Routine work today typically ignores inversion theory and presumes the mathematical limit within which multiples may be handled as a shot waveform. Despite many further theoretical developments and the continuing active interest of many practical workers, routine deconvolution is little changed. I will state in simple terms what I believe to be the essence of deconvolution. Every seismogram has a spectrum. The spectrum is a product of many causes.
Some causes are of fundamental interest.
Others are extraneous. It is annoying when a seismogram is resonant just because of some near-surface phenomena. Deconvolution is basically a process in which strong resonances are measured, and then a filter is designed to suppress them. The filter is designed to have a spectrum that is roughly inverse to the spectrum of the raw data. From the earliest times, seismologists have found that reflection seismic data rarely makes sense much outside the frequency band 10-100 Hz, so as a final step, frequencies outside the band are removed.