# 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…

## 118 Citations

On the nature of the P-wave velocity gradient in the inner core beneath Central America

- GeologyJournal of Earth Science
- 2013

We conduct an experiment to investigate whether linearity in the observed velocity gradient in the volume of the inner core sampled by the PKP ray paths beneath Central America is a robust…

Convergence Tests for Transdimensional Markov Chains in Geoscience Imaging

- GeologyMathematical Geosciences
- 2019

It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization, while maintaining the statistical characteristics of the ensemble.

Tomographic filtering via the generalized inverse: a way to account for seismic data uncertainty

- Geology
- 2020

Tomographic-geodynamic model comparisons are a key component in studies of the present-day state and evolution of Earth’s mantle. To account for the limited seismic resolution, ‘tomographic…

Blockworlds 0.1.0: A demonstration of anti-aliased geophysics for probabilistic inversions of implicit and kinematic geological models

- Geology
- 2021

Abstract. Parametric geological models such as implicit or kinematic models provide low-dimensional, interpretable representations of 3-D geological structures. Combining these models with…

Inversion of receiver functions without deconvolution—application to the Indian craton

- Geology
- 2014

S U M M A R Y Receiver functions are a powerful tool to isolate and interpret receiver-side structure effects in teleseismic seismic records. They are easily constructed by deconvolving one component…

Bayesian trans-dimensional full waveform inversion: synthetic and field data application

- Geology
- 2020

Seismic full waveform inversion (FWI) is a state-of-the-art technique for estimating subsurface physical models from recorded seismic waveform, but its application requires care because of high…

Magnitude frequency, spatial and temporal analysis of large seismicity catalogs: The Californian Experience

- Geology
- 2015

Recent years have seen a substantial increase in the amount of available seismic catalog data. Extracting information from these data, on a case-by-case basis is gradually becoming infeasible. In…

Interpreting Radial Anisotropy in Global and Regional Tomographic Models

- Geology, Mathematics
- 2015

We review the present status of global and regional mantle tomography and discuss how resolution has improved in the last decade with the advent of full waveform tomography and exact numerical…

Varying dimensional Bayesian acoustic waveform inversion for 1D semi-infinite heterogeneous media

- Mathematics
- 2015

Consequences of parameterization choices in surface wave inversion: Insights from transdimensional Bayesian methods

- GeologyGeophysical Journal International
- 2018

S U M M A R Y Inversion of surface wave data for crustal and upper-mantle structure is a staple of passive seismology, particularly since the advent of techniques enabling surface wave dispersion…

## References

SHOWING 1-10 OF 53 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…