^{}Everybody
knows about getting travel times correct.
Let us define a data space , a model space ,and an operator called ``Kinematics''
that gets the travel times correct.
The conjugate-transpose gives processing operators
like ``moveout and stack'',
and like the sequence ``normal moveout,
dip moveout, stack, zero-offset migration''.

Different people have different ideas about amplitudes. We will have four different amplitudes to deal with here. Think of them as diagonal matrices ,,,and that we all know how to invert.

Professor Fussy Logic, a deep thinker from The Continent,
is not satisfied with kinematics
because he likes to get amplitudes *correct*.
This gives him lots of weighting functions.
Some of his weights are in model space and some in data space.
Some of his weights
are best represented in Fourier space,
such as .We cannot fully decipher all his thoughts about amplitudes
but to some (unknown) level of approximation
we can think about his work as

(3) |

Dr. Mucho Moola, is founder-owner of a successful geophysical contracting company. (It would be impolitic of me to reveal his exact identity but you can think of him as an MIT PhD of the '60s or an SEP PhD of the '70s.) Dr. Mucho Moola likes to get amplitudes correct too, but he could tell you a dozen reasons why that has nothing to do with a correct modeling theory. Starting from his notion that ``all data is important'' and from the kinematic operator ,by various schemes that are ``company confidential'' he finds weighting functions and such that

(4) |

(5) |

(6) |

Ms. Sepper, a new student at SEP, wants to reconcile logic with success. She figures that Professor Fussy Logic has the problem formulated right but his solution is impractical whereas Dr. Mucho Moola is successful (despite ignoring the physical theory) because he has a good approximation to the inverse of a matrix with the same kinematics as Professor Fussy Logic's matrix. She sets out to apply Dr. Mucho Moola's inverse method to Professor Fussy Logic's problem. Starting with equation (3), she premultiplies by and she also inserts in a strategic location getting

(7) |

(8) |

- 1.
- According to Ms. Sepper's formula, whose weights are more important, Professor Fussy Logic's and or Dr. Mucho Moola's and ?
- 2.
- In view of competition from Dr. Mucho Moola's secret
*Q*process, how should Ms. Sepper advertise her product? - 3.
- How much would you like to invest in the new company? Why?

11/16/1997