Gaussian process models-II. Lessons for discrete inversion

Andrew P. Valentine, Malcolm Sambridge

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)

    Abstract

    By starting from a general framework for probabilistic continuous inversion (developed in Part I) and introducing discrete basis functions, we obtain the well-known algorithms for probabilistic least-squares inversion set out by Tarantola & Valette. In doing so, we establish a direct equivalence between the spatial covariance function that must be specified in continuous inversion, and the combination of basis functions and prior covariance matrix that must be chosen for discretized inversion. We show that the common choice of Tikhonov regularization (Cm-1 = σ 2I) arises from a delta-function spatial covariance, and that this lies behind many of the artefacts commonly associated with discretized inversion. We show that other choices of spatial covariance function can be used to generate regularization matrices yielding substantially better results, and permitting localization of features even if global basis functions are used. We are also able to offer a straightforward explanation for the spectral leakage problem identified by Trampert & Snieder.

    Original languageEnglish
    Pages (from-to)1648-1656
    Number of pages9
    JournalGeophysical Journal International
    Volume220
    Issue number3
    DOIs
    Publication statusPublished - 1 Mar 2020

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