Seismology and Inverse theory

Description

This course deals with:

1. Discrete linear or easily linearizable problems and
2. Strongly nonlinear problems.

We first of all examine the Lanczos method, based on the decomposition into eigenvectors and we introduce the concepts of: over or under-dimensioning, resolution, information, error, etc.
The central part of the course is devoted to the generalized stochastic inverse which makes it possible to introduce the notion of a priori information.
The last part of the course introduces the so-called Montecarlo methods which make it possible to solve strongly nonlinear problems by sampling the space of models in a more or less complete and more or less optimized way.
 

Compétences visées

We use observations (measurements) to adjust the parameters of models that describe the physical systems that we are studying. This course provides the mathematical tools essential for this operation, which allows observations (data) to be fed back into models. The adjustment of a simple line of "least squares" and obtaining a three-dimensional image of the distribution of seismic wave speeds inside the Earth, are more or less simple examples of application of "inverse methods".