Ricker wavelets in their various guises

The so-called Ricker wavelets remain in vogue among many synthetic seismogram producers, though the physical basis for the theory of such wavelets was proved to be invalid many years ago. For most synthetic seismogram studies, however, the important thing is to be able to model the wavelet remaining after processing. The wavelets used are long-range approximations to the true Ricker wavelet and the advantages claimed for them are that they are easily computed and unambiguously specifiabie by one parameter only (a frequency or period). Unfortunately they not only differ from processed wavelets in many cases, but a variety of conventions regarding their specification has crept in over the years and now there is confusion over what any practitioner means by his particular 'Ricker wavelet'. This article reviews all the known forms (and some unknown ones) that Ricker wavelets can take and points out the possible confusions that can occur as well as their lack of accord with real or processed wavelets. A recently arrived form is the minimum-phase Ricker wavelet which is examined and shown to possess a time delay which depends on the sample interval used in computing it. A two-parameter Ricker-type wavelet is described that allows greater versatility. The main conclusions are that Ricker wavelets employed by others are to be treated with extreme suspicion, and that Ricker wavelets should never be used at all if one has any choice.