 

equally well. Until such a model is developed, the proposals herein recommend that if continuous curves 

based on the NGA data base are to be used to infer the coefficients at intermediate values of 

S

v , then 

those values should be inferred using linear interpolation of the coefficients as specified at the mid-point 

of each site class interval. This approach has the advantages that coefficients predicted for values of 

S

v

near the mid-point of each site class will agree exactly with those adopted for the site class as predicted 

directly using the NGA GMPEs. Examination of Figures 13 and 14 implies that linear interpolation 

provides a simple, but reasonably good approximation for intermediate values of 

S

v

 . It also has the 

advantage that no additional inconsistencies are introduced between adopted site coefficients and those 

implied directly from the NGA GMPEs. 

ACKNOWLEDGEMENTS 

This study was motivated by the Task 8 NGA West 2 project coordinated by the Pacific Earthquake 

Engineering Research Center (PEER) and requests for proposals for consideration by the Provision 

Update Committee (PUC) for ASCE/SEI 7-10. Special acknowledgments are due to: Project Director, 

Yousef Bozorgnia; PUC Member, C.B. Crouse; Project PI, Jonathan Stewart; and Steering Committee 

Members, Donald Anderson, Kenneth W. Campbell, C.B. Crouse, Robert W. Graves, I.M. Idriss, Maury 

S. Power, and Walter J. Silva, with a special note of thanks to graduate student Emel Seyhan for all of her 

hard work and contributions. Jonathan Stewart and Emel Seyhan kindly provided compilations of NGA 

GMPE results on which this study is based. Suggestions by the Steering Committee and reviews 

provided by A. Frankel, M. Celebi, and G. Glassmoyer were helpful. 
 23 11/14/12 

Figure 14. NGA mid-period site coefficients at S1=0.1 as proposed herein (Tables 1, 2, and 3; red step 

function) and mid-period coefficients inferred by Stewart and Seyhan (Table 6.2, 2012, purple step 

function) superimposed on mid-period site coefficients at S1=0.1 (Fig. 13) as inferred from Loma Prieta 

strong motion data (black curves). The plots show that the mid-period coefficients proposed in Tables 1, 2, 

and 3 are in close agreement with those measured from the Loma Prieta strong-motion recordings. The 

coefficients depicted by the purple curves significantly under predict the measured coefficients. 

Application of the purple coefficients using the simplified procedures as currently adopted in ASCE/SEI 7-10 

implies a significant uniform reduction in MCER design motions, dependent on the model chosen by Stewart 

and Seyhan (2012) to predict the site coefficients. 

0

1

2

3

4

5

6

100 300 500 700 900 1100 1300

Mid-Period Amplification, Fv

Vs30 (m/s)

Loma Prieta Strong-Motion Data

Fv - 95%

 Fv = (1067 / Vs )^0.64

Fv + 95%

NGA MP Avg 0.1g (Borcherdt, 2012)

Fv = (1050 / Vs)^0.65 (Borcherdt, 1994)

Table 6.2 (Stewart & Seyhan, 2012)

Table 6.2 (Stewart & Seyhan, 2012)

NGA MP Avg 0.1g (Borcherdt, 2012)

Fv Loma Prieta

Site Class E

Site Class D

Site Class C

Site Class B

Comparison of Measured Fv Site Coefficients at S1 = 0.1 with Proposed NGA Changes
 24 11/14/12 

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