A comparison of distance dependent scaling relations of these two regions to the Atkinson and Boore (1995) model for eastern North America demonstrates the effects of differences in Q(f). In addition the New Madrid data require larger values of g(r) at distances greater than 150 km than the Atkinson and Boore (1995) model.

Since the initiation of the National Earthquake Hazard Reduction Program in the 1970's and because of interest in defining seismic source zones for the siting of critical facilities, regional seismic networks have been acquiring data throughout the country. Because of limitations in communication bandwidth, these networks consisted primarily of vertical component sensors, which do not require the horizontal motions needed for aseismic design.

The problem is made worse by unknown site effects, poorly defined earthquake source size, and poorly calibrated seismic instruments. If the model of ground motion is taken to be the composite effects of the source, propagation distance and the site, e.g., the logarithmic measure of the peak ground motion is related to the logarithms of each of the factors by the relation

Aki (1980) introduced and Frankel et al. (1990) used a coda normalization technique to attempt this. In the frequency domain, the spectrum of the signal of interest, A _S (f) at frequency, f can be represented as a product of terms:

The seismic coda follows the largest signal. Its Fourier amplitude spectrum in windows centered on a total lapse time (time after origin time), tau can be represented as

The essence of the Aki (1980) and Frankel et al. (1990) technique is to empirically determine the functional C ( f, tau ) and then to use the coda level at a reference lapse time tau _ref compute the ratio A _S (f) / A _C ( f , tau _ref ) Note that this ratio, eliminates the source and site terms mathematically.

If this can be done, then the scaled signal will only have the effects of radiation pattern and path. Averaging over many earthquakes will then give the effective path operator, a composite of the source and path effects. The assumptions and data processing for this to work are very important:

1. It is assumed that the coda and signal frequencies are the same so that the instrument filtering effect can be removed. This is only true for point Fourier amplitude spectra, but is approximately true if smoothed spectra or narrow band pass filtered time domain signals are used.
2. The measure of coda amplitude must be smooth across frequency to avoid dividing by zero. This can be handled in the time domain with narrow band pass filtered signals by working with the complex envelope or an RMS average.
3. The coda excitation is assumed independent of distance from the source, as long as the reference lapse time used is such that transition from the direct S wave to the coda is avoided. Typically, one uses coda data for tau > 2 t _S where t _S is the direct S travel time.
4. The frequency dependent site term for the coda is assumed to be identical to that of maximum ground motion. This is a tricky assumption since the direct wave and the coda are completely different wavefields. The coda at large lapse times consists of scattered shear waves trapped within the crust. For distances greater than about 100 km, the main S-wave field also consists of shear waves trapped within the crust, and the angle of incidence of the various ray components of the wavefield at the site would be similar. At short distances, the main S-wave arrival may consist of only a single incident ray, and thus the frequency dependent site effect may be different. This difference in the S and coda wave site terms may be reduced if the site consists of a layer of very low shear-wave velocities over rock, which is certainly the case for many seismograph station sites in the central US.

If the coda normalization works, then

In our approach, the coda normalization technique is use to determine an initial estimate of DISTANCE = log D(r) , which is then used in a least squares regression for the SRC, SITE and DISTANCE. By using this a priori estimate, both the usefulness of the coda normalization technique and the effects of unknown source and site terms can be assessed.

The DISTANCE functional used is a non-parametric function, e.g., piecewise linear segments to permit the data to define the distance scaling. Data are available in the 10 - 500 km distance range for both New Madrid and the Southern Great Basin. The parametric form is used to permit the data themselves to define the geometrical spreading and because Atkinson and Mereu (1992) demonstrate that simple functional forms are not appropriate for real data.

The peak ground motion at each frequency is modeled by the relation:

To avoid model bias by a predefined functional form for D(r), the analysis assumes that D(r) = SUM c _iN_i(r), where N_i(r) is a linear interpolation function, and the C _i determined. To permit a solution constraints are applied:

• SUM SITE_l = 0
• D(40 km) = 0
• c_i-1 - 2 c_i + c_i+1 = 0

These conditions are applied by adding additional equations to the linear equations to be solved. These additional equations are multiplied by large weights to force the condition. The last condition has a smaller weight than the other two, since we do not want to force a pure linear distance dependence. The real purpose is to span gaps in the data. In a non-linear solution, one could also force the distance term to be physical, e.g., no significant increase with distance.

All data are from instruments with responses given in terms of pole-zero system transfer functions. The recorded time histories are deconvolved using recursive digital filters to form ground velocity in the 0.5 - 40 Hz band. The ground velocity is then

• band pass filtered using a cascade of an 8 pole Butterworth high pass filter at fn/1.414 Hz and an 8 pole Butterworth low pass filter at fn*1.414 Hz. The peak filtered ground velocity is noted. The filter frequencies used are 1, 2, 3, 4, 6, 8, 10, 12, 14 and 16 Hz.
• processed to estimate the RMS signal level as a function of time for coda analysis
• and processed to estimate coda energy for application of Hosbiba's technique.

Before any data are used for analysis of peak motion with distance, the peak RMS amplitude (usually coincident in time with the peak amplitude) must be 3 times greater than the RMS noise prior to the P arrival.

This network was operated by the USGS for DOE to monitor seismic activity about the proposed Yucca Mountain facility. The following table indicates the regression results at different frequencies.

FREQ NOBS MEAN_RESIDUAL SIGMA      SIGMA_BAR NEVNT NSTN NDIST

   1  746  0.206E-07    0.156E+00  0.573E-02 165   65   17
   2 1224 -0.738E-08    0.169E+00  0.484E-02 165   65   17
   3 1338 -0.729E-08    0.170E+00  0.464E-02 165   65   17
   4 1386 -0.416E-08    0.166E+00  0.445E-02 165   65   17
   6 1414 -0.155E-07    0.167E+00  0.445E-02 165   65   17
   8 1396 -0.832E-08    0.167E+00  0.448E-02 165   65   17
  10 1345  0.811E-08    0.164E+00  0.446E-02 165   65   17
  12 1255  0.632E-08    0.163E+00  0.460E-02 165   65   17
  14 1152  0.358E-07    0.160E+00  0.471E-02 165   65   17
  16 1032  0.500E-07    0.157E+00  0.489E-02 165   65   17

Here FREQ is the filter center frequency in Hz, NOBS is the number of observed peak values, MEAN_RESIDUAL is the mean residual of fit over all distances. The small value indicates that at least one criteria of a good fit is met. SIGMA is the standard of dat about the mean. This is the expected distribution of any single observation. SIGMA_BAR is the estimated standard error of the mean. NEVNT is the number of events, NSTN is the number of stations and NDIST is the number of distance coefficients used in the regression.

Figure 1 provides shows regression analysis results at two frequencies of 2 and 10 Hz. The bottom panel, RESIDUAL, displays the individual residuals as a function of distance. The horizontal red line indicates zero residual. Log 10 units are used throughout. The purpose of the figure is to test the present of any of residuals with distance, which would indicate an imperfection in the determination of the D(r) term. The center panel shows the final D(r) term (blue) with its error bars. The trend in red is an initial estimate of the D(r) term based on a coda normalization technique (Aki, 1980; Frankel et al., 1990). The upper panel presents the individual coda normalized data used to make the initial D(r) estimate.

The coda normalization works well at all frequencies when its D(r) and that from the regression are compared. The two differ at larger distances. This may not be a failing of the coda normalization technique, but rather one with the data sets. The network data are triggered, with a constraint on the length of the maximum trigger. Thus little coda data are available for events at larger distances. On the other hand, the peak amplitude analysis needed only the peak motions and did not rely on coda information. Thus at larger distances the peak values were on the traces, even though the coda was truncated. This is seen in the increased density of data points at larger distances for the peak amplitude analysis.

Figure 2 shows the D(r) term at all 16 frequencies. The jagged curves at high frequencies at larger distances are due to a lack of data and the requirement that the distance formula fit actual, even though poor data. We see that in the time domain that the peak amplitude varies as r^-1.5. Similar analysis of the Fourier amplitude spectra indicates that the spreading function at short distance is r^-1.0. This is different than many assumptions about ground motion, but reflects the observational evidence that duration increases with distance (Figure 6, below)

This network was operated by Saint Louis University for the USGS and the USNRC to monitor seismic activity in the New Madrid Seismic Zone. Data were also available from stations operated by the University of Memphis. In addition data from the PANDA deployment in the central region of the New Madrid seismic zone provided significant data at short distances. The following table indicates the regression results at different frequencies.

FREQ NOBS MEAN_RESIDUAL SIGMA      SIGMA_BAR NEVNT NSTN NDIST
   1  767  0.235E-06    0.216E+00  0.780E-02 237   83   17
   2 1127  0.112E-06    0.222E+00  0.660E-02 237   83   17
   3 1453  0.346E-07    0.233E+00  0.610E-02 237   83   17
   4 1726  0.314E-07    0.236E+00  0.569E-02 237   83   17
   6 2126 -0.673E-08    0.237E+00  0.515E-02 237   83   17
   8 2251 -0.192E-07    0.237E+00  0.499E-02 237   83   17
  10 2277 -0.523E-07    0.233E+00  0.489E-02 237   83   17
  12 2241 -0.257E-07    0.230E+00  0.487E-02 237   83   17
  14 2179 -0.316E-07    0.229E+00  0.490E-02 237   83   17
  16 2099 -0.269E-07    0.233E+00  0.508E-02 237   83   17

Here FREQ is the filter center frequency in Hz, NOBS is the number of observed peak values, MEAN_RESIDUAL is the mean residual of fit over all distances. The small value indicates that at least one criteria of a good fit is met. SIGMA is the standard of dat about the mean. This is the expected distribution of any single observation. SIGMA_BAR is the estimated standard error of the mean. NEVNT is the number of events, NSTN is the number of stations and NDIST is the number of distance coefficients used in the regression.

Figure 3 provides shows regression analysis results at two frequencies of 2 and 10 Hz, and is similar to Figure 1 in presentation. We note that for New Madrid, the coda normalization estimate of D(r) at short frequencies departs significantly from the regression results. Compared to the Southern Great Basin stations, the New Madrid stations providing information at short distances are all on top of 600 meters of alluvial/fluvial deposits. This may mean that the assumption of the equivalence of the peak motion and coda site terms is not valid at low frequency, where site resonance effects are expected.

Figure 4 shows the D(r) term at all 16 frequencies. At short distances the curves are very similar, except for the 1.0 Hz data. The time domain peak amplitude data again exhibit a r^-1.5 dependence at short distance, especially for higher frequencies, whereas the Fourier amplitude spectra, not show here, have a r^-1.0 dependence.

The current model proposed for use in eastern North America is that of Atkinson and Boore (1995). This model relies primarily on data from the Eastern Canada Telemetred Network (ECTN) to define the distance scaling of earth quake ground motion, and several large earthquakes in eastern and western Canada to define source spectra scaling. The paper provides all information required by random process theory to predict ground motion. The same filters used in the analysis of Southern Great Basin and New Madrid data were used to make estimates of filtered ground velocity as a function of distance. In addition the simulations were made for an M_W = 3.0 event, to be similar to magnitudes observed in the New Madrid study. This choice of simulation magnitude is necessary because source duration affects the scaling of time domain amplitudes.

Figure 5 presents the Atkinson-Boore estimates. In the distance range of 15 - 80 km we again see the r^-1.5. Note this is a model prediction, based ultimately upon their observations.

The data were also analyzed to model the seismic coda for times greater than twice the S-wave travel time by the functional relation

The A(t,f) was modeled as a piecewise linear function of the form A(t) = SUM b _iN_i(t) The constraints applied were as follow:

• SUM SITE = 0
• A(10 sec) = 0
• b_i-1 - 2 b_i + b_i+1 = 0

As expected, we found the SITE term estimate for the coda and peak motion studies to be similar. In addition the source terms were related as follow:

Coda Excitation from Regression on Source, Site terms:

Model:   Coda SRC  =  Peak SRC  +  A  +  B log f

Region            A             B

SGB         0.840(+-0.076)  0.653(+-0.091)
NMD         0.278(+-0.063)  1.250(+-0.076)

Individual Observations

	Freq	Coda = Peak + C  ErrC
SGB
  	1	0.486		0.20
  	2	0.945		0.12
  	3	1.101		0.15
  	4	1.195		0.18
  	6	1.203		0.16
  	8	1.310		0.16
  	10	1.355		0.14
	12	1.403		0.16
	14	1.400		0.23
	16	1.412		0.46
NMD
	1	0.256		0.22
	2	0.825		0.14
	3	1.104		0.13
	4	1.257		0.13
	6	1.221		0.12
	8	1.302		0.13
	10	1.375		0.13
	12	1.440		0.13
	14	1.521		0.13
	16	1.614		0.13

This is a purely empirical relation that can be used with the two equations to predict the relation of peak motion to coda level. It may also serve as a constraint of models of scattering. The minor caveat is in the nature of the SRC terms. The condition SUM SITE = 0 forces all common features of the site terms into the source term. Assuming that the features are common to both, then the A and B coefficients are not biased. Coda theory (Hoshiba, 1991; and Zeng, 1991) indicate that the coda energy is proportional to (1/Q scattering). The 'A' coefficient indicates that the difference in scattering Q between the two regions may be a factor of 10!

For the purposes of ground motion estimation, it is convenient to use a random process theory model (Boore, 1983) to estimate expected motions because of the simplicity of incorporating filter, source and other effects to estimate a wide variety of parameters. For example a model that successfully fits our filtered velocity observations could be used to predict peak ground velocity, even though we did not regressions on this parameter.

To make an estimate of peak motion, RPT requires only the observed spectra and an estimate of time domain duration. Thus knowledge of duration and Fourier spectra as a function of distance is required. We processed our data as follows. The bandpass filtered time series were used to estimate the signal duration defined as the time window that the INTEGRAL of velocity squared varies between 5% and 75% of the maximum. The integration starts shortly before the S arrival. The Fourier transform if the ground velocity is determined within this window and an RMS average of the amplitude spectra is taken within the bounds of fn/1.414 and fn*1.414 Hz. The reason for doing this is that the filtered time series was already available, and that a signal to noise criteria can be used to automatically reject poor data. As an added check on the appropriateness of the duration definition, the duration and spectra were used with random process theory to predict the peak amplitude and the 95% confidence level on the peak. For the most part, the agreement with actual data was at 90%.

Figures 6 and 7 show the durations at selected frequencies for the SGB and NMD networks.

The 6 Hz frequency was chosen for display because there were fewer observations at higher frequency for SGB. There was a definite tendency for the duration to decrease with increasing frequency, which is due in part to the shorter filter transient. At larger distances the NMD and AB95 curves are similar, but the NMD are slightly higher.

Peak ground motion estimates are controlled by a combination of duration, geometric spreading and anelastic attenuation. An initial attempt at modeling the observed filtered peak motions of Figures 2 and 4 was made. The parameters used for the two regions and also those of AB95 are given:

           NMD                SGB               AB95 
Q
        Qo     ETA       Qo       ETA       Qo       ETA
        900    0.30      230      0.6       680      0.36
DURATION
         R      T           R      T           R      T
        0.0    0.0         0.0    0.0         0.0    0.0
       40.0   10.0        15.0    3.75       10.0    0.0
       75.0   15.95       90.0    7.75       70.0    9.6
      150.0    9.95      105.0    5.80      130.0    7.8
      200.0   11.95      150.0    6.10     1000.0   42.6
      250.0   15.95     1000.0   17.40                  
      500.0   23.95                                     
DISTANCE
        R1     R2   POW     R1     R2   POW    R1     R2   POW
        0.0   50.0 -1.00    0.0   40.0 -1.0    0.0   70.0 -1.0
       50.0  120.0 -0.25   40.0  100.0 -0.5   70.0  130.0  0.0
      120.0  200.0  0.00  100.0  150.0  0.0  130.0 1000.0 -0.5
      200.0  220.0 -0.50  150.0  500.0 -0.5                   
      220.0  500.0 -1.00                                      

Here Q(f) = Q_o f ^ETA , duration T is linearly interpolated as a function of distance R, and the geometrical spreading of the S/Lg spectra is R ^POW for R₁ <= R <= R₂ .

Figures 8 and 9 show the RPT predictions for these parameters. These can be compared to observed data of Figures 2 and 4.

The RPT estimates made here seem to fit the data for the SGB and NMD data sets. However, the choice of Q and geometrical spreading were Hacks. It is necessary to constrain these parameters from the data set. Because of the variability of duration and geometrical spreading with distance, it is difficult to obtain Q from the time domain observations. Because T and Q tradeoff at large distance, a regression of the Fourier transform of filtered ground velocity was performed in the same manner as peak motion. The functional form of the D(r) term is virtually identical to that for the peak motion. This may question the use of a 1/SQRT(R) spreading at large distances.

Synthetic seismogram modeling using modal summation for a new model for the CUS based on the waveforms inversion of a broadband seismogram exhibits features similar to those observed, e.g., a large peak in vertical component motion near 200 km. At distances beyond this peak, the 1/SQRT(R) spreading starts to kick in, which implies that this spreading begins once the first strong supercritical arrival sequence has occurred. The same modeling shows that the SH motion does not have the possess the same high amplitude peak near 200 km, but behaves in a more uniform manner over the entire distance range.

Synthetic seismograms were made using two earth models. The model based on the waveform modeling of the September 26, 1995 Missouri earthquake demonstrates significant increase in amplitude in the 100-300 km distance range, in agreement with the observations of Figure 4. Unfortunately the durations are too short, even though there is a strong correlation between short duration and large amplitude. This means that the variability of duration with distance, as seen in Figures 6 and 7 is real and is related to regional crustal and upper mantle structure.

We are further processing synthetic seismograms to examine the nature of the geometric spreading of the Fourier amplitude spectra in the region of peak motion. This study will help understand the proper form of the distance term.

An effective Q for use with random process theory estimates of peak ground motion was developed in an ad hoc basis. Models of the seismic signal (Hoshiba, 1991; Zeng et al., 1991) show the inter-relation of scattering and intrinsic Q. The total attenuation of peak motion is a function of both intrinsic and scattering Q, while the coda level is a function of scattering Q.

If the coda envelope is studied for times greater than 2 t_S, where t_S is the S-wave travel time, the shape of the coda can be parameterized by a coda-Q value. Using the complete theory of the coda, which is a function of both scattering and intrinsic Q, Hoshiba (1993) compared the predicted coda shape to the observed, e.g., compared the predicted to observed coda-Q parameter. For some data sets and frequencies , coda-Q is indicative of intrinsic Q rather than scattering Q.

It is hoped that the values estimated using the technique will explain the experically determined differences in the Coda and Peak motion source terms, e.g., that the scattering Q's may differ by a factor of 10.

The following sets of figures present fitted coda shapes by a coda Q parameterization and also present signal information in a form suitable for analysis using Hoshiba's (1991) (also Mayeda et al., 1992) techniques. To fit the coda Q shape, we assume a functional form

where 0.4343 arises from log e, pi=3.1415927..., f is the frequency, and Q_c is coda Q. In the raw processing, an empirical coda shape is first determined from all data together with a level for each trace. A second step of processing applies a regression to fit the common coda shape to the above equation. A plot of the adjusted signal envelope is made for each frequency for verifying data quality and program operation. For this study the A(t) is the RMS average of filtered ground velocity in 5 second windows, overlapping every 2.5 seconds.

To perform the Hoshiba analysis, each trace level is adjusted so that the late coda signal overlaps, effectively correcting for source and site differences among traces. Then the integrated signal energy is determined by integrating the adjusted filtered ground velocity squared in windows 0-15, 15-30 and 30-45 seconds following S. The signal energies are plotted as a function of hypocentral distance. These data points can then be fit by Hoshiba's master curves in terms of intrinsic and scattering Q. It is noted that Hoshiba's curves are for an isotropic wholespace scattering medium, and not for a crustal waveguide. However, a preliminary though experiment shows that the increasing signal duration with distance overcomes the reduced number of scatterers to give a wholespace like coda amplitude to the first order. Because of the unknown crustal waveguide effects, the Q values obtained using Hoshiba's master curves will be called 'apparent' rather true values.

Southern Great Basin

Figure 10 shows the coda normalized envelopes for the SGB data at 2 Hz. The signals are plotted as a function of travel time, and colors are used to identify different portions of the signal: black, signal before P; red, signal between P and S; green, signal between S and twice the S travel time; and blue, signal in the stable coda. The heavy red line is the empirically determined coda shape function (for SGB data, this could only be determined at low frequencies because of limitations in the total data triggers, and is forced to be Q_c(f) = 114 f^0.91). (This value is very similar to that of Rogers et al.. (1987) who has a better data set at all frequencies). The symbols indicate the peak envelope value and the normalized peak amplitude used above to provide an initial estimate of D(r).

Figures 11 and 12 present the signal energy for 2 and 8 Hz, respectively. The red circle gives the energy in the 0-15 window following S. The green triangles are for the 15-30 second window, the blue '+' are for the 30-45 second windows, and the few 'X' are for the 30-100 second window. In all figures below, r² E(r) is plotted, following Mayeda et al. (1992).

In these figures, the Greek letter eta is the coefficient of total energy loss per unit distance. It is defined as eta = omega / Q V , (note that the decay of amplitude with distance is eta = omega / 2 Q V . The energy loss is the sum of an intrinsic attenuation and scattering attenuation. The albedo factor, B_o, is the ratio of scattering to total attenuation, e.g., eta _s / ( eta _i + eta _s ) . In the context of Zeng's (1991) formulation of the wholespace, acoustic scattering problem, eta controls the attenuation of the peak amplitude with distance. Both the scattering and intrinsic attenuation affect the coda shape.

New Madrid

Figure 13 shows the normalized signal envelope for New Madrid at 2 Hz. The envelope was well defined over the 1 - 16 Hz frequency range, and a functional fit of the form Q_c(f) = 735 f^0.5 was made. Figures 14-16 show the signal energy in the 0-15, 15-30, and 30-45 second windows for 2, 8, and 16 Hz respectively.

The results of initial runs of the Hoshiba analysis yields these values. Figures 11-12, and 14-16 result from a more detailed search to define confidence regions. At high frequencies, the SGB and NMD eta values are similar. This is also obvious in the observed data of Figures 2 and 4. At low frequencies, e.g., 2 Hz, total attenuation, and hence Q differ by a factor of about 3, which is consistent with the ad hoc numbers used in the RPT modeling. It is interesting that the albedos are very similar in both regions as a function of frequency.

The results of the Hoshiba analysis are indicators of the actual attenuation process, but they do not provide the true values for two reasons. First, only vertical component data are used which means that radiation pattern and free surface conversion of S->Z may violate the assumption that true S-energy is being estimated. The second reason, is that at larger distances, the effects of the crustal waveguide are not included in the Hoshiba theory.

Hoshiba Analysis (coda level defined at 75 and 150 seconds )
Error analysis will be added later: 

  Freq	eta		B0	etas		etai
SGB
     1	1.99500E-02	0.55	1.09700E-02	0.89770E-02
     2	1.99500E-02	0.30	0.59850E-02	1.39650E-02
     3	1.99500E-02	0.20	0.39900E-02	1.59600E-02
     4	2.51200E-02	0.20	0.50240E-02	2.00960E-02
     6	1.99500E-02	0.10	0.19950E-02	1.79550E-02
     8	1.99500E-02	0.05	0.09975E-02	1.89525E-02
    10	1.25900E-02	0.05	0.06295E-02	1.19605E-02
NMD
     1	0.19950E-02	0.95	0.18950E-02	0.09975E-02
     2	0.70260E-02	0.34	0.23720E-02	0.46540E-02
     3	0.63100E-02	0.30	0.18930E-02	0.44170E-02
     4	0.63100E-02	0.20	0.12620E-02	0.50480E-02
     6	0.79430E-02	0.20	0.15886E-02	0.63544E-02
     8	1.00000E-02	0.20	0.20000E-02	0.80000E-02
    10	1.00000E-02	0.15	0.15000E-02	0.85000E-02
    12	1.25900E-02	0.25	0.31475E-02	0.94425E-02
    14	1.25900E-02	0.25	0.31475E-02	0.94425E-02
    16	1.25900E-02	0.25	0.31475E-02	0.94425E-02

All three scaling relations, SGB, NMD and AB95 are similar at distances less than 70 km. The decrease of amplitude faster than 1/R is a combination of a 1/R spectral scaling with an increase of signal duration with distance.

At larger distances the effects of anelastic attenuation are apparent, especially when comparing the SGB relations to the other two. However, there are significant differences in the scaling, especially at low frequencies, beyond 150 km between the New Madrid and the AB95 curves. Since analysis of both data sets separated source, site and distance effects, and since the residuals of Figure 3 are independent of distance, the New Madrid results cannot be dismissed. AB95 cannot be used for the central United States vertical component motion. The New Madrid results can be understand in term an a velocity model that requires a positive gradient in the upper mantle beneath the Moho. This gradient is required to fit the broadband velocity to 1.0 Hz observed at the IRIS station CCM, 175 km, from the Missouri earthquake of September 26, 1990.

There is strong evidence that a R^-0.5 spreading term in the Fourier amplitude spectra is not appropriate in the 100-500 km distance range.

Several lessons were learned

• To calibrate the duration, distance spreading and Q parameters for Random Process Theory simulation, the Q and distance spreading were determined by fitting the Fourier Transform of the motion. The duration was adjusted to fit the time domain peak motion.
• The data normalization at 40 km, exaggerates regional differences, because of the implicit assumption that the excitation of the reference motion at 40 km is independent of the region. Note that the term excitation is now used in place of the source effect SRC. The excitation at 40 km depends upon the source but also upon the wave propagation (spreading, Q and duration) out to 40 km. Preliminary results for New Madrid indicates that AB95 overpredicts motion out to 70 km, and underpredicts beyond 150 km. At short distances the difference is due to the longer duration for New Madrid signals. At larger distances, the difference is due to the enhanced wave arrivals from Moho supercritical S arrivals.
• The last observation is that the signal duration at New Madrid is frequency dependent, with longer durations at lower frequencies! This may reflect differences in the nature of wave propagation and sensitivity to multipathing.

Finally the PANDA data set also contained horizontal component data, the analysis of which will be a topic for a future paper that attempts to define absolute scaling, horizontal to vertical ratios and frequency dependent site effects for the New Madrid alluvial sites.

S. Harmsen of the USGS provided the digital data from the SGB network.

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Atkinson, G. M., and R. F. Mereu (1992). The shape of ground motion attenuation curves in southeastern Canada, Bull. Seism. Soc. Am. 82, 2014-2031.

Atkinson, G. M., and D. M. Boore (1995). Ground-motion relations for eastern North America, Bull. Seism. Soc. Am. 85, 17-30.

Boore, D. M. (1983). Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra, Bull. Seism. Soc. Am. 73 1865-1894.

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