Undergraduate course

1. Definition:
Inverse Theory deals with the determination of the model
parameters from the data. In our case it is the estimation of
subsurface structure from surface measurements.

2. A model may be defined as the mathematical
relation (either analytical or empirical) that
relate the independent variable X with the
dependent variable Y in the form:
Y= a + b X
In this model, the model parameters are a and
b. In algebraic notation they are the unknowns
of the equation. In matrix form this relation
may be written as:
A m = d

3. m is the vector of model parameters a & b
D is the data vector

4. To define the theory in
more practical way we use
the beach example where
we expect a pirates
treasure is burried under
the sand. The treasure is
made of gold which is much
more dense than sands.
Thus we propose to use the
gravity method.

5. The problem is that we
Thus the methodology here is forward modeling not inverse.
The ideal model of the beach may be sketched as:

6. The computation algorithm we will adopt will
As we have 45 blocks we end up with:
We also end up with no unique solution.

7. The models may be categorized as:

8. Problems we face: