Processing versus inversion

Practical people often regard inversion theorists with suspicion, much as one might regard those gripped by an exotic religion. There is not one theory of inversion of seismic data, but many--maybe more theories than theoreticians. The inventors of these theories are all ingenious, and some are illustrious, but many ignore the others' work. How can this be science or engineering? The diversity of viewpoint arises from the many practical problems that need to be solved, from the various ways that noise can be modeled, from the incompleteness of data, and above all, from the many approaches to simplifying the underlying model.

Practitioners too are a diverse group of shrewd and talented people, many illustrious in their highly competitive industry. As a group they have the advantage of the ``real world'' as a helpful arbitrator. Why do they prefer a adjoint operator when the correct answer, almost by definition, stems from the inverse? Adjoint processing requires no more than the data one has actually collected. It requires no noise model, never uses divisions so cannot divide by zero, and often uses only additions (no subtractions) so cannot amplify small differences. Anyone taking the first step beyond adjoint processing loses these supports. Unfortunately, adjoint operators handle missing data as if it were zero-valued data. This is obviously wrong and is known to limit resolution.

I hope to illuminate the gaps between theory and practice which are the heart and soul of exploration seismology, as they are of any living science.

Fortunately there is a middle way between adjoint processing and inversion, and this book is a guide to it. Adjoint processing and inversion stand at opposite ends of the spectrum of philosophies of data processing, but, as we will see in chapter , adjoint processing is also the first step of inversion. Whether the second and any subsequent steps are worthwhile depends on circumstances.

The theme of this book is not developed in an abstract way but instead is drawn from the details of many examples: normal moveout, stacking, velocity analysis, several kinds of migration, missing data, tomography, deconvolution, and weighted deconvolution. Knowing how processing relates to inversion suggests different opportunities in each case.