Stochastic Inversion Of 3D Ert Data

A new stochastic inversion algorithm to invert three-dimensional (3D) electrical resistivity<br>tomography (ERT) data has been implemented. The statistical information about the correlation<br>among the model parameters and the correlation among observed data was employed to stabilize<br>the ill-posed 3D ERT inverse problem. The data noise covariance matrix was diagonal based on<br>the assumption of uncorrelated data noises. The model parameter covariance matrix, however,<br>could be a full matrix depending on the correlation length between the model parameters. The<br>resulting unsymmetric linear system was solved by bi-conjugate gradient (BICG) methods, such<br>as BICGSTAB, a stabilized variant of BICG algorithm, and TFQMR, a transpose-free quasiminimal<br>residual algorithm.<br>An advantage of this algorithm is that any prior knowledge about the model parameters<br>can be easily incorporated in the inversion process in the form of covariance model type and<br>correlation length. This is the basis for our future implementation of a joint hydrologicalgeophysical<br>inversion. This stochastic inverse technique will be used for characterizing,<br>monitoring, and predicting fluid movement in heterogeneous vadose zone.