sacampl

Introduction

David Boore has written many papers related to strong ground motion and also developed a set of computer programs to support his research. His home page giving publications, computer codes and lectures is https://www.daveboore.com/ore.com/. The SMSIM (stochastic-method simulation) package is widely used. Originally included in this package was a program to estimate site-amplification through the use of the quarter-wavelength approximation

[Boore, D.M. and L.T. Brown (1998). Comparing shear-wave velocity profiles from inversion of surface-wave phase velocities with downhole measurements: Systematic differences between the CXW method and downhole measurements at six USC strong-motion sites, Seismol. Research Letters 69, 222-229. (778 Kb)]

Although the SiteAmp code is distributed separately from the current SMSIM package, the site_amp.for (dated Aug 13, 2001) is used here to check the CPS sacampl program.

sacampl

This program uses a velocity model in the MDOEL96 format of Computer Programs in Seismology and command line arguments. For the current version the response is computed at frequencies between 0.1 and 20Hz at increments of 0.1Hz. The command sequence is

 Usage: sacamp -M model   [-P | -S ] [-A angdeg | -AYPay_parameter] [-TXT] [-?] [-h]
 -M model   (default none )  Earth model file
 -P         (default false )  P response
 -S         (default true  )  S response
 -A  angdeg (default none )  S angle incidence at base
 -RAYP  ray_parameter (default none) (s/km) if model in km
        NOTE: Either the angle or the ray parameter is required
 -TXT       (default false) Output in file sacamp.txt
 -?         (default none )  this help message 
 -h         (default none )  this help message

The default output will be two Sac binary amplitude spectra files named AMP.sac.am and KAMP.sac.am. The first file contains the quarter-wavelength site effect. The second is the first multiplied by the site attenuation factor [ - $e x p (- π f κ)],where κ = Σ (t i /q i)$ $gives the
attenuation effect of all layers above the base
layer of the model.In the
computation of κ, I assume vertical wave
propagation.$

$exp( - \pi f \kappa )$

$\kappa = \sum (t_i / Q_i )$

Comparison

The table gives the data files and command sequence to run the two programs. SITE_AMP has a interactive input while sacampl is controlled form the command line.

site_amp	sacampl
Model
t_amp.dat: Sample input file to site_amp Depth SVel Dens 1/Q 0 0.300 2.0 0.10 0.010 0.300 2.0 0.10 ! constant from 0.000 to 0.010 0.010 0.600 2.0 0.06 0.020 0.600 2.0 0.06 ! constant from 0.010 to 0.020 0.020 0.800 2.0 0.05 0.040 0.800 2.0 0.05 ! constant from 0.020 to 0.040 0.040 1.500 2.2 0.02 0.060 1.500 2.2 0.02 ! constant from 0.040 to 0.060 0.060 2.500 2.5 0.01 0.160 2.500 2.5 0.01 ! constant from 0.060 to 0.160	soil.mod: MODEL.01 Soil model with Q ISOTROPIC KGS FLAT EARTH 1-D CONSTANT VELOCITY LINE08 LINE09 LINE10 LINE11 H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS 0.0100 1.5 0.3 2.0 0.05 0.10 0 0 1 1 0.0100 1.5 0.6 2.0 0.03 0.06 0 0 1 1 0.0200 1.6 0.8 2.0 0.025 0.05 0 0 1 1 0.0200 3.0 1.5 2.2 0.01 0.02 0 0 1 1 0.1000 5.0 2.5 2.5 0.005 0.01 0 0 1 1 0.0 6.0 3.5 2.7 0.000 0.000 0 0 1 1
Execution
SITE_AMP Enter name of model file (cr to quit): t_amp.dat Does model file contain either Q or 1/Q (y/n)? y Q is in model file; note that Q < 1.0 is taken is 1/Q. *Specify a kappa for exp(-pikf) (y/n)?* n Enter name of output file (cr = <stem>.asc): t.txt Do you want to specify density coefficients (y,n)? n The program must determine the line on which the data start. To help do this, here are the first three lines of the input file: Line 1: Sample input file to site_amp Line 2: Depth SVel Dens 1/Q Line 3: 0 0.300 2.0 0.10 Enter the line on which the data start (2 or 3): 3 The model appears to be piecewise continuous; if so, press ENTER; if not, press n: (hit return her) Enter source velocity and density: 3.5 2.7 Enter angle-of-incidence at source level (in degrees): 10 Specify frequencies(y/n)?: y Tabulated frequencies(y/n)?: n Individual frequencies(y/n)?: n No, so enter freqlow, freqhigh, nfreq: 0.1 20 200 Log-spaced frequencies(y/n)?: n FINISHED --- Loop back for another case Enter name of model file (cr to quit): (hit return here)	sacampl -M soil.mod -S -A 10 -TXT

The site_amp creates the file t.txt while sacampl creates the Sac files AMP.sac.am and KAMP.sac.am and the text file sacampl.txt. Here we compare selected columns (13,14,16) of the site_amp output to the sacampl.txt. Note for this comparison the sacampl.txt has been sorted in terms of decreasing frequency. The columns display the frequency, site site amplification without Q attenuation, and the effective amplification that includes the Q effect of the entire column, e.g., column 2 multiplied by ( - $exp( - \pi f \kappa )$ .

Incident angle of 10 degrees

site_amp

sacampl

t_amp-f   t_amp-a   t_ampak
2.000E+01 3.939E+00 2.659E+00
1.000E+01 3.939E+00 3.236E+00
9.000E+00 3.939E+00 3.301E+00
8.000E+00 3.939E+00 3.366E+00
7.000E+00 3.814E+00 3.324E+00
6.000E+00 3.596E+00 3.196E+00
5.000E+00 3.411E+00 3.092E+00
4.000E+00 3.114E+00 2.879E+00
3.000E+00 2.687E+00 2.533E+00
2.000E+00 1.817E+00 1.747E+00
1.000E+00 1.240E+00 1.216E+00
9.000E-01 1.208E+00 1.186E+00
8.000E-01 1.178E+00 1.159E+00
7.000E-01 1.150E+00 1.134E+00
6.000E-01 1.124E+00 1.111E+00
5.000E-01 1.100E+00 1.089E+00
4.000E-01 1.078E+00 1.069E+00
3.000E-01 1.056E+00 1.050E+00
2.000E-01 1.036E+00 1.032E+00
1.000E-01 1.018E+00 1.016E+00

 Freq(Hz)    Amp     Amp(kappa)
 2.000E+01 3.939E+00 2.659E+00
 1.000E+01 3.939E+00 3.236E+00
 9.000E+00 3.939E+00 3.301E+00
 8.000E+00 3.939E+00 3.366E+00
 7.000E+00 3.814E+00 3.324E+00
 6.000E+00 3.596E+00 3.196E+00
 5.000E+00 3.411E+00 3.092E+00
 4.000E+00 3.039E+00 2.809E+00
 3.000E+00 2.488E+00 2.346E+00
 2.000E+00 1.692E+00 1.627E+00
 1.000E+00 1.217E+00 1.193E+00
 9.000E-01 1.188E+00 1.168E+00
 8.000E-01 1.162E+00 1.144E+00
 7.000E-01 1.137E+00 1.121E+00
 6.000E-01 1.114E+00 1.101E+00
 5.000E-01 1.092E+00 1.081E+00
 4.000E-01 1.071E+00 1.063E+00
 3.000E-01 1.052E+00 1.046E+00
 2.000E-01 1.034E+00 1.030E+00
 1.000E-01 1.016E+00 1.014E+00

The site amplification is based on the velocity density model. The kappa effect is for the entire column from the base of the model upward. The comparison for an S-wave incident at an angle of 10 degrees is quite good. For an incidence angle of 45 degrees, the comparison is now

Incident angle of 45 degrees

site_amp

sac_amp

t_amp-f   t_amp-a   t_ampak
2.000E+01 3.340E+00 2.255E+00
1.000E+01 3.340E+00 2.745E+00
9.000E+00 3.340E+00 2.799E+00
8.000E+00 3.340E+00 2.855E+00
7.000E+00 3.235E+00 2.819E+00
6.000E+00 3.050E+00 2.711E+00
5.000E+00 2.895E+00 2.624E+00
4.000E+00 2.645E+00 2.445E+00
3.000E+00 2.285E+00 2.155E+00
2.000E+00 1.562E+00 1.502E+00
1.000E+00 1.116E+00 1.094E+00
9.000E-01 1.094E+00 1.075E+00
8.000E-01 1.075E+00 1.059E+00
7.000E-01 1.059E+00 1.044E+00
6.000E-01 1.044E+00 1.032E+00
5.000E-01 1.032E+00 1.022E+00
4.000E-01 1.022E+00 1.014E+00
3.000E-01 1.013E+00 1.007E+00
2.000E-01 1.007E+00 1.003E+00
1.000E-01 1.002E+00 1.000E+00

 Freq(Hz)    Amp     Amp(kappa)
 2.000E+01 3.340E+00 2.255E+00
 1.000E+01 3.340E+00 2.745E+00
 9.000E+00 3.340E+00 2.799E+00
 8.000E+00 3.340E+00 2.855E+00
 7.000E+00 3.235E+00 2.819E+00
 6.000E+00 3.050E+00 2.711E+00
 5.000E+00 2.895E+00 2.624E+00
 4.000E+00 2.581E+00 2.386E+00
 3.000E+00 2.116E+00 1.995E+00
 2.000E+00 1.455E+00 1.399E+00
 1.000E+00 1.095E+00 1.074E+00
 9.000E-01 1.077E+00 1.058E+00
 8.000E-01 1.061E+00 1.044E+00
 7.000E-01 1.047E+00 1.033E+00
 6.000E-01 1.035E+00 1.023E+00
 5.000E-01 1.024E+00 1.014E+00
 4.000E-01 1.016E+00 1.008E+00
 3.000E-01 1.009E+00 1.003E+00
 2.000E-01 1.004E+00 1.000E+00
 1.000E-01 1.001E+00 9.991E-01

Here there are slight differences at frequencies less than 5Hz.

The comparison give confidence in the sacampl program.

Use of sacampl

The reason for writing this program was to be able to have the site amplification in the format of a Sac file and to use the same velocity model format as used in the execution of synthetic seismogram codes of Computer Programs in Seismology. In the examples that follow this site amplification is compared to plane-wave synthetics and complete wavenumber integration synthetics. To emulate the site amplification response, the computations are based on two set of models: a halfspace to represent the hard rock site, and the same model with a thin veneer of low velocity materials to represent a soil site. The procedure will be to compute Green's functions at the surface of the two models, compute the Fourier amplitude spectra, and then to form the ratio of spectra at the soil site to the hard rock site. These will be compared to the sacampl prediction.

The computations that follow require the March, 2024 release of Computer Programs in Seismology which now better supports the Amplitude spectra format of Sac files by gsac.

Plane Wave Study

Complete Synthetic Study

Surface wave approach

Discussion

This program was written very quickly. As such there may be some differences with respect to the results of site_amp. For the simple comparison made above, these differences do not seem significant.

The comparison of the site response estimation using synthetics shows that the SH response is similar to that given by sacampl. The surprising results is the large radial component amplification.

As remarked in the plane-wave study for large angles of incidence, and as seen in the time domain study at large distances, for which the angle of incidence is large, the site effect of the radial component because very large. As a matter of fact at an epicentral distance of 20 km, angle of incidence of 63^o the radial ratio is very large at a frequency of 3 Hz. The surface wave approach show a large resonance at about 4 Hz. The surface-wave study indicates the importance of the radial ellipticity, but cannot include the tempering factors of attenuation which will reduce the level at high frequencies.

Summary

The output of
sacampl may be useful as a first approximation of site amplification. Since it is run from the command line, it would be easy to loop through different velocity models in a bath processing environment.

The only caveat here is that the site response of the Fourier amplification and not the Response Spectra amplification