Convergence tests for transdimensional Markov chains in geoscience imaging
- Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, thisClassic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.…
Author details: | Márk SomogyváriORCiDGND, Sebastian ReichORCiDGND |
---|---|
DOI: | https://doi.org/10.1007/s11004-019-09811-x |
ISSN: | 1874-8961 |
ISSN: | 1874-8953 |
Title of parent work (English): | Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences |
Publisher: | Springer |
Place of publishing: | Heidelberg |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/05/20 |
Publication year: | 2020 |
Release date: | 2022/11/28 |
Tag: | MCMC modelling; convergence assessment; transdimensional inversion |
Volume: | 52 |
Issue: | 5 |
Number of pages: | 18 |
First page: | 651 |
Last Page: | 668 |
Funding institution: | Geo.X, the Research Network for Geosciences in Berlin and Potsdam; [SO_087_GeoX]; Deutsche Forschungsgemeinschaft (DFG)German Research; Foundation (DFG) [CRC 1294] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
5 Naturwissenschaften und Mathematik / 55 Geowissenschaften, Geologie / 550 Geowissenschaften | |
Peer review: | Referiert |