We can achieve the optimal estimation by minimizing the functions in
equations (3) and (4), or maximizing
the functions in equations (5) and (6).
Would we get an identical result if we use the two different methods?
To answer this question, let us examine the relations between these objective
functions:

(7)

and

E_{n}(t,x,p) = 1-C_{n}(t,x,p).

(8)

It is clear that, for the normalized objective functions,
minimizing E_{n}(t,x,p)
is completely equivalent to maximizing C_{n}(t,x,p).
The first term on the right-hand side of equation (7) is the
weighted energy of the subsection. This term
usually maintains to be constant. Therefore,
for unnormalized objective functions, we can draw a similar conclusion to
that of the normalized objective functions.
In view of the calculation of these functions,
the coherence measures are easier to calculate
than the error measures.
Next:NON-LINEAR OPTIMIZATION Up:OBJECTIVE FUNCTIONS Previous:Coherence measure
Stanford Exploration Project
12/18/1997