Deconvolution means to “undo” a convolution process. We may view each seismic trace as the result of convolving the subsurface seismic reflectivity with a seismic wavelet. Deconvolution can then be used to remove the seismic wavelet from the input seismic trace in order to yield the seismic reflectivity as the output. As a common time processing method, the main benefits of deconvolution include increasing data bandwidth and therefore resolution, suppressing periodicity such as multiples, and removing known wavelets. In practice we often only have the input seismic trace and want to find both the wavelet and the reflectivity. This non-uniqueness problem leads to the approach of predictive deconvolution, which assumes that the predictable components of the input trace belong to the seismic wavelet and the unpredictable components of the input trace belong to the reflectivity. To remove the effect of a known filter, we may use a frequency domain deconvolution which employs a “water level” to prevent division by zero.

As the amplitude and phase of real data vary with time, the deconvolution operator may be applied within a time window of the data. An adaptive deconvolution is a practical way to divide the data trace into time windows that overlap with each other, to apply deconvolution for each window, and then to integrate the deconvolved results together. By quantifying the distribution of seismic wiggles using the concept of entropy, minimum entropy deconvolution seeks to minimize the number of spikes on a seismic trace; this method works well in cases of few major reflectors. Finally, a method called extrapolation by deterministic deconvolution (EDD) is shown as a way to take predictions from sites of joint observations and to extrapolate into nearby sites that have only a single observation. This method provides the possibility of using seismic data to anticipate filtered versions of wellbore measurements.