BFXT

The Frequency-Distance (FX) transform may be computed for a shot gather. The output files are bfxtampl.seg and bfxtphaz.seg if a forward transform is computed. The command line arguments are:
  bfxt  infile1  iopt   infile2  
  
 infile1 =name of X-T input file (space,time)
  
  iopt    1=forward transform (unwrap phase)
          2=forward transform (no unwrap phase)
         -1=inverse transform (two input files)
  
 infile1 =name of input file AMPLITUDES(iopt=-1 Only)
 infile2 =name of input file PHASE(iopt=-1 Only)
  
 NOTE: Forward transform requires only one input file
       Inverse transform requires two input files

Figure 91: BFXT: (A) trace equalized shot gather using BEQU 12.0.9 (B) the amplitude spectrum after equalization with BEQU. Not shown is the phase transform.
\includegraphics[scale=.9]{Figurebfxt.pdf}

The example shown in Figure 91A shot gather has a sample interval of $\Delta t = .0005~sec$ and 2500 samples per trace. The code uses a Radix 2 FFT, and in this case the sample interval is modified and there are 2048 samples per trace. The Figure 91B plot has to be relabeled since we are using BSU plot program BPLT here, and that program is limited to assuming all data are in time. A frequency axis replaces the time axis, and frequencies run from zero to the Nyquist. It appears to the headers as if the maximum sample is at a time of 1.0. In actual fact, the maximum sample is at 1000 Hz. Some scaling is going on to make plotting easier.

So Figure 91B is plotted to a maximum of 0.1 which turns out to be 100 Hz. So what is going on? BFXT calls a subroutine, nrad2.f which computes the first power of two larger than the number of samples in the shot gather, call it N2. A frequency domain sample interval is computed on this larger number of samples (the code pads with zeros to fill it out). Thus, $\Delta f = 1/(N2 \cdot \Delta t)$. But because we are dealing with time domain codes for other things we might do, we scale the sample interval, dividing it by 1000. Thus a Nyquist of 1000 Hz (maximum sample frequency in FX domain) becomes 1.0, as if it were 1.0 seconds. When going back into the time domain (TX), all this is reversed.