# Team 2: Uncertainty Quantification in Geophysical Inverse Problems

Monday, August 1, 2005 - 10:00am - 10:20am

EE/CS 3-180

Nicholas Bennett (Schlumberger-Doll Research)

Solving an inverse problem means determining the parameters of a model given a set of measurements. In solving many practical inverse problems, accounting for the uncertainty of the solution is very important to aid in decision-making. A standard approach to do this begins by choosing a model parametrization and then using a Bayesian approach to make inferences on the model parameters from measurement data. However, this quantified uncertainty is a function of the model parametrization and for many inverse problems, there are many model parametrizations that account for the data equally well. A well known approach to accounting for model uncertainty is Bayesian Model Averaging where many model parametrizations are considered. Wavelet model updates provide an efficient means of sifting through a family of model parametrizations given by decimated wavelet bases. By decimated wavelet basis we mean a subset of the model's coordinates in a wavelet basis.

When working with measurement data sets which are particularly noisy or large in terms of their data storage size, it is natural to consider denoising or compressing the data also using a decimated wavelet representation. Kalman filters can be used to update the solution (including its uncertainty) when denoising or locally changing the resolution of the measurement data by changing the decimation.

We shall explore how to compute likely representations of both model and measurements in the context of solving a few model geophysical inverse problems.

When working with measurement data sets which are particularly noisy or large in terms of their data storage size, it is natural to consider denoising or compressing the data also using a decimated wavelet representation. Kalman filters can be used to update the solution (including its uncertainty) when denoising or locally changing the resolution of the measurement data by changing the decimation.

We shall explore how to compute likely representations of both model and measurements in the context of solving a few model geophysical inverse problems.