Use of freqlimits in <b>sac/gsac</b> transfer command

Introduction

The following Email was received from Somasish Bose on March 21, 2011

I shall find the surface wave dispersion curve for the events with epicentre distance 25 to 90 degree with sample rate 1, so the delta(sample interval ) is also 1 .

Now to remove the instrument response i have used the following command...

transfer from polezero subtype POLEZEROFILE to none frequency f1 f2 f3 f4

i am confuse to select f1, f2, f3, f4 .....so i used only the following command

transfer from polezero subtype POLEZEROFILE to none

please help me to select f1, f2, f3, f4
looking forward for your valuable reply .....

Response

To respond, we will consider the earthquake of 2012/10/28 03:04:11.0 56.769N 131.927W Mw=7.7 recorded on the vertical component sensors at MGMO (37.154N 92.269W).

My purpose in examining this event is to

test the performance of the broadband system which creates the trace NMMGMO_HHZ__.SAC
test the performance of the accelerometer which creates the trace NMMGMO_HNZ__.SAC
test the instrument response component of the metadata description of each channel.

If the instruments are performing correctly and if the given instrument responses are correct, then
the deconvolved ground motions must be the same.

Sample data

The next figures show the raw traces and also their Fourier amplitude spectrum. I have only applied the command rtr to remove the linear trend for the plot. This is very useful for the HNZ channel.

There are several thing to note. First the HHZ channel is a measure of gound velocity in the instrument passband, while the HNZ channel is proportional to ground acceleration. Thus the spectra should differ by a factor of 2πf. This difference is seen in the frequency range from 0.1 to 1.0 Hz. A careful examination indicates that there are significant differences in the spectra at low and high frequencies than cannot be accounted for by the factor of 2πf.

The instrument responses are compared in the next figure. The units are in counts/micron.

I know the response because the polezero files have many informative comments. These comments are written by the IRIS and the SLU modified rdseed programs. For your information, the important parts of the polezero files are as follow:

* CHANNEL(NSCL)NMMGMO HHZ * NETWORK NM * STATION MGMO * COMPONENT HHZ * LOCATION * INPUT UNIT NM * OUTPUT UNIT COUNT * DESCRIPTION Mountain Grove, MO * RATE (HZ) 100.0 * OWNER Cooperative New Madrid Seismic Network * COORD(SEED) NM MGMO: 37.1540 -92.2687 453.0 * ORIENTATION NM MGMO -- HHZ: 0.0 -90.0 0.0 * LAT-SEED 37.154 * LONG-SEED -92.2687 * ELEV-SEED 453.0 * INSTRMNTTYPE Trillium40=0577=40Sec=Q330HR=2631 * INSTRMNTCMNT Mountain Grove, MO^Cooperative New Madrid Seismic Network^^ * **** CONSTANT 2.7815E+05 ZEROS 6 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -6.8800E+01 0.0000E+00 -3.2300E+02 0.0000E+00 -2.5300E+03 0.0000E+00 POLES 7 -1.1030E-01 1.1110E-01 -1.1030E-01 -1.1110E-01 -8.6300E+01 0.0000E+00 -2.4100E+02 1.7800E+02 -2.4100E+02 -1.7800E+02 -5.3500E+02 7.1900E+02 -5.3500E+02 -7.1900E+02

* CHANNEL(NSCL)NMMGMO HNZ * NETWORK NM * STATION MGMO * COMPONENT HNZ * LOCATION * INPUT UNIT NM * OUTPUT UNIT COUNT * DESCRIPTION Mountain Grove, MO * RATE (HZ) 100.0 * OWNER Cooperative New Madrid Seismic Network * COORD(SEED) NM MGMO: 37.1540 -92.2687 453.0 * ORIENTATION NM MGMO -- HNZ: 0.0 -90.0 0.0 * LAT-SEED 37.154 * LONG-SEED -92.2687 * ELEV-SEED 453.0 * INSTRMNTTYPE ES-T=3303=2.0g=Q330SR=2631 * INSTRMNTCMNT Mountain Grove, MO^Cooperative New Madrid Seismic Network^^ * **** CONSTANT 1.0536E+10 ZEROS 2 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 POLES 4 -9.8100E+02 -1.0090E+03 -9.8100E+02 1.0090E+03 -3.2900E+03 -1.2630E+03 -3.2900E+03 1.2630E+03

freqlimits option

The sac/gsac command transfer has the option freqlimits f1 f2 f3 f4. This option applied a zero phase filter to the transfer process. This filter has the form

0 for f < f1

cosine taper between 0 and 1 for f1 < f < f2

1 for f2 < f < f3

cosine taper between 1 and 0 for f3 < f < f4

0 for f > f4

To illustrace the taper operation, I ran the following commands (the italics are comments):

r imp.sac read a time series consisting of an impulse transfer from none to polezero subtype NMMGMO_HHZ__.SAC.pz freqlimits 0.01 0.02 1 2 fft psp plot the spectra

the following plots overlay the original plot obtained without the freqlimits in black and the one using the freqlimits in red. From this plot you can understand how the freqlimits option works

Deconvolution

In the next examples, we will deconvolve the traces to ground velocity using two different freqlimits options. To avoid too much text here, I will indicate what was done for the HHZ channel. Exactly the same was done for the HNZ channel. The commands used were as follow:

r NMMGMO_HHZ__.SAC rtr transfer from polezero subtype NMMGMO_HHZ__.SAC.pz to vel freqlimits 0.005 0.01 40 50 w NMMGMO_HHZ__.SAC_0.005_0.01_40_50

and in the second example

r NMMGMO_HHZ__.SAC rtr transfer from polezero subtype NMMGMO_HHZ__.SAC.pz to vel freqlimits 0.050 0.10 5 10 w NMMGMO_HHZ__.SAC_0.050_0.10_5_10

The results are compared in the next set of figures. The file name shows in the image indicates the values of the freqlimits parameters used.

Recall that the ground motion must be the same. When using the very low frequencies, we see that there is noise before the P-wave arrival, however at later simes, g.,d about 800 sec into the trace, there is a good correspondence. This tells me that the accelerometer will provide a good indication of low frequency ground motion if the ground motion is large compared to noise.

The conclusion that I obtain is that

The instruments are functioning correctly
The given instrument responses are correct

Recommendations

The next question addresses the choise for the parameters of the freqlimits option.

The simple answer is that the passband must include the signal that you are interested in.

When I perform regional moment tensor inversion, I run the following commands in a bash shell script. Assume the the shell variable TRACE provides the name of the waveform.

#####
#    Use Computer Programs in Seismology saclhdr to get values from the trace header
#####
KSTNM=`saclhdr -KSTNM $TRACE`
KCMPNM=`saclhdr -KCMPNM $TRACE`
DELTA=`saclhdr -DELTA $TRACE`
FHH=`echo $DELTA | awk '{print 0.50/$1}' `
FHL=`echo $DELTA | awk '{print 0.25/$1}' `
#####
#    FHH is the Nyquist frequency and FHL is 1/2 the Nyquist frequency
#    This step is performed so that the filtering is valid for all
#    sample rates
#####

gsac << EOF
r ${TRACE}
transfer from polezero subtype ${TRACE}.pz  TO VEL FREQLIMITS 0.002 0.003 ${FHL} ${FHH}
w deconvolved_trace.sac
q
EOF

Last changed March21, 2014

0		for f < f1
cosine taper between 0 and 1		for f1 < f < f2
1		for f2 < f < f3
cosine taper between 1 and 0		for f3 < f < f4
0		for f > f4