Much of the available signal theory, particularly that developed for radar and telephone purposes, is based on the assumption that a pure signal having some well defined shape or characteristic is transmitted from a source and is later received, contaminated by noise, at some distant recording point. The noise is usually assumed to be additive in nature. The problem then becomes one of retrieving the known signal from the noise and, if the signal has been distorted or damaged in transmission, of restoring it to its original shape or character. Techniques which do this extremely well have been developed, and are well known.
Unfortunately, most of the operations in petroleum seismic exploration fail to meet the basic assumption. The source signal, when produced by any impulse energy source such as conventional explosives, is a single, relatively short sharp impulse not readily defined on land work. It lacks any known constant definitive shape or signature and thus can not be extracted in the processing. Even if it could be defined, as the recording of the source signature in marine work is, the subsequent influences of instruments and transmission through the earth modify the pulse to an uncertain form so, inevitably, the processing must proceed under certain assumptions or approximations.
It is not possible, on a routine basis, actually to measure or observe the seismic wavelet at any intermediate stage between the shot and the geophone. We can only input energy into the ground,and observe the end result of the reflection process