Program src/green/disan/gabor.f
===============================
Navigation: [/](/) [src/](src) [green/](src_green) [disan/](src_green_disan)

**Calculate gabor matrix**

Theory: Group-slowness analysis
-------------------------------
The theory behind this program is described by
[[Forbriger (2003. Inversion of shallow-seismic wavefields: I. Wavefield transformation. Geophys. J. Int., 153, 719-734, appendix B)|http://dx.doi.org/10.1046/j.1365-246X.2003.01929.x]]:

If 
```latex
  u(t,r)
```
is a seismogram at location *r*,
the spectrogram (Gabor matrix) is defined by
```latex
  \begin{equation}
    f(\omega,t)=\int\limits_{-\infty}^{+\infty} u(t^\prime,r)\,h(t^\prime-t)\,
      e^{i\omega t^\prime}\,\text{d} t^\prime
  \end{equation}
```
with a Gaussian taper
```latex
  \begin{equation}
    h(\tau)=\exp\bigl(-(\tau/\sigma)^2\bigr).
  \end{equation}
```
This essentially is the Fourier-transform of a tapered version of the
waveform with the taper centered at *t*.
```latex
  $\sigma=53\,\text{m}$
```
means a half width of 90m for the taper.

Properties of this 'moving-window analysis' are discussed by Kodera et
al. (1976) and Wielandt and Schenk (1983).