
title{
     Information from smiles: mono-plane-annihilator weighted regression
     }
author{
      Jon F. Claerbout
      }

The way we usually estimate parameters in reflection seismology
is that we maximize the coherence of supposedly redundant measurements.
Thus, we estimate velocity and statics shifts
by maximizing something like the power in the stacked data.
I propose a new optimization criterion
for estimating model parameters and missing data
to supplement traditional criteria.
An interpreter looking at a migrated section that contains
two dips in the same place knows that something is wrong.
Superposition is a wave concept, not a geological concept.
To minimize the presence of multiple dips in the same place,
we should use in any regression
the mono plane annihilator (MOPLAN) filter as the weighting operator.
Its output is already zero when only one dip is present (good).
Otherwise it has a nonzero output (departure from monoplane model).
Because dips change, the MOPLAN operation must be done LOcally (LOMOPLAN).
Minimizing the LOMOPLAN output should enable us
to improve estimation of model parameters and missing data.
Philosophically,
the LOMOPLAN is half an inverse covariance matrix of the desired model.
Although the LOMOPLAN concept applies to models, not data,
experience shows that processing field data with a LOMOPLAN
quickly identifies data quality problems.

-----------------------------------------------------------

Jon F. Claerbout:
(M.I.T., B.S. physics, 1960; M.S. geophysics, 1963; Ph.D. geophysics, 1967)
joined the geophysics faculty at Stanford University in 1967 and became
a consultant to the Chevron Oil Field Research Company (1967-73).
He received the Best Presentation Award from the Society of Exploration
Geophysicists for his paper, {\em Extrapolation of Wave Fields,}
and received the Society's Fessenden Award ``in recognition of his outstanding
and original pioneering work in seismic wave analysis.''
In 1973 he founded the Stanford Exploration Project (SEP).
In 1977 he was elected a Fellow of the American Geophysical Union.
He published three books:
{\em Fundamentals of Geophysical Data Processing,}
in 1976; {\em Imaging the Earth's Interior} in 1985, and
{\em Earth Soundings Analysis: Processing versus Inversion} in 1992.
In 1985 he became an honorary member of the SEG and in 1988
he was elected to membership in the National Academy of Engineering.
In 1992 he received the SEG Maurice Ewing Medal, the society's highest award.
