Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

Derek R. Olson, Anthony P. Lyons, Douglas A. Abraham, Torstein O. Sbø

Research output: Contribution to journalArticle

Abstract

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding the appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits a significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had a significant parameter correlation, but also contained multiple modes. It is concluded that the mixture between two K distributions is the most applicable to this dataset.

Original languageEnglish (US)
Pages (from-to)761-774
Number of pages14
JournalJournal of the Acoustical Society of America
Volume145
Issue number2
DOIs
StatePublished - Feb 1 2019

Fingerprint

outcrops
inference
statistics
rocks
scattering
probability density functions
Bayes theorem
Statistics
Rock
Bayesian Inference
synthetic apertures
Norway
sonar
false alarms
Mixture Model
coasts
physics
acoustics
estimates

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

@article{b1872d2c13564dfa98cbf3da5aea30e9,
title = "Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions",
abstract = "The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding the appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits a significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had a significant parameter correlation, but also contained multiple modes. It is concluded that the mixture between two K distributions is the most applicable to this dataset.",
author = "Olson, {Derek R.} and Lyons, {Anthony P.} and Abraham, {Douglas A.} and Sb{\o}, {Torstein O.}",
year = "2019",
month = "2",
day = "1",
doi = "10.1121/1.5089892",
language = "English (US)",
volume = "145",
pages = "761--774",
journal = "Journal of the Acoustical Society of America",
issn = "0001-4966",
publisher = "Acoustical Society of America",
number = "2",

}

Scattering statistics of rock outcrops : Model-data comparisons and Bayesian inference using mixture distributions. / Olson, Derek R.; Lyons, Anthony P.; Abraham, Douglas A.; Sbø, Torstein O.

In: Journal of the Acoustical Society of America, Vol. 145, No. 2, 01.02.2019, p. 761-774.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Scattering statistics of rock outcrops

T2 - Model-data comparisons and Bayesian inference using mixture distributions

AU - Olson, Derek R.

AU - Lyons, Anthony P.

AU - Abraham, Douglas A.

AU - Sbø, Torstein O.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding the appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits a significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had a significant parameter correlation, but also contained multiple modes. It is concluded that the mixture between two K distributions is the most applicable to this dataset.

AB - The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding the appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits a significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had a significant parameter correlation, but also contained multiple modes. It is concluded that the mixture between two K distributions is the most applicable to this dataset.

UR - http://www.scopus.com/inward/record.url?scp=85061670180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061670180&partnerID=8YFLogxK

U2 - 10.1121/1.5089892

DO - 10.1121/1.5089892

M3 - Article

VL - 145

SP - 761

EP - 774

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 2

ER -