Transdimensional tomography with unknown data noise

Thomas Bodin, Malcolm Sambridge, Nick Rawlinson, Pierre Arroucau

Research output: Contribution to journalArticlepeer-review

181 Citations (Scopus)


A meaningful interpretation of seismic measurements requires a rigorous quantification of the uncertainty. In an inverse problem, the data noise determines how accurately observations should be fit, and ultimately the level of detail contained in the recovered model. A common problem in seismic tomography is the difficulty in quantifying data uncertainties, and thus the required level of data fit. Traditionally, the complexity of the solution model (defined by both the number of basis functions and the regularization) is defined arbitrarily by the user prior to inversion with only limited use of data errors. In the context of multiscale problems, dealing with multiple data sets that are characterized by different noise variances and that span the Earth at different scales is a major challenge. Practitioners are usually required to arbitrarily weigh the contribution of each data type into the final solution. Furthermore, the basis functions are usually spatially uniform across the velocity field and regularization procedures are global, which prevents the solution model from accounting for the uneven spatial distribution of information. In this work we propose to address these issues with a Hierarchical Bayesian inversion. The new algorithm represents an extension of the transdimensional tomography to account for uncertainties in data noise. This approach has the advantage of treating the level of noise in each data set, as well as the number of model parameters, as unknowns in the inversion. It provides a parsimonious solution that fully represents the degree of knowledge one has about seismic structure (i.e. constraints, resolution and trade-offs). Rather than being forced to make decisions on parametrization, level of data fit and weights between data types in advance, as is often the case in an optimization framework, these choices are relaxed and instead constrained by the data themselves. The new methodology is presented in a synthetic example where both the data density and the underlying structure contain multiple length scales. Three ambient noise data sets that span the Australian continent at different scales are then simultaneously inverted to infer a multiscale tomographic image of Rayleigh wave group velocity for the Australian continent. The procedure turns out to be particularly useful when dealing with multiple data types with different unknown levels of noise as the algorithm is able to naturally adjust the fit to the different data sets and provide a velocity map with a spatial resolution adapted to the spatially variable information present in the data.
Original languageEnglish
Pages (from-to)1536-1556
Number of pages21
JournalGeophysical Journal International
Issue number3
Early online date1 Jun 2012
Publication statusPublished - Jun 2012

Bibliographical note

We thank Kerry Gallagher for discussions on Hierarchical Bayes, Alberto Malinverno, Andrew Curtis and Stan Dosso for useful feedback, and Erdinc Saygin for assisting with seismic data. This project was supported by French-Australian Science and Technology travel grant (FR090051) under the International Science Linkages program from the Department of Innovation, Industry, Science and Research, and Australian Research Council Discovery project DP110102098. Calculations were performed on the TerraWulf II,
a computational facility supported through the AuScope inversion laboratory. AuScope Ltd is funded under the National Collaborative Research Infrastructure Strategy (NCRIS) and the Education Infrastructure Fund (EIF), both Australian Commonwealth Government Programmes.


  • inverse theory
  • seism
  • surface waves and free oscillations
  • probability distributions


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