Instrumental Response


Program objectives

The instrument used to perform a record distorts the original true-signal given an output signal, which must be instrument corrected to get this true signal. For this reason, a further process called deconvolution must be performed to recover the true input signal. Unfortunately, this input signal is never recovered completely. Thus, the signal recovered by the instrumental correction is not exactly equal to the original true-signal. Nevertheless, if the instrumental correction is well done, the recovered signal can be used instead of the original signal, with a small error (Brigham, 1988). This classical process is described in detail by Bath (1974). You can compute this process by means of the present program, as it will be described below.

Program description

The RESPONSE program and its files, which are needed to run this application, are enclosed into a ZIP file named "response.zip". When you have got the ZIP file and you have uncompressed this file, you have eight files named response.exe, response.dat, series.dat, S034.dat, S4310.dat, dmft.dat, SEED.txt and spectrum.dat. The file response.exe contains a program (in FORTRAN code for PC) for the computation of the instrumental correction. All the program capabilities are controlled by parameters enclosed in the file named response.dat. This file is in the free format and contains the parameters:

NRESP, NOPTION
file, sta, datime, cha, net

The description of all parameters is as follows:

NRESP = With value 0 computes the instrumental response for plotting. With value 1 the Fourier spectrum of a time record is instrument corrected.
NOPTION = With value 1 computes the instrumental response for the BroadBand seismographs, with value 0 computes the instrumental response for the LP-WWSSN seismographs.
file = Name of the input-data file with the information for the BroadBand seismographs (NOPTION = 1 ).
sta = Name of the BroadBand station (NOPTION = 1 ).
cha = Component of the BroadBand station (NOPTION = 1 ).
datime = Date in which the trace has been recorded (NOPTION = 1 ).
net = Seismic network (NOPTION = 1 ).

Running the program

If we select NOPTION = 1, the program will compute the instrumental response of BroadBand seismographs. In this case, an ASCII file with the instrument information must be supplied in the format of the IRIS SEED Reader (Release 4.15). The name of this input-data file must be written in the input-data file response.dat (in the sta parameter). If we select NOPTION = 0, the parameters (file, sta, datime, cha, net) are ignored. The input-data file response.dat, enclosed in the ZIP file mentioned above, contains a list of adequate values of these parameters to use, with the also enclosed file named SEED.txt, if NOPTION = 1 is selected.

Write out a file for plotting of the instrumental response (NRESP = 0)

When you enter NRESP = 0, the program computes the instrumental response (frequency, amplitude, phase) and write out an output-data file named resp.dat very suitable for plotting, as it is shown in Figure 1 for NOPTION = 1 (BroadBand) and NOPTION = 0 (LP-WWSSN).
Fig. 1. Instrumental response for a BroadBand seismograph (blue line) and for a LP-WWSSN seismograph (red line).

Computation of the instrument correction for the Fourier spectrum of a trace (NRESP = 1)

Firstly, we need obtain the Fourier spectrum of the trace. For it, the SERIES program can be very useful. This program can be run with the input files named S034.dat and S4310.dat (which traces are shown in Figure 2), which are enclosed into the ZIP file above mentioned, to get their corresponding Fourier spectra. The SERIES program will compute the Fourier spectrum of each trace, using the input-data file named series.dat (also enclosed in the above-mentioned ZIP file), in which the input-data and the output-data file names are written. The SERIES program can give us the Fourier spectrum of each trace shown in Figure 2, to be used with the RESPONSE program.


Fig. 2. Traces contained in the the input files named S034.dat (plotted with red line) and S4310.dat (plotted with blue line).

The SERIES program give us the output-data file named s034_spec.dat, which contains the Fourier spectrum of the trace contained in the input-data file named s034.dat. This program also gives the output-data file named S4310_spec.dat, which contains the Fourier spectrum of the trace contained in the input-data file named S4310.dat. The RESPONSE program will compute the instrument correction for the Fourier spectrum of the S034 trace, using the output-data file s034_spec.dat renamed to the input-data file amphas.dat. The Fourier spectrum instrument corrected will be enclosed into the output-data file resp.dat, which must be renamed to resp034.dat for an easy identification. For the S4310 trace, the RESPONSE program is executed in the same way, obtaining a new resp.dat that must be renamed to resp4310.dat for an easy identification. When we have the Fourier spectra of the S034 and S4310 traces instrument corrected, we can get the corresponding time records by using of the SPECTRUM program. For it, the files resp034.dat and resp4310.dat are used as input-data files and the file named spectrum.dat contains the input-data and the output-data file names to be used by this program. When we run this program with the option 0, the output-data files named s034c.dat and s4310c.dat will be generated. The traces contained in these files are shown in Figure 3.


Fig. 3. Traces contained in the the output files named S034c.dat (plotted with red line) and S4310c.dat (plotted with blue line).

The short period is magnified, after the instrumental correction, much more for the LP-WWSSN instrument than for the BroadBand instrument, as it can be seen in Figure 3. This difference is due to the different amplitude spectra of these instruments (Figure 1). The amplitude spectrum of the BroadBand instrument is more flat than the amplitude spectrum of the LP-WWSSN instrument. For this reason, the periods out of the period range from 5 to 45 seconds, are magnified by the instrumental correction for LP-WWSSN seismographs. In Figure 4, we can see that the phase spectrum is more perturbed by the LP-WWSSN instrument than by the BroadBand instrument. The time lag introduced in the seismogram recorded by the LP-WWSSN instrument, is major than the time lag introduced by the BroadBand instrument. The group velocity curves shown in Figure 4 can be obtained using the MFT program, considering as input-data files the files: S034.dat, S4310.dat, S034c.dat and S4310c.dat. The epicentral distance for the traces S034 and S034c is 630 km, for the traces S4310 and S4310c the epicentral distance is 1300 km.


Fig. 4. Dispersion curves obtained from the traces S034 and S034c (plotted with red line) and from the traces S4310 and S4310 (plotted with blue line).

References

Bath M., 1974. Spectral analysis in Geophysics. Elsevier, Amsterdam.

Brigham E. O., 1988. The Fast Fourier Transform and Its Applications. Prentice Hall, New Jersey.