Analysis of the Rayleigh pulse

Seismologists make frequent use of wavelets (also referred to as signals, signatures, or pulses), particularly in such fields as seismic filtering, wavelet processing, wave‐propagation modeling, and trace inversion. Whenever possible, the actual seismic wavelet of the real source should be considered (Hosken, 1988). However, frequently, particularly in wave‐propagation modeling, one must consider a synthetic source wavelet. This should, if possible, be given by a simple mathematical formula and possess an easy description for its most important spectral properties (e.g., amplitude and phase spectrum, main frequency, Hilbert transform, etc.). Moreover, the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained.