SEG Distinguished Lecture – Geophysical Inversion: Which Model Do You Want?

With a broad suite of geophysical inversion tools now available, it is seductively easy to submit your data, turn the crank, and obtain a model. But is the model meaningful? Are the data properly fit? How much does the model depend on the data, and how much on parameters in the inversion code, such as model discretization and regularization penalty? The inversion process depends as much, if not more, on the error structure of the data and inversion parameters as the data themselves. We all know that geophysical inversion is non-unique, but many people are surprised just how different models can be that fit the data equally well. And what exactly constitutes an adequate fit to the data? Without a rigorous analysis of error structure, choice of misfit can be highly subjective. Some rely on “L-curves”, but it can be shown that they too are subjective and depend very much on the choice of plotting parameters. Seeking to drive misfit down as low as possible can also be perilous – the least squares best fitting models for some problems are known to be pathological, and it is likely that this is true in general. In this lecture I shall attempt to provide an understanding of the practical issues associated with geophysical inversion, and provide a roadmap for avoiding common pitfalls.