Book contents
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Series page
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Copyright page
- Contents
- Contributors
- Preface
- Acknowledgements
- Part I Introduction
- Part II ‘Fluid’ Earth Applications: From the Surface to the Space
- Part III ‘Solid’ Earth Applications: From the Surface to the Core
- 11 Trans-Dimensional Markov Chain Monte Carlo Methods Applied to Geochronology and Thermochronology
- 12 Inverse Problems in Lava Dynamics
- 13 Data Assimilation for Real-Time Shake-Mapping and Prediction of Ground Shaking in Earthquake Early Warning
- 14 Global Seismic Tomography Using Time Domain Waveform Inversion
- 15 Solving Larger Seismic Inverse Problems with Smarter Methods
- 16 Joint and Constrained Inversion as Hypothesis Testing Tools
- 17 Crustal Structure and Moho Depth in the Tibetan Plateau from Inverse Modelling of Gravity Data
- 18 Geodetic Inversions and Applications in Geodynamics
- 19 Data Assimilation in Geodynamics: Methods and Applications
- 20 Geodynamic Data Assimilation: Techniques and Observables to Construct and Constrain Time-Dependent Earth Models
- 21 Understanding and Predicting Geomagnetic Secular Variation via Data Assimilation
- 22 Pointwise and Spectral Observations in Geomagnetic Data Assimilation: The Importance of Localization
- Index
- References
11 - Trans-Dimensional Markov Chain Monte Carlo Methods Applied to Geochronology and Thermochronology
from Part III - ‘Solid’ Earth Applications: From the Surface to the Core
Published online by Cambridge University Press: 20 June 2023
Book contents
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Series page
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Copyright page
- Contents
- Contributors
- Preface
- Acknowledgements
- Part I Introduction
- Part II ‘Fluid’ Earth Applications: From the Surface to the Space
- Part III ‘Solid’ Earth Applications: From the Surface to the Core
- 11 Trans-Dimensional Markov Chain Monte Carlo Methods Applied to Geochronology and Thermochronology
- 12 Inverse Problems in Lava Dynamics
- 13 Data Assimilation for Real-Time Shake-Mapping and Prediction of Ground Shaking in Earthquake Early Warning
- 14 Global Seismic Tomography Using Time Domain Waveform Inversion
- 15 Solving Larger Seismic Inverse Problems with Smarter Methods
- 16 Joint and Constrained Inversion as Hypothesis Testing Tools
- 17 Crustal Structure and Moho Depth in the Tibetan Plateau from Inverse Modelling of Gravity Data
- 18 Geodetic Inversions and Applications in Geodynamics
- 19 Data Assimilation in Geodynamics: Methods and Applications
- 20 Geodynamic Data Assimilation: Techniques and Observables to Construct and Constrain Time-Dependent Earth Models
- 21 Understanding and Predicting Geomagnetic Secular Variation via Data Assimilation
- 22 Pointwise and Spectral Observations in Geomagnetic Data Assimilation: The Importance of Localization
- Index
- References
Summary
Abstract: Trans-dimensional Markov chain Monte Carlo (MCMC) treats the number of model parameters as an unknown, and provides a natural approach to assess models of variable complexity. We demonstrate the application of these methods to geochronology and thermochronology. The first is mixture modelling, physically a finite dimension problem, which aims to extract the number and characteristics of component age distributions from an overall distribution of radiometric age data. We demonstrate the MCMC method with Gaussian and skew-t component distributions, the latter containing the former as a special case, applied to a suit of U-Pb zircon data from a sediment in northern France. When considering the posterior distributions obtained from the MCMC samplers, the asymmetrical skew distribution models imply fewer components than the symmetrical Gaussian distribution models. We present some heuristic criteria based on different ways to look the results and aid in model choice in the mixture modelling problem. The second application is a thermal history model, physically a continuous time-temperature function but here parametrised in terms of a finite number of time temperature nodes. We consider a suite of synthetic data from a vertical profile to demonstrate the variable resolution in models constrained from single and multiple samples. Provided the implicit assumptions made when grouping multiple samples are valid, the multi-sample approach is preferable as we exploit the variable information on the model (thermal history) contained in different samples.
Keywords
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2023
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