The Wavelet Zoo
Learning objectives
- Recognise the Ricker, Ormsby, Klauder, and minimum-phase wavelets by shape
- Read a trapezoidal (flat-top) spectrum and relate it to ringing in time
- Explain that a wavelet is fixed by its amplitude spectrum AND its phase
- See that a minimum-phase wavelet front-loads its energy
Beyond the Ricker
Real data carries wavelets shaped by the source, the earth, and processing, and the Ricker is only the simplest of them. Four show up again and again, and putting them on the same two axes makes their family traits obvious.
- Ricker. One peak, two side lobes, a bell-shaped spectrum. Set entirely by its peak frequency.
- Ormsby. A zero-phase wavelet with a flat-topped, trapezoidal passband set by four corner frequencies. A sharply bounded band rings more in time, the price of the flat top.
- Klauder. The autocorrelation of a linear vibroseis sweep, so it is the wavelet a vibrator delivers after correlation. A nearly flat band gives long, low side lobes.
- Minimum phase. The same amplitude spectrum as the Ricker, but its energy is front-loaded and causal rather than symmetric.
Amplitude Spectrum Is Not the Whole Wavelet
The minimum-phase case makes the deepest point. Select it and the spectrum panel is identical to the Ricker, yet the time wavelet looks nothing like it: the energy has moved to the front. A wavelet is fixed by two things, its amplitude spectrum and its phase, and the phase is not a detail. It decides where the energy sits and where a reflection appears to arrive. That is exactly the trap the inverse-crime section warned about, and it is the subject of the next section, where rotating the phase moves your picks.