Transdimensional inference in the geosciences
@article{Sambridge2013TransdimensionalII, title={Transdimensional inference in the geosciences}, author={Malcolm Sambridge and Thomas Bodin and Kerry Gallagher and Hrvoje Tkal{\vc}i{\'c}}, journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2013}, volume={371} }
Seismologists construct images of the Earth's interior structure using observations, derived from seismograms, collected at the surface. A common approach to such inverse problems is to build a single ‘best’ Earth model, in some sense. This is despite the fact that the observations by themselves often do not require, or even allow, a single best-fit Earth model to exist. Interpretation of optimal models can be fraught with difficulties, particularly when formal uncertainty estimates become…
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References
SHOWING 1-10 OF 52 REFERENCES
Transdimensional tomography with unknown data noise
- Geology
- 2012
SUMMARY
A meaningful interpretation of seismic measurements requires a rigorous quantification of the uncertainty. In an inverse problem, the data noise determines how accurately observations…
A self-parametrizing partition model approach to tomographic inverse problems
- Mathematics
- 2009
Partition modelling is a statistical method for nonlinear regression and classification, and is particularly suited to dealing with spatially variable parameters. Previous applications include…
Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem
- Geology
- 2002
Summary
A key element in the solution of a geophysical inverse problem is the quantification of non-uniqueness, that is, how much parameters of an inferred earth model can vary while fitting a set…
Trans-dimensional geoacoustic inversion.
- MathematicsThe Journal of the Acoustical Society of America
- 2010
This paper develops a general trans-dimensional Bayesian methodology for geoacoustic inversion that results in environmental estimates that quantify appropriate seabed structure as supported by the data, allowing sharp discontinuities while approximating smooth transitions where needed.
Receiver function inversion by trans‐dimensional Monte Carlo sampling
- Mathematics
- 2010
SUMMARY
A key question in the analysis of an inverse problem is the quantification of the non-uniqueness of the solution. Non-uniqueness arises when properties of an earth model can be varied…
Seismic tomography with the reversible jump algorithm
- Geology
- 2009
SUMMARY The reversible jump algorithm is a statistical method for Bayesian inference with a variable number of unknowns. Here, we apply this method to the seismic tomography problem. The approach…
Transdimensional inversion of receiver functions and surface wave dispersion
- Geology
- 2012
This work presents a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation and shows that the Hierarchical Bayes procedure is a powerful tool in this situation, able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors.
Trans-dimensional inverse problems, model comparison and the evidence
- Mathematics
- 2006
SUMMARY In most geophysical inverse problems the properties of interest are parametrized using a fixed number of unknowns. In some cases arguments can be used to bound the maximum number of…
Inversion of massive surface wave data sets: Model construction and resolution assessment
- Geology
- 2004
[1] A new scheme is proposed for the inversion of surface waves using a continuous formulation of the inverse problem and the least squares criterion. Like some earlier schemes a Gaussian a priori…
A Bayesian approach to inverse modelling of stratigraphy, part 1: method
- Geology
- 2009
The inference of ancient environmental conditions from their preserved response in the sedimentary record still remains an outstanding issue in stratigraphy. Since the 1970s, conceptual stratigraphic…