Taming Uncertainty in Geophysical Inversion

Abstract

The concept of uncertainty in geophysical inversion is often confined to quantification of errors in parameters estimated from some data. A broader definition is to include uncertainty arising from the assumptions made in posing the inverse problem in the first place. These may include assumptions about the physics of the relationship between observations and unknowns, the class of parameterisation assumed for the unknowns, and guesses about the statistical character of random noise contaminating the data. Typically these assumptions are required to arrive at a tractable mathematical problem to solve using geophysical inversion methods. In this paper we outline an inversion approach that allows a broader definition of uncertainty which includes each of these classes of assumption. Including uncertainty in the model parametrization or in the nature of the noise statistics can lead to more realistic inversion results, but not always with increased error bars on the model parameters. For example, relaxing rigid assumptions in the nature of the parametrisation, even in simple problems can result in smaller and more realistic model error estimation. Using the data to decide between different classes of parameterization, physical assumptions or observational noise process is often called ‘model choice’ in statistics, an area that is often overlooked in the geosciences. Over the past 5 years the trans-dimensional inversion approach has increasingly found applications across a variety of inference problems in the geosciences, with new applications appearing regularly.