Inverse Theory

Dr. Amin E. Khalil

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)

Contents

• Formulation of the inverse problems• Overview on probability and probability

density functions• Least squares method

Formulation of the Inverse Problem

Beginning from the relation:

Whered= 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

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

Probability

uncorrelated correlated