Klauder filter

A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time t = 0 ms.

The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency flower (perhaps 2–8 Hz), its upper frequency fupper (often about 100–200 Hz), and its duration T, commonly about 6–12 s.


 * $$A(t) = \mathrm{Re} \left[ \frac{\sin (\pi k t (T-t)}{\pi k t \mathrm{e}^{2 \pi \mathrm{i} f_0 t} } \right] $$

where k is the rate of change of frequency with time:


 * $$k = \frac{f_\mathrm{upper} - f_\mathrm{lower}}{T} \ $$

and f0 is the mid-frequency of the bandwidth:


 * $$f_0 = \frac{f_\mathrm{upper} + f_\mathrm{lower}}{2} \ $$

Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side.