Seismic tomography and the assessment of uncertainty

Seismic tomography is a powerful tool for illuminating Earth structure across a range of scales, but the usefulness of any image that is generated by this method is dependent on our ability to quantify its uncertainty. This uncertainty arises from the ill-posed nature of the tomographic inverse problem, which means that multiple models are capable of satisfying the data. The goal of this review is to provide an overview of the current state of the art in the assessment of uncertainty in seismic tomography, and issue a timely reminder that compared to the rapid advances made in many other areas of Earth imaging, uncertainty assessment remains underdeveloped and is often ignored or given minimal treatment in published studies. After providing a historical perspective that dates back to the pioneering work of the early 1970s, the factors that control solution nonuniqueness are discussed, which include data coverage, data noise, choice of parameterization, method used for data prediction and formulation of the inverse problem. This is followed by a description of common methods used to assess solution uncertainty and a commentary on their strengths and weaknesses. The final section of the review presents four case studies involving data sets from Australia and Europe that use different methods to assess uncertainty. The descriptive nature of this review, which does not contain detailed mathematical derivations, means that it is suitable for the many nonspecialists who make use of seismic tomography results but may not have a full appreciation of their reliability.