Seven Essays on Minimum Entropy
, by Jon F. Claerbout
A geophysicist peering into a microscope viewing biological tissue will
have no trouble focusing the microscope. The focusing is not done by
measuring the focal length of the lenses and matching the distance to the eye and
specimen. The focusing is done by enhancement of some characteristic of the image.
This is possible despite the likelihood that the geophysicist has little or no
previous experience with the image or microscope. What characteristic of the
image is sought? Perhaps it is short sptial wavelength, perhaps bandwidth
in spatial spectra, perhaps dynamic range in intensity. In Minimum Entropy
(ME) data analysis research we try to dtermine physical parameters (such as
distance or focal length) by means of adjustments which shaprpen an image.
Despite visions of scientific precision conjured up by the word "entropy" our
work is still largely empirical, though I believe it is very promising. These
essays give an account of current efforts to apply and systematize this kind
of inductive learning in reflection seismology. The essays are largely
independent of one another. Theyy may be read out of sequence and without
reference to earlier work. Titles with brief descriptions are:
Applications of ME Processing - A new family of processes in
reflection data analysis are possible.
Geometric Inequality versus Power Inequality - A comparative
analysis of two previous approaches.
The Basic Debubble Algorithm - How to do it.
Non-Stationarity: Application to Common-Shot Profile - An
attempt to specify a production program.
Seismogram Inversion - How to use ME to zap multiple reflections.
ME Extrapolation and Spectrum - Counterpoint to Burg's
maximum entropy method.
Convex Inequalities and Statistical Mechanics - Physicists and
chemists had been using the concept of entropy long before information
theorists took it up. Here is what they mean by it and how it
relates to our imaging concepts.
STANFORD