Trans-dimensional geoacoustic inversion

• Published in: The Journal of the Acoustical Society of America Vol. 128; no. 6; pp. 3393 - 3405
• Main Authors: Dettmer, Jan, Dosso, Stan E., Holland, Charles W.
• Format: Journal Article
• Language: English
• Published: Melville, NY Acoustical Society of America 01-12-2010; American Institute of Physics
• Subjects: Acoustics; Algorithms; Bayes Theorem; Computer Simulation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Geologic Sediments; Geology; Markov Chains; Models, Theoretical; Monte Carlo Method; Motion; Physics; Seawater; Signal Processing, Computer-Assisted; Sound; Sound Spectrography; Time Factors; Underwater sound; Marine geology; Underwater acoustics; Ocean floors; Inverse problem
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.3500674

This paper develops a general trans-dimensional Bayesian methodology for geoacoustic inversion. Trans-dimensional inverse problems are a generalization of fixed-dimensional inversion that includes the number and type of model parameters as unknowns in the problem. By extending the inversion state space to multiple subspaces of different dimensions, the posterior probability density quantifies the state of knowledge regarding inversion parameters, including effects due to limited knowledge about appropriate parametrization of the environment and error processes. The inversion is implemented here using a reversible-jump Markov chain Monte Carlo algorithm and the seabed is parametrized using a partition model. Unknown data errors are addressed by including a data-error model. Jumps between dimensions are implemented with a birth-death methodology that allows transitions between dimensions by adding or removing interfaces while maintaining detailed balance in the Markov chain. Trans-dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self-regularizing algorithm based on data information content, not on subjective regularization functions. Together, this results in environmental estimates that quantify appropriate seabed structure as supported by the data, allowing sharp discontinuities while approximating smooth transitions where needed. This approach applies generally to geoacoustic inversion and is illustrated here with seabed reflection-coefficient data.