Past, present, and future of geophysical inversion—A new millennium analysis

Geophysicists have been working on solutions to the inverse problem since the dawn of our profession. An interpreter infers subsurface properties on the basis of observed data sets, such as seismograms or potential field recordings. A rough model of the process that produces the recorded data resides within the interpreter’s brain; the interpreter then uses this rough mental model to reconstruct subsurface properties from the observed data. In modern parlance, the inference of subsurface properties from observed data is identified with the solution of a so‐called “inverse problem.” In contrast, the “forward problem” consists of the determination of the data that would be recorded for a given subsurface configuration and under the assumption that given laws of physics hold. Until the early 1960s, geophysical inversion was carried out almost exclusively within the geophysicist’s brain. Since then, we have learned to make the geophysical inversion process much more quantitative and versatile by recourse to a growing body of theory, along with the computer power to reduce this theory to practice. We should point out the obvious, however, namely that no theory and no computer algorithm can presumably replace the ultimate arbiter who decides whether the results of an inversion make sense or nonsense: the geophysical interpreter. Perhaps our descendants writing a future third Millennium review article can report that a machine has been solving the inverse problem without a human arbiter. For the time being, however, what might be called “unsupervised geophysical inversion” remains but a dream.