Inverse theory
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This document provides an overview of a lecture on inverse theory given by Dr. Amin E. Khalil to 4th year Geophysics students at Helwan University in Egypt. The lecture covers formulating inverse problems, probability density functions, and the least squares method. It gives an example of using temperature measurements from a borehole to deduce the model parameters a and b from the linear relationship T=a + bz.
Inverse theory
- 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