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Locating lines among scattered points

Hall, Peter ; Tajvidi, Nader LU and Malin, P. E. (2006) In Bernoulli 12(5). p.821-839
Abstract
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 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... (More)
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 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. (Less)
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
spatial process, San Andreas fault, Poisson process, point process, ley-line, large-deviation probability, earthquake, hypothesis test
in
Bernoulli
volume
12
issue
5
pages
821 - 839
publisher
Chapman and Hall
external identifiers
  • wos:000241620800004
  • scopus:71249152001
ISSN
1350-7265
language
English
LU publication?
yes
id
14b71a3d-ad88-42f1-956f-915de9ccd0d8 (old id 384226)
alternative location
http://projecteuclid.org/euclid.bj/1161614948
date added to LUP
2016-04-01 15:20:42
date last changed
2020-01-12 18:25:14
@article{14b71a3d-ad88-42f1-956f-915de9ccd0d8,
  abstract     = {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 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.},
  author       = {Hall, Peter and Tajvidi, Nader and Malin, P. E.},
  issn         = {1350-7265},
  language     = {eng},
  number       = {5},
  pages        = {821--839},
  publisher    = {Chapman and Hall},
  series       = {Bernoulli},
  title        = {Locating lines among scattered points},
  url          = {http://projecteuclid.org/euclid.bj/1161614948},
  volume       = {12},
  year         = {2006},
}