604 17 Inversion of Potential Field Data
local search tools we have discussed earlier. Global search tools do not have
any problem for getting trapped in the local minima pockets. Because the
movements in the parameter space is by random jumping and not through
any systematic mathematical procedures. Once the forward problem is solved
invers e problem can be solved by random jump in model space and trial
and error. That eliminates the stability problem of a sensitivity matrix and
local minima pr oblem . These inversion approaches move towards the global
minimum instead of a local minimum and hence they are cla ssified as global
optimization tools. These global optimization tools choose a model by random
walk, compute the forward problem, compute the discrepancy between the
field data and model data in the form of an error function or cost function or
energy function, move to the next model by random jump and follow the same
procedure till you reach a model where the discrepancy is minimum between
the field data and the model data.
The members in this family of random walk are (i) Monte Carlo inversion
(ii) Simulated Annealing and (iii) Genetic Algorithm. Neural Network does
not come strictly under the random walk techniques. Monte Carlo method is
an unguided random walk technique without any artificial intelligence. Simu-
lated Annealing and Genetic Algorithm are guided random walk tools having
artificial intelligence. Neural network on the otherhand is a tool with artificial
intelligence but with a partially random approach at the beginning regarding
selection of weights. SA is designed bringing some analogy from the chemical
thermodynamics and chemical annealing process of metals. Genetic Algorithm
mimics the biological processes and goes through the survival for the fittest
test. Neural Network imitates the behaviours and functioning of the neurons
in the brain.That is why these networks are trained to do some specific jobs.
These tools are very powerful in the sense that MC, SA, GA search the
entire parameter space by random jumping. Since there is no mathematics for
inversion, there is (i) no problem of finding out the analytical derivatives or
frechet derivatives (ii) there is no stability problem in inversion. But problem
of non uniqueness remains because of the finite resolving power of the scalar
and vector p otentials and the parameters generated o ut of these potentials can
be collected from the field free from any noise. (iii) both linea r and nonlinear
problems can be handled with equal ease (iv) these optimization tools become
more powerful to handle 2-D/3-D problems.
Since several thousands computations of forward problem are involved, an
efficient and minimum time run algorithm for forward problem computation is
essential to use these tools. Other wise the computation time requir e ment will
be prohibitive. Monte Ca rlo inversion needs more than one million forward
problem computations. The same process will continue for 10,000 times in
Simulated Annealing and more in Genetic Algorithm because GA works with
a population of initial models. Artificial Neural Network(ANN) is strictly not
a member of the global optimization tools. ANN to ols are trained several
times to do a particular type of job by adjustment of weights in the hidden
layers through backward propagation of information from output to input.