undergraduate lecture

1. Inverse Theory
Dr. Amin E. Khalil

2. Overview
• These information are taken from the book of
William Menke, 1989. The target audience of
these lectures are the students of the 4th year
Geophysics Program at the faculty of Science
Helwan University (class 2011-2012)

3. Contents
• Formulation of the inverse problems
• Overview on probability and probability
density functions
• Least squares method

4. Formulation of the Inverse Problem
Beginning from the relation:
Where
d= the vector of data (observations)
m= the vector of model parameters (unknown)
G= the data kernel(representing the values of the
coefficients of the model equation.
Gmd

5. In this example the temperature measured in a borehole
is assumed to increase linearly with depth following the
relation T=a + bz, here a and b are the model parameters
to be deduced