Gaussian process models—I. A framework for probabilistic continuous inverse theory. Issue 3 (19th November 2019)

• Record Type: Journal Article
• Authors: Valentine, Andrew P; Sambridge, Malcolm
• Is Part Of: Geophysical journal international. Volume 220:Issue 3(2020)
• Page Start: 1632
• Page End: 1647
• Publication Date: 2019-11-19
• Subjects: Inverse theory -- Probability distributions -- Statistical methods; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggz520
• Languages: English
• ISSNs: 0956-540X

Abstract

SUMMARY: We develop a theoretical framework for framing and solving probabilistic linear(ized) inverse problems in function spaces. This is built on the statistical theory of Gaussian Processes, and allows results to be obtained independent of any basis, avoiding any difficulties associated with the fidelity of representation that can be achieved. We show that the results of Backus–Gilbert theory can be fully understood within our framework, although there is not an exact equivalence due to fundamental differences of philosophy between the two approaches. Nevertheless, our work can be seen to unify several strands of linear inverse theory, and connects it to a large body of work in machine learning. We illustrate the application of our theory using a simple example, involving determination of Earth's radial density structure.