### Geophysical inverse problems

Geophysics is a rich source of inverse problems and the first field of research in which statistical (Bayesian) inversion was widely adopted: subsurface can be probed with a large number of modalities and each modality involves a large number of parameters, only few of which are typically interesting. Furthermore, other modelling errors and uncertainties such as domain truncation are practically unavoidable.

We have considered electromagnetic and wave propagation related modalities, with the latter being the main focus currently. However, we study the related uncertainty modelling in general, including the multimodality joint inversion and estimation of risks in prospecting. A particular focus is on estimation of water resources (video on youtube).

*( Left:) the problem geometry. The perfectly matched layer (PML) is denoted by the shaded area. (Right:) animation shows the electric field.*

**Full-wave seismic inversion using spectral element method**

The spectral-element method (SEM) has several features that make it an attractive candidate for large-scale wave simulations. The method combines the accuracy of the global pseudospectral method with the flexibility of the FE method and it is well suited for parallel computing. The SEM was first introduced in the context of computational fluid dynamics, but it has recently gained popularity in seismology.

In our work, the specfem-software is used to simulate seismic wave propagation through an aquifer (modeled as porous, water saturated rock). In the associated inverse problem, we estimate the volume of water in the rock. To speed-up the computation, the inverse problem is solved using Bayesian approximation error method.

*Animation shows the total velocity field on the ground surface. The location for the geometry is on the South-Island of New Zealand (near Christchurch).*

**Contact**

**Past and present collaborators**

A. Malehmir, Uppsala University, Department of Earth Sciences

N. F. Dudley Ward, University of Canterbury, Civil and Natural Resources Engineering

A. Pasanen, Geological Survey of Finland

T. Cui, Monash University, School of Mathematical Sciences

K. Niinimäki, l’Université Paris-Sud, Imagerie par Résonance Magnétique Médicale et Multi-Modalités

Z. Rawlinson, GNS Science