# Inverse problems

The calculation of theoretical (synthetic)
seismograms in seismology is not done for its own sake. In most branches
the ultimate goal is to compare the theoretical calculations with
observations. In this **data fitting process (the inverse problem)**
seismograms are calculated for earth models through iterative procedures
or extensive searches of the model space. So far this model search was
carried out using predominantly linear or linearized approaches. Arguably
the most elegant method to solve inverse problems is the **probabilistic
approach** whereby a probability density function is calculated that is
descriptive of the information available accounting for observations and
uncertainties in theory and observations. Even though we are aware that
with complete 3D solutions we are far away from being able to employ
**Monte Carlo** type approaches to solve seismic inverse problems on a
large scale our goal is to investigate whether – for example through
combination of techniques mentioned above – we can start to go beyond
linearized inversion using full waveforms. This will involve the use of
clever **global search algorithms** such as simulated annealing,
genetic algorithms, evolutionary programming or neighbourhood
algorithm.