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Locating lines among scattered points

Hall, Peter; Tajvidi, Nader; Malin, P. E.

Description

Consider a process of events on a line L, where, for the most part, the events occur randomly in both time and location. A scatterplot of the pair that represents position on the line, and occurrence time, will resemble a bivariate stochastic point process in a plane, P say. If, however, some of the points on L arise through a more regular phenomenon which travels along the line at an approximately constant speed, creating new points as it goes, then the corresponding points in P will occur...[Show more]

dc.contributor.authorHall, Peter
dc.contributor.authorTajvidi, Nader
dc.contributor.authorMalin, P. E.
dc.date.accessioned2015-12-07T22:20:27Z
dc.identifier.issn1350-7265
dc.identifier.urihttp://hdl.handle.net/1885/19616
dc.description.abstractConsider a process of events on a line L, where, for the most part, the events occur randomly in both time and location. A scatterplot of the pair that represents position on the line, and occurrence time, will resemble a bivariate stochastic point process in a plane, P say. If, however, some of the points on L arise through a more regular phenomenon which travels along the line at an approximately constant speed, creating new points as it goes, then the corresponding points in P will occur roughly in a straight line. It is of interest to locate such lines, and thereby identify, as nearly as possible, the points on L which are associated with the (approximately) constant-velocity process. Such a problem arises in connection with the study of seismic data, where L represents a fault-line and the constant-velocity process there results from the steady diffusion of stress. We suggest methodology for solving this needle-in-a-haystack problem, and discuss its properties. The technique is applied to both simulated and real data. In the latter case it draws particular attention to events occurring along the San Andreas fault, in the vicinity of Parkville, California, on 5 April 1995.
dc.publisherChapman & Hall
dc.sourceBernoulli
dc.source.urihttp://projecteuclid.org:80/Dienst/UI/1.0/Summarize/euclid.bj/1161614948
dc.subjectKeywords: Earthquake; Hypothesis test; Large-deviation probability; Ley-line; Point process; Poisson process; San Andreas fault; Spatial process
dc.titleLocating lines among scattered points
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume12
dc.date.issued2006
local.identifier.absfor010404 - Probability Theory
local.identifier.ariespublicationu3488905xPUB9
local.type.statusPublished Version
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationTajvidi, Nader, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationMalin, P. E., Duke University
local.description.embargo2037-12-31
local.bibliographicCitation.issue5
local.bibliographicCitation.startpage821
local.bibliographicCitation.lastpage839
dc.date.updated2016-02-24T10:16:21Z
local.identifier.scopusID2-s2.0-71249152001
CollectionsANU Research Publications

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