Geophysical inversion

Summary

Geophysical inversion is the estimation of properties of the Earth's interior from measurements made mostly at the surface. The properties are, for example, density, seismic velocity or electrical conductivity. It is an inverse problem: a physical forward model predicts data from a model of the Earth, and inversion runs this map backwards. The data are finite and noisy and the forward map often smooths, so the problem is usually ill-posed. The non-uniqueness of potential field inversion is a standard example. Practical inversions therefore add prior information, most often by Tikhonov regularization, and report how well each feature of the model is resolved.