**Deconvolution** is a process universally applied to seismic data, but is one that
is mysterious to many geoscientists.

Deconvolution
compresses the basic wavelet in the recorded seismogram and attenuates
reverberations and short-period multiples. Hence it increases resolution
and yields a more interpretable seismic section.

Note the
differences in the illustration.
The quality of modern seismic data owes a great deal to the success
of deconvolution. Seismic processing often involves several stages
of deconvolution, each of a different type and with a different
objective.

Deconvolution
usually involves convolution with an inverse filter. The idea is
that this will undo the effects of a previous filter, such as the
earth or the recording system. The difficulty in designing an inverse
filter is that we hardly ever know the properties of the filter
whose effects we are trying to remove.

Different
kinds of deconvolution are generally described by the different
adjectives. They usually designate the type of assumptions made
in the process.

Deterministic
deconvolution can be used to remove the effects of the recording
system, if the system characteristics are known. This type also
can be used to remove the ringing that results from waves undergoing
multiple bounces in the water layer, if the travel time in the water
layer and the reflectivity of the seafloor are known.

In the
case of the earth, the previous filtering that was applied is not
known, and thus the deconvolution takes on a statistical nature.
In this situation the needed information comes from an autocorrelation
of the seismic trace. Because the embedded wavelet from the source
is repeated at each reflecting interface, this repetition is captured
by the autocorrelation and used to design the inverse filter.

The embedded
wavelet ordinarily dominates the early part of an autocorrelation,
whereas multiples dominate the later part. Hence different parts
of the autocorrelation are used to determine different filters for
different types of deconvolution.

The embedded
wavelet then can be recovered from the early part of the autocorrelation,
but, because the autocorrelation contains amplitude information
only, an assumption about phase is required. Minimum phase in the
recorded data is usually assumed and normally this is a good assumption.
The output of the deconvolution, however, is normally zero phase.
The enormous interpretive benefits of zero phase data have been
discussed in previous Geophysical Corner columns ("Seismic/Geology
Links Critical," November 1996 and "Zero Phase Can Aid Interpretation,"
April 1997).

Autocorrelations
may be calculated over several time windows in an attempt to allow
for changes in the shape of the embedded wavelet as it travels through
the earth. This is called adaptive deconvolution.

Spiking
deconvolution shortens the embedded wavelet and attempts to make
it as close as possible to a spike. The frequency bandwidth of the
data limits the extent to which this is possible. This is also called
whitening deconvolution, because it attempts to achieve a flat,
or white, spectrum.

This kind
of deconvolution may result in increased noise, particularly at
high frequencies.

Predictive
deconvolution uses the later portions of the autocorrelation to
remove the effects of some multiples. Predictability means that
the arrival of an event can be predicted from knowledge of earlier
events. Different formulations are used, including maximum and minimum
entropy, a measure of disorder.

Sparse-spike
deconvolution attempts to minimize the number of reflections, thus
emphasizing large amplitudes.

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