Journal ArticleDOI
Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation
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In this article, the authors considered the efficiency of trans-dimensional (trans-D) Bayesian inversion based on reversible-jump Markov chain Monte Carlo (rjMCMC) sampling, with application to geophysical inverse problems for a depth-dependent earth or seabed model of an unknown number of layers.Abstract:
This paper considers the efficiency of trans-dimensional (trans-D) Bayesian inversion based on reversible-jump Markov-chain Monte Carlo (rjMCMC) sampling, with application to geophysical inverse problems for a depth-dependent earth or seabed model of an unknown number of layers (seabed acoustic reflectivity inversion is the specific example). Trans-D inversion is applied to sample the posterior probability density over geoacoustic/geophysical parameters for a variable number of layers, providing profile estimates with uncertainties that include the uncertainty in the model parameterization. However, the approach is computationally intensive. The efficiency of rjMCMC sampling is largely determined by the proposal schemes which are applied to generate perturbed values for existing parameters and new values for parameters assigned to layers added to the model. Several proposal schemes are considered here, some of which appear new for trans-D geophysical inversion. Perturbations of existing parameters are considered in a principal-component space based on an eigen-decomposition of the unit-lag parameter covariance matrix (computed from successive models along the Markov chain, a diminishing adaptation). The relative efficiency of proposing new parameters from the prior versus a Gaussian distribution focused near existing values is examined. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is also considered as a means to increase the acceptance rate of new layers. The relative efficiency of various proposal schemes is compared through repeated inversions with a pragmatic convergence criterion.read more
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Journal ArticleDOI
Transdimensional seismic inversion using the reversible jump Hamiltonian Monte Carlo algorithm
Mrinal K. Sen,Reetam Biswas +1 more
TL;DR: In this article, the number of layers is also treated as a variable in the reverse jump Markov chain Monte Carlo (RJMCMC) approach, which is a tool for model exploration and uncertainty quantification.
Journal ArticleDOI
Geophysical imaging using trans-dimensional trees.
Rhys Hawkins,Malcolm Sambridge +1 more
TL;DR: This work presents a novel framework using transdimensional sampling over tree structures that offers greater flexibility, performance and efficiency for geophysical imaging problems than previous sampling algorithms.
Journal ArticleDOI
3-D Monte Carlo surface wave tomography
TL;DR: In this paper, a 1-step 3D non-linear surface wave tomography method was proposed to reveal the subsurface structure of the Earth using the reversible jump Markov chain Monte Carlo (McMC) algorithm with a fully 3D model parametrization.
Journal ArticleDOI
Frequency domain full waveform elastic inversion of marine seismic data from the Alba field using a Bayesian trans-dimensional algorithm
TL;DR: An algorithm to recover the Bayesian posterior model probability density function of subsurface elastic parameters, as required by the full pressure field recorded at an ocean bottom cable due to an impulsive seismic source is presented.
References
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Equation of state calculations by fast computing machines
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
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TL;DR: A fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
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Markov Chain Monte Carlo in Practice
TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.
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Information theory, inference, and learning algorithms
TL;DR: In this paper, the mathematics underpinning the most dynamic areas of modern science and engineering are discussed and discussed in a fun and exciting textbook on the mathematics underlying the most important areas of science and technology.