Bayesian inference from terrestrial gravimetry measurements of near-surface anomalies using a bespoke reversible-jump Markov chain Monte Carlo algorithm

Rodgers, Anthony David (2017). Bayesian inference from terrestrial gravimetry measurements of near-surface anomalies using a bespoke reversible-jump Markov chain Monte Carlo algorithm. University of Birmingham. Ph.D.

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Abstract

This work describes a Bayesian algorithm developed to tackle the problem of inference from two-dimensional grids of terrestrial gravity measurements. Near-surface voids such as pipelines and tunnels were the motivating application. The forward models used to approximate the gravity signal due to these potentially complex underground anomalies were sums of simple geometrical shapes: the sphere, finite horizontal cylinder and cuboid. The model parameters of these shapes are related non-linearly to the gravity signal. The reversible-jump Markov chain Monte Carlo algorithm was used, allowing changes to the number of objects comprising the forward model. The natural parsimony of the algorithm was shown to be key for obtaining depth information without the need for arbitrary regularisation. Exploring the Bayesian posterior distribution in this way, spatial, geometrical and anomaly mass information can be obtained as outputs from the inference process, given prior information regarding the soil-anomaly density contrast. This was demonstrated both with synthetic noisy gravity and gravity gradient data and with field gravity data obtained using the Scintrex CG-5 commercial gravimeter. The methodology used to obtain field survey data using the CG-5 over multiple days is described, with discussion of the assignment of measurement uncertainty. A 134 point measurement grid was taken above two spatially separate concrete anomalies, for which volume and density information were known. The data was input into the Bayesian inference algorithm, the forward model parameters were successfully inferred within the total uncertainty.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

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