Boore-Atkinson Provisional NGA Empirical Ground …peer.berkeley.edu/.../ba_provisional_equations_v1.70.pdf · Boore-Atkinson Provisional NGA Empirical Ground-Motion Model for the

Boore-Atkinson Provisional NGA Empirical Ground-Motion Model for the Average Horizontal

Component of PGA, PGV and SA at Spectral Periods of

0.05, 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 4, and 5 Seconds

by

David M. Boore U.S. Geological Survey Menlo Park, California

and

Gail M. Atkinson

Carleton University Ottawa, Ontario, Canada

v. 1.7 (October, 2006)

C:\peer_nga\report\ba_provisional_equations_v1.70.doc, Modified on 10/30/2006

Provisional Empirical Ground-Motion Model

By

David M. Boore Gail M. Atkinson

Introduction This report contains provisional empirically-based equations for predicting peak acceleration, peak velocity, and pseudo spectral acceleration at periods of 0.05, 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 4, and 5 seconds. This report builds on earlier reports; see the end of this report for a table of revisions. This report and accompanying files are available from the online publications link on the first author’s web site (http://quake.usgs.gov/~boore/). Limited time was available to investigate the provisional equations. In earlier versions of the equations, residual plots were prepared and studied, but time did not allow that to be done for the equations reported herein. We don’t anticipate that the residuals plots would have changed much (except that the trend in residuals with distance will have been largely removed). Comparisons of the predicted motions were made against the distance and magnitude dependence of the data (the former for the smallest earthquake in the dataset and the ten earthquakes with magnitudes between 7.0 and 8.0,as well as the 1989 Loma Prieta, 1994 Northridge, and 1995 Kobe earthquakes). Among other things, many residual plots should be prepared, and the regressions should be repeated with randomly selected earthquakes and/or data removed from the dataset (in order to investigate the leverage of specific data on the results and to estimate the epistemic uncertainty in the results). We did, however, repeat the regressions excluding the 1999 Chi-Chi mainshock (no aftershock data were used in our regressions). The ground-motion predictions with and without the Chi-Chi mainshock are quite similar; excluding the Chi-Chi data leads to somewhat smaller motions for M 7.5 and larger motions for M 5.5 at distances within about 10 km. The functional form of the equations is given below, and the coefficients can be found in the Excel file ba_oct27_usnr.xls (the first row of coefficients in the file contains coefficients for 4pga nl ; period values of 0 and -1 correspond to peak acceleration and peak velocity, respectively). This is a major revision of the report issued by PEER on May 31, 2006. It includes a smoothed rather than abrupt transition for the nonlinear part of the amplification in the vicinity of pga_low (0.06g). The previous version could result in a kink in plots of ground motion vs. distance. The following figure shows an example using the May 31, 2006 and the July, 2006 (smoothed) version of the equations (in subsequent figures reference is sometimes made to the October 06, 2006, equations; these are identical to


1

the July, 2006, equations---only the report, and hence the date, changed). The computation was for a low shear-wave velocity (180 m/s), with the consequence that the deamplification due to nonlinear site response balances the increase in rock motions with decreasing distance within about 20 km:

Figure 1. Comparing peak acceleration with and without smoothing of the amplification for the peak acceleration used in the nonlinear site response around 0.06g.

This report and the accompanying equations differ from previous reports in the specification of the pseudo-depth h (as discussed in a later section); as a result, the equations in this version of the report differ from those in the July, 2006, and October 06, 2006, reports. Data Selection During the course of the project, the first author spent a large amount of time on spot checking the database. A small sampling of that work is contained in these files: notes_on_tabas_records.pdf


2

regarding_pump_station_10_record.pdf lex_lgpc_comparison.pdf More Data for Cape Mendocino 1992.pdf CM92_interface_or_not_4nga.pdf notes_on_rinaldi_record.pdf daves_notes_whats_wrong_with_duzce.doc steidl_email_LA00_10jan03.pdf His reports are available on request. Data were excluded based on a number of criteria; each criterion was assigned a number in a column of containing flatfile record number and flag. Only data with flag = 0 were used in developing the empirical ground-motion prediction equations. The criteria and assignments for each NGA flatfile record number are given in the two Excel files (included in the zip file containing this report and the spreadsheet of regression coefficients): recnum_flag.xls flag_definitions.xls For the convenience of the reader, here is a copy of the reasons for not including the data, taken from flag_definitions.xls: one h component Jensen Admin Bldg? no V30 Spikes, baseline problems (see my email of 12/20/04 and my notes lex_lgpc_comparison.pdf) dam abutments dam toe base of column base of pier BASEMENT, 12.7M BELOW GROUND, 1.8M ABOVE BEDROCK BASEMENT, 6.4M BELOW GROUND Greater than or equal to 3 stories S triggers older events not included in BJF, probably because distances are too uncertain proprietary records with restrictions on use earthquake in oceanic crust stable continental region (SCR) events basement recordings Geomatrix C, D, E, F, G, H, J (but not including Lexington Dam for LP89,LA Dam for NR94, and Martis Creek Dam for 2001 Moduplicate record? aftershocks Chi-Chi_quality D (Lee et al) chi_chi_colocated (remove record from older instrument), Many such records removed earlier because they are quality class D second trigger dam crest


3

only SMART1 data for this quake, should be considered a one observation earthquake (recall BJF criteria). one h component Note that about half the records in the NGA flatfile are aftershocks of the 1999 Chi-Chi earthquake. We did not use aftershock records because there is some concern that the spectral scaling of aftershocks differs from mainshocks (see Boore and Atkinson, 1989, and Atkinson, 1993). The ground-motion values are NOT geometric mean values, but rather are values that are not dependent on the particular orientation of the instruments used to record the horizontal motion (in which case the geometric mean can be 0.0 if the motion were perfectly polarized along one component direction). The measure used is discussed in the paper by Boore et al. (2006). In this report equations are given for pgv , pga , and psa at 0.05, 0.1, 0.2, 0.3, 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 sec. Note that equations for peak ground displacement (pgd) are not given in this report, nor will they be in subsequent reports. In our view, pgd is too sensitive to the low-cut filters used in the data processing to be a stable measure of ground shaking. We recommend using response spectra at long periods instead of pgd. Explanatory Variables Following the philosophy of Boore et al. (1993, 1994, 1997), simple equations were sought in the analysis. The explanatory variables are moment magnitude M, JBr distance, and continuous for site

characterization (as given in the last column of the file NGA Flatfile_nonPublic_V7.27.xls by the combination of Silva’s interpretation of NCREE measurements for Taiwan, Brian Chiou’s correlation method for Taiwan, etc., updated with the file Update 1 (02-17-06) to NGA Flatfile V7.2 (07-11-05).xls, which uses some of Rob Kayen’s estimates). The fault

mechanism was specified by the plunge of the P- and T-axes, as detailed in fault_classification_using_p_t_axes.pdf and daves_notes_mechrake_c3_stage1_stage2_pga_25july2005.pdf (available from the first author upon request).

30V

30V

The analysis used the distances estimated by R. Youngs for earthquakes with no finite-fault models. The functional form does not include such things as depth-to-top of rupture or hanging wall/footwall terms, or basin depth. We offer our equations as


4

an alternative to the more complicated equations of other NGA developers, and expect them to be somewhat easier to implement in many applications. Methodology STAGE 1 REGRESSIONS (DISTANCE DEPENDENCE): The analysis used the two-stage regression discussed by Joyner and Boore (1993, 1994). All regressions were done period-by-period; there was no smoothing of coefficients (with the exception of the pseudodepth h, as discussed below). The distance dependence is determined in the first stage. In the August 2005 version of the equations, a good fit to the distance decay was obtained using a single effective geometrical-spreading term--- what is termed here the “ ” coefficient (see equation 4, shown later in this report,

for the form of the equation specifying the distance dependence). (Note the increasing sparseness of data beyond about 80 to 100 km and the sparseness of data at distances less than about 3 km) as seen in the figure below).

1c

0.1 1 10 100 10004

5

6

7

8

rjb (km)

M

strikeslipnormalreverseslip

recordings used by BA05 stage1 regression for 0.2 sec

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Figure showing distribution of recordings used in the analysis for s differentiated by fault mechanism (points with 0.2T = JBr less

than 0.1 km have been plotted at 0.1 km).

But because the data from several earthquakes under-represented in the database clearly show a curvature (in log-log space), we did a separate analysis of a more complete dataset for three small events (compiled by J. Boatwright and L. Seekins) and for the 2004 Parkfield earthquake. The effective anelastic coefficient obtained from this analysis was then used in

the regression of the NGA dataset for the August 2005 version of the equations. (Attempts to let both and be free resulted in positive values

of for some periods, and this would lead to an increase of ground motion

for great enough distances). For the August 2005 set of equations, after experimenting with various constraints, values of were fixed in the

regression of the NGA dataset, with only the coefficient, pseudodepth ,

and event terms as free variables (“event terms” is shorthand for the arithmetic average of the logarithm of the observations, corrected to a reference velocity of 760 m/s using the equation given later for , adjusted

to a distance of 5 km) (see daves_notes_mechrake_c3_stage1_stage2_pga_25july2005.pdf). The NGA data were first adjusted for linear and nonlinear site amplification to a value of 760 m/s, using

3c

1c 3c

3c

3c

1c h

SF

30V sF below. Only data for 80jbr ≤ km were used

in the regression for the August 2005 equations, but all values of were

considered. 30V

Note that the soil amplifications were taken from Choi and Stewart (2005) for both linear and nonlinear amplifications (with a slight modification of the latter, as discussed later). The site amplification coefficients were not solved for in the regression analysis reported here. The equations given in the August 2005 report were developed using data only within 80 km, with the assumption that the distance dependence was independent of magnitude. Residual plots, as well as plot of motions from individual large earthquakes, showed a consistent mismatch between data and predictions for distances beyond 50 to 80 km. A number of ground-motion simulations supported this observation. To add magnitude dependence, we used all data less than 400 km and tried letting the coefficient be a regression variable. The resulting equations,

however, showed a tendency for increasing motions with distance (for large distances), for longer periods, as shown in this figure:

4c


6

We finally incorporated magnitude-dependent distance decay by letting the coefficient be a free variable in the regressions. The variable is that

used on the previous equations, as determined from the analysis discussed in daves_notes_mechrake_c3_stage1_stage2_pga_25july2005.pdf.

2c 3c

Consideration was given to the amount of change at various distances when data only to 80 km was used, compared to using data to 400 km. See Choice of RLE400 or RLE80 equations.pdf for a discussion and relevant plots (this file is included in the zip file containing this report). Determining the Pseudodepth (h): When we also let the pseudodepth h be free, we found that the curves for large earthquakes showed some overlap at close distances, as shown here:


7

On the other hand, it is clear from the figure above that the ground motions at close distances are strongly controlled by the value of the pseudodepth. In previous versions of our equations the final set of provisional equations were determined by fixing the pseudodepth at smoothed versions of those given in the August 2005 report, with only and as free regression

coefficients for the stage1 regression (in addition to “event” terms, which are basically the average ground motions for a single event projected to a distance of ). In this version we used a set of pseudodepths close to

those obtained by letting h be a free variable in the regressions. Our procedure was as follows (see the next figure for the various values of h and for the quadratic curves referred to in the following discussion): 1) we solved for h as a free parameter in the regression, where the regressions for pgv, pga, and each oscillator period as performed independently; 2) we fit a quadratic in terms of to the values of h; 3) we noticed that the h value for s was very small (it was less than the value for pga), and so we replaced that value with the h for pga and redid the quadratic fit; 4) we used the fitted quadratic to determine h values to be used in the stage 1 regressions. We also adjusted the h values for the pgv regressions to be that for the s regression. This choice was motivated by the magnitude scaling for pgv and for response spectra, shown later. Bommer and Alarcón (2005) conclude that the pseudovelocity response spectrum at 0.5 sec is roughly equivalent to

h1c 2c

refr

logT0.05T =

1.0T =

pgv , although simulations by the first author suggest that the relation is a function of both magnitude and distance. In addition, the magnitude scaling shown later suggests that the magnitude dependence of pgv is closer to that of the 3.0T = s response spectra than the s 0.5T =


8

response spectra; the h values change little for larger values of period (as seen in the next figure), so we chose the h value corresponding to s as a compromise. The value of h for acceleration is guided by the unequivocal statement that pseudoacceleration response is equivalent to

1.0T =

pga at periods much less than 0.1 sec. We modified the value of h slightly, from the value obtained from the h-as-a-free-variable result to the value assumed for the s oscillator. 0.05T = Note in the figure below that the values of h from the previous reports are consistently larger than used in this report (and that the values used by Boore et al., 1997, are in general quite different than those used in this report; this may be because Boore et al. did not consider nonlinear response, which tends to reduce motions on soil sites at close distances, which could lead to larger values of h than is the soil nonlinearity is taken into account). The figure below also shows the various values of the “geometrical spreading” coefficient ; the values of this coefficient are only slightly

dependent on the values of h. 1c

Later, in the section “Comparison of Predictions with Boore et al. (BJF97)” we also show comparisons of ground motions predicted using the October 06, October 25 (with h as a free parameter in the regressions), and October 27 sets of equations.


9

0.1 0.2 1 2 100

2

4

6

H

value used for PGV in August 2005, July 2006, & October 06 2006 equationsvalue from Oct. 25 solve-for-h PGV regressionvalue used in Oct. 27 BA PGV regressvalue used for PGA in July 2006 & October 06 2006 equationsvalue from Oct. 25 solve-for-h PGA regressionvalue used in Oct. 27 BA PGA regressfit to h from Oct. 25 regressionfit to modified h from Oct. 25 regressionBJF97 HAugust 2005, July 2006, & October 06 2006 equationsBA Oct. 25 solve-for-h regressionBA Oct. 25 h, modifiedBA Oct. 27 equations

0.1 0.2 1 2 10-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

Period (sec).

c01

value used for PGV in August 2005, July 2006, & October 06 2006 equationsvalue used in Oct. 27 BA PGV regressvalue used for PGA in July 2006 & October 06 2006 equationsvalue used in Oct. 27 BA PGA regressAugust 2005, July 2006, & October 06 2006 equationsBA Oct. 25 solve-for-h regressionBA Oct. 27 equations

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STAGE 2 REGRESSIONS (MAGNITUDE SCALING): The event terms from the first regression were used in a weighted stage2 regression. As discussed in Joyner and Boore (1993), the stage2 regression was iterative in order to solve for 2σ . Only events with more than one

observation were used in the regression. The following algorithm was used for the magnitude dependence:

1. Do a single quadratic fit. If the M for which the quadratic starts to decrease (Mmax) is greater than 8.5, use this regression for the magnitude dependence.

2. If Mmax is less than 8.5, then do a two-segment regression, hinged at

Mh, with a quadratic for M ≤ Mh and a linear function for Mh < M. If the slope of the linear function is positive, use this regression for the magnitude dependence. We chose Mh = 7.0 based on subjective inspection of nonparametric plots of data (many such plots were produced and studied before commencing the regression analysis).

3. If the slope of the linear segment is negative, redo the regression

constraining the slope of the line above Mh to be 0.0. Note that the equations for almost all periods less than or equal to 1.0 sec required the constraint of zero slope; this is saying that for these periods the data themselves indicated oversaturation. We felt that because of limited data, oversaturation was too extreme at this stage of equation development, and we chose to be conservative by imposing saturation rather than oversaturation.

The magnitude dependence was first done grouping all mechanisms. Plots of event terms vs. magnitude showed that normal fault earthquakes had motions consistently below those for strikeslip and reverse for most periods. For this reason, another set of equations was developed in which the magnitude dependence was constrained by the run using unspecified mechanism, with only the intercept term (the value for M refM= ) as a free

parameter. All analyses were done using Fortran programs developed by DMB; these programs are available on request. The Equations The equation for predicting ground motions is: 30ln (M) ( , M) ( , , M)M D jb S jb TY F F r F V r εσ= + + + , (1)


11

where ε is the fractional number of standard deviations of a single predicted value of from the mean value of (e.g., lnY lnY 1.5ε = − would be 1.5 standard deviations smaller than the mean value). The coefficient Tσ is period

dependent, as given by the columns sigtu (for mechanism unspecified) and sigtm (for mechanism specified) in ba_oct27_usnr.xls. The magnitude scaling is given by these equations: For M hM≤

, (2) 2

1 2 3 4 5 6(M) (M ) (M )M hF eU e S e N e R e M e M= + + + + − + − h

For M> hM

2

1 2 3 4 7 8(M) (M ) (M )M hF eU e S e N e R e M e M= + + + + − + − h , (3) where U , , , and S N R are used to specify the mechanism, as given by the values in the following table: Mechanism U S N R unspecified 1 0 0 0 strikeslip 0 1 0 0 normal 0 0 1 0 reverse 0 0 0 1 The distance scaling is given by 1 2 3 4( ,M) [ (M )]ln( / ) [ (M )]( )D jb ref ref ref refF r c c M r r c c M r r= + − + + − − , (4)

where

2 2jbr r h= + (5)

and distances are in units of km. The site amplification is given by the equation S LIN NF F F L= + , (6)

where the linear and nonlinear terms are denoted by and . LINF NLF


12

The linear term is given by

30ln( / )LIN lin refF b V V= , (7)

where the units of the velocities are m/sec. In our May 31 PEER report, the nonlinear term was given by For 4 _pga nl pga low≤ : ln( _ / 0.1)NL nlF b pga low=

For 4 _pga nl pga low> :

ln( 4 / 0.1)NL nlF b pga nl=

where the nonlinear factor is controlled by the slope , as given by the

equations below (see May 31 PEER report) and the pga values are given in g. (Note that for

nlb

0.0NLF = 4 0.pga nl 1= , because Choi and Stewart point out that

the “linear” amps were derived for motions with about this mean (median?) amplitude.) The discontinuous derivative of with respect to at the hinge

pga of pga_low leads to a kink in plots of ground motion vs distance (as shown in an earlier plot). A way around this is to use a cubic polynomial

SF ln( 4 / 0.1)pga nl

(8)

2 31 1ln( _ / 0.1) ln( 4 / ) [ln( 4 / )] [ln( 4 / )]NL nlF b pga low b pga nl a c pga nl a d pga nl a= + + + 1

between 14pga nl a= and 24pga nl a= (on either side of pga_low). The

coefficients can be found using the constraints that the polynomial and its slope must equal and its slope when NLF 14pga nl a= and when 24pga nl a= .

These constraints lead to the following equations for the cubic coefficients b, c, and d: 0.0b = (9) 2(3 ) /nlc y b x x= ∆ − ∆ ∆ (10)

(11) 3(2 ) /nld y b x= − ∆ − ∆ ∆x


13

where 2 1ln( / )x a a∆ = (12)

and (13) 2ln( / _ )nly b a pga low∆ = To summarize for the nonlinear part of the site amplification: for 14pga nl a≤ :

ln( _ / 0.1)NL nlF b pga low= (14)

for : 1 24a pga nl a< ≤ (15) 2 3

1 1ln( _ / 0.1) [ln( 4 / )] [ln( 4 / )]NL nlF b pga low c pga nl a d pga nl a= + + for : 2 4a pga nl<

ln( 4 / 0.1)NL nlF b pga nl= (16)

The nonlinear factor is controlled by the slope , as given by the following

equations: nlb

For 30 1V v≤ 1nlb b= (17)

For 1 30 2v V v< ≤ (18) 1 2 30 2 1 2( ) ln( / ) / ln( / )nlb b b V v v v= − + 2b For 2 30 refv V v< ≤

2 30 2ln( / ) / ln( / )nl ref refb b V v v v= (19) For 30refv V<

0.0nlb = (20)


14

and 4pga nl is given by the equation for above, but with coefficients that will differ somewhat from the coefficients for Y

lnYpga= (the coefficients for

4pga nl were developed earlier; they need only give approximately correct values for the peak acceleration on rock-like sites, as long as internal consistency is maintained---as is the case here, with the site amplifications being used to reduce the observations to a reference velocity before doing the regressions, and the same site amplifications being used when predicting ground motions using the results of the regressions). The coefficients for

4pga nl are in the first row of coefficients in ba_oct27_usnr.xls. More discussion of the nonlinear and linear corrections is contained in daves_notes_on_including nonlinear_amps_26july2005.doc and daves_notes_comparing_teamx_bjf_14augustjuly2005.doc, available upon request. Here are plots of and : linb nlb

Figure showing comparison of the slope that controls the linear amplification

function, from Boore et al. (1997) and Choi and Stewart (2005).


15

Figure showing comparison of the slope that controls the nonlinear amplification function.

Here is a plot of the nonlinear contribution to site amplification showing how the cubic polynomial gives a smoothed version of the original amplification. The amplification is for m/s: 30 180V =

0.02 0.03 0.04 0.1 0.20.6

0.7

0.8

0.9

1

pga4nl (g)

Non

linea

rA

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[exp

(FN

L)]

For pga, V30 = 180 m/sOriginalSmoothed (a1 = 0.03, a2 = 0.09)

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And here are plots of the combined amplification for 0.2T s= and , with and without smoothing:

3.0T s=

0.01 0.02 0.1 0.2 1 20.1

0.2

1

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10

pga

Am

plifi

catio

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V30

=76

0m

/s

T = 0.2 sV30 = 100 m/soldV30 = 180 m/soldVs = 360 m/soldV30 = 760 m/sV30 = 1500 m/s

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0.01 0.02 0.1 0.2 1 20.1

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Am

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Comparison with Data Inserted below are plots of ground motions vs. distance for all earthquakes in the dataset with magnitude between 7 and 8 (see legend for specification of earthquake). In addition, we have included plots for the 1994 Northridge, 1995 Kobe, and 1989 Loma Prieta earthquakes. To help judge the relative source scaling, the plots include data and predictions for the smallest earthquake (note that data for that earthquake is missing for T = 3 sec because the largest useable period is 2.6 s). In all plots, records with JBr

less than 0.1 km have been plotted at 0.1 km. The curves are from the regression fits and include the “event” terms found for the specific regression---they are intended to help assess the first stage regression and do not include event-to-event variability (see the plots of “event” for the stage2 regressions for this variability). Curves for both the previous version and the latest version of the equations are shown. The new version does a somewhat better job of fitting the sparse close-in data.


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0.1 1 10 1000.1

1

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rJB (km)

Ypgv

0.1 1 10 1001

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rJB (km)

Y

pga

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Y

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0.1 1 10 1001

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YT = 0.2 sec

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Northridge (M = 6.69)Yorba Linda (M = 4.27)Oct. 27 equationsOct. 06 equations

T = 3.0 sec


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0.1 1 10 1000.1

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Ypgv

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T = 1.0 sec

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Kobe (M = 6.90)Yorba Linda (M = 4.27)Oct. 27 equationsOct. 06 equations

T = 3.0 sec


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Ypgv

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Y

pga

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Oct. 27 equationsOct. 06 equationsLoma Prieta (M = 6.93)Yorba Linda (M = 4.27)

T = 3.0 sec


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rJB (km)

Y

pga

0.1 1 10 1001

10

100

1000

rJB (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

YT = 0.2 sec

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Oct. 27 equationsOct. 06 equationsCape Mendocino (M = 7.01)Yorba Linda (M = 4.27)

T = 3.0 sec


22

0.1 1 10 1000.1

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100

rJB (km)

Ypgv

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1000

rJB (km)

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pga

0.1 1 10 1001

10

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Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

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Hector Mine (M = 7.13)Yorba Linda (M = 4.27)Oct. 27 equationsOct. 06 equations

T = 3.0 sec


23

0.1 1 10 1000.1

1

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rJB (km)

Ypgv

0.1 1 10 1001

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1000

rJB (km)

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pga

0.1 1 10 1001

10

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rJB (km)

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0.1 1 10 1001

10

100

1000

rJB (km)

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rJB (km)

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Oct. 27 equationsOct. 06 equationsDuzce (M = 7.14)Yorba Linda (M = 4.27)

T = 3.0 sec


24

0.1 1 10 1000.1

1

10

100

rJB (km)

Ypgv

0.1 1 10 1001

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100

1000

rJB (km)

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pga

0.1 1 10 1001

10

100

1000

rJB (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

YT = 0.2 sec

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10

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1000

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Oct. 27 equationsOct. 06 equationsLanders (M = 7.28)Yorba Linda (M = 4.27)

T = 3.0 sec


25

0.1 1 10 1000.1

1

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rJB (km)

Ypgv

0.1 1 10 1001

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100

1000

rJB (km)

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pga

0.1 1 10 1001

10

100

1000

rJB (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

YT = 0.2 sec

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10

100

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rJB (km)

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Oct. 27 equationsOct. 06 equationsTabas (M = 7.35)Yorba Linda (M = 4.27)

T = 3.0 sec


26

0.1 1 10 1000.1

1

10

100

rJB (km)

Ypgv

0.1 1 10 1001

10

100

1000

rJB (km)

Y

pga

0.1 1 10 1001

10

100

1000

rJB (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

YT = 0.2 sec

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10

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rJB (km)

Y

Oct. 27 equationsOct. 06 equationsManjil (M = 7.37)Yorba Linda (M = 4.27)

T = 3.0 sec


27

0.1 1 10 1000.1

1

10

100

rJB (km)

Ypgv

0.1 1 10 1001

10

100

1000

rJB (km)

Y

pga

0.1 1 10 1001

10

100

1000

rJB (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

YT = 0.2 sec

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10

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T = 1.0 sec

0.1 1 10 1001

10

100

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rJB (km)

Y

Oct. 27 equationsOct. 06 equationsKocaeli (M = 7.51)Yorba Linda (M = 4.27)

T = 3.0 sec


28

0.1 1 10 1000.1

1

10

100

rJB = (km)

Ypgv

0.1 1 10 1001

10

100

1000

rJB = (km)

Y

pga

0.1 1 10 1001

10

100

1000

rJB = (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB = (km)

YT = 0.2 sec

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0.1 1 10 1001

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rJB = (km)

Y

T = 1.0 sec

0.1 1 10 1001

10

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rJB = (km)

Y

BA Oct. 27Oct. 27 equationsOct. 06 equationsSt. Elias (M = 7.54)Yorba Linda (M = 4.27)

T = 3.0 sec


29

0.1 1 10 1000.1

1

10

100

rjb

167

pgv

0.1 1 10 1001

10

100

1000

rjb

167

pga

0.1 1 10 1001

10

100

1000

rjb

167

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rjb

167

T = 0.2 sec

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Oct. 27 equationsOct. 06 equationsChi-Chi (M = 7.62)Yorba Linda (M = 4.27)

T = 3.0 sec


30

0.1 1 10 1000.1

1

10

100

rJB (km)

Ypgv

0.1 1 10 1001

10

100

1000

rJB (km)

Y

pga

0.1 1 10 1001

10

100

1000

rJB (km)

Y

T = 0.1 sec

0.1 1 10 1001

10

100

1000

rJB (km)

YT = 0.2 sec

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Oct. 27 equationsOct. 06 equationsDenali Fault (M = 7.90)Yorba Linda (M = 4.27)

T = 3.0 sec


31

Here are plots of the “event” terms (average ln motion at rref = 5 km) as a function of magnitude, with the regression curve superimposed. The fault type for each earthquake is indicated, as are curves for mechanism unspecified and for strikeslip, normal, and reverse faults (the type of mechanism is indicated by color).

4 5 6 7 8

2

10

20

100

M

Y(r

=5

km)

pgv

4 5 6 7 820

100

200

1000

2000

M

pga

4 5 6 7 820

100

200

1000

2000

M

Y(r

=5

km)

T = 0.05 sec

4 5 6 7 8

100

200

1000

2000

M

T = 0.1 sec

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_1.d

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T = 0.2 sec

4 5 6 7 820

100

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M

SSNormalReverseMechanism unspecifiedstrikeslipnormalreverse

T = 0.3 sec


32

4 5 6 7 8

10

100

1000

M

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=5

km)

T = 0.5 sec

4 5 6 7 81

10

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M

T = 1.0 sec

4 5 6 7 81

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4 5 6 7 80.1

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SSNormalReverseMechanism unspecifiedstrikeslipnormalreverse

T = 5.0 sec

Comparison of Predictions with Boore et al. (BJF97) We now show comparisons of the new predicted ground motions with those from the Boore et al. (1997) equations. We first show a comparison of the magnitude-distance distribution of the data used in each set. The first plot is for pga and the second plot is for 1.0T = s.


33

0.1 1 10 1004

5

6

7

8

rjb (km)

M

BA_NGABJF97

recordings used by BA_NGA stage1 regression for PGA

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recordings used by BA_NGA stage1 regression for T=1.0 secF

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34

Note that many more data are used in the new equations, and that the data fill in gaps at close distances for all magnitudes, they add many more data at small magnitudes at all distances, they add data for large magnitudes, and they fill out the distribution so that no longer is there a strong correlation between distance and magnitude. We now show comparisons of ground motions for m/s, followed by a set of comparisons for m/s

(the velocity for each plot is given in the plot legend). For m/s the

plots are for pga and for T = 0.1, 0.2, 1.0, and 2.0 sec, as indicated in the y-axis title. For m/s we show plots for the 12 ground-motion

intensity measures considered in this report. The latter set of plots compare predictions from the October 06 (same as July 2006), the October 25 (with h as a free parameter in the regressions), and the October 27 sets of equations, as well as the ground motions from the BJF97 equations (for pga and for oscillator periods between 0.1 and 2 s)). We discuss the results here rather than after the figures: we think that the comparisons are good for M and

30 310V = 30 760V =

30 310V =

30 760V =

JBr ranges for which data were available for the BJF97 equation development.

Large differences are in regions for which data formerly were not available, putting little constraint on the assumption of distance-independent magnitude scaling. Also note that no nonlinear soil response was included in the BJF97 equations; the nonlinear soil response now included leads to noticeable differences for the V30=310 m/s comparison for shorter periods, closer distances, and larger magnitudes. Regarding the differences between BJF97 and our current equations for

s sec at close distances and large M: 1) There were almost no data available in BJF97 for M~7.5 and

1T =JBr < 10 km (see earlier plot). The data

are for JBr centered about 30 km. The discrepancy between the predictions

from the BJF97 and the new equations is not nearly as strong for JBr near 30

km as it is for JBr < 10 km. Probably a good part of the discrepancy at JBr

~ 30 km is due to including more data for large quakes in our current equations. The values of BJF97 at close distances are strongly controlled by the assumption of distance-independent M scaling (so the scaling is driven by the JBr ~ 30 km data). The current equations allow for some distance-

dependence to the magnitude scaling.


35

1 2 10 20 10010

20

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rjb

PG

A(c

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M 5.5, 6.5, 7.5; mech u, V30 = 310 m/sBJF97BA_Oct27

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SA

(cm

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1 2 10 20 10010

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1 2 10 20 100

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V(c

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M 5.5, 6.5, 7.5; mech u, V30 = 760 m/sBA Oct. 06BA Oct. 25 free hBA Oct. 27

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M 5.5, 6.5, 7.5; mech u, V30 = 760 m/sBJF97BA Oct. 06BA Oct. 25 free hBA Oct. 27

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52

We include here a comparison of standard deviations for the new equations and for the BJF97 equations. Note that the standard deviations are significantly larger for the new equations. The larger standard deviations will offset to some extent the smaller ground motions for large magnitudes in the construction of seismic hazard maps. In a future version we might include a distance-dependent epistemic uncertainty to try to capture some of the uncertain involved with the pseudodepth variable h (which is controlled by the sparse data at close distances). Table. Comparison of intra-event (σ), inter-event (τ), and total (σT) standard errors for the BA_October27 (mechanism unspecified) and the Boore et al. (1997) equations. For the latter, the intra-event error is S1, which does not include component-to-component variation. This is appropriate in view of the measure of ground-motion intensity being used in this report. per σ: ba_oct27 σ: bjf97 τ: ba_oct27 τ: bjf97 σT: ba_oct27 σT: bjf97 pgv 0.51 0.29 0.59 pga 0.50 0.43 0.26 0.18 0.57 0.47

0.05 0.58 0.37 0.68 0.10 0.53 0.44 0.33 0.00 0.62 0.440.20 0.52 0.44 0.29 0.00 0.60 0.440.30 0.55 0.44 0.27 0.01 0.61 0.440.50 0.56 0.44 0.26 0.05 0.61 0.441.00 0.57 0.45 0.31 0.12 0.65 0.472.00 0.58 0.47 0.40 0.21 0.70 0.523.00 0.57 0.50 0.41 0.28 0.70 0.574.00 0.58 0.39 0.70 5.00 0.60 0.41 0.73

Influence of the 1999 Chi-Chi mainshock on the predicted motions We now compare our new equations derived with and without data from the 1999 Chi-Chi, Taiwan, mainshock. Excluding Chi-Chi generally leads to smaller, not larger, motions, at distances less than 10—30 km, except for M = 5.5, where the predictions from the equations without Chi-Chi lead to slightly larger motions. The comparisons are for 30 760V = m/s. The first set is for mechanism

unspecified for pga and T = 0.1, 0.2, 1.0, 2.0, 3.0 sec. The second set is for reverse mechanism and pga, T = 0.2 and T = 1.0 sec. The oscillator period is given in the y-axis title.


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Acknowledgments We thank Rakesh Saigal for drawing our attention to some confusing terminology in v. 1.5. Art Frankel was a useful thorn in our side, asking lots of insightful questions and catching an error in the stage1 plots. References Atkinson, G.M. (1993). Earthquake source spectra in eastern North America, Bull. Seism. Soc. Am. 83, 1778—1798. Bommer, J. J. and J. E. Alarcón (2005). The prediction and use of peak ground velocity, J. of Earthquake Engineering 9, (in press). Boore, D. M. and G. M. Atkinson (1989). Spectral scaling of the 1985 to 1988 Nahanni, Northwest Territories, earthquakes, Bull. Seism. Soc. Am. 79, 1736—1761.


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Boore, D. M., W. B. Joyner, and T. E. Fumal (1993). Estimation of response spectra and peak accelerations from western North American earthquakes: An interim report, U. S. Geological Survey Open-File Report 93-509, 72 pp. Boore, D. M., W. B. Joyner, and T. E. Fumal (1994). Estimation of response spectra and peak accelerations from western North American earthquakes: An interim report, Part 2, U. S. Geological Survey Open-File Report 94-127, 40 pp. Boore, D. M., W. B. Joyner, and T. E. Fumal (1997). Equations for estimating horizontal response spectra and peak acceleration from western North American earthquakes: A summary of recent work, Seism. Research Letters 68, 128—153. Boore, D. M., J. Watson-Lamprey, and N. A. Abrahamson (2006). GMRotD and GMRotI: Orientation-independent measures of ground motion, Bull. Seism. Soc. Am. 96, 1502—1511. Choi, Y. and J. P. Stewart (2005). Nonlinear site amplification as function of 30 m shear wave velocity, Earthquake Spectra 21, 1—30. Joyner, W.B. and D.M. Boore (1993). Methods for regression analysis of strong-motion data, , Bull. Seism. Soc. Am. 83, 469—487. Joyner, W. B. and D. M. Boore (1994). Errata, , Bull. Seism. Soc. Am. 84, 955—956.


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Date Modifications 02 August 2006 Improve specification of sigma in the

equation for ln Y.

13 September 2006 Minor revisions [added “2005” after “August”, typos, etc]); attempt to clean up discussion of nonlinear amplifications.

22 September 2006 Added this table of modification; replaced amplification figure with the one showing the new and old amplifications (with and without smoothing). Added footer containing filename and creation date.

11 October 2006 ● Revised equations: Periods of 0.05, 0.3, 0.5, 4.0, and 5.0 sec added, and the equations for the other periods were changed slightly because the values of h and c03 were taken from a quadratic fit to the values used previously. ● Revised text: Extensive revision, including comparison of motions from new equations with those from Boore et al. (1997).

12 October 2006 Corrected stage1 figures (plotting points for which JBR is less than 0.1

km at 0.1 km) and at Art Frankel’s request, added stage1 plots for 1994 Northridge, 1995 Kobe, and 1989 Loma Prieta earthquakes (all with M < 7.0)

13 October 2006 Add comparison of motions predicted from equations derived with and without the 1999 Chi-Chi, Taiwan, mainshock.

28 October 2006 Major revision to equations, due to change in assumed values of h.


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