Locating lines among scattered points
(2006) In Bernoulli 12(5). p.821839 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) constantvelocity 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) constantvelocity process. Such a problem arises in connection with the study of seismic data, where L represents a faultline and the constantvelocity process there results from the steady diffusion of stress. We suggest methodology for solving this needleinahaystack 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:
https://lup.lub.lu.se/record/384226
 author
 Hall, Peter ; Tajvidi, Nader ^{LU} and Malin, P. E.
 organization
 publishing date
 2006
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 spatial process, San Andreas fault, Poisson process, point process, leyline, largedeviation probability, earthquake, hypothesis test
 in
 Bernoulli
 volume
 12
 issue
 5
 pages
 821  839
 publisher
 Chapman and Hall
 external identifiers

 wos:000241620800004
 scopus:71249152001
 ISSN
 13507265
 language
 English
 LU publication?
 yes
 id
 14b71a3dad8842f1956f915de9ccd0d8 (old id 384226)
 alternative location
 http://projecteuclid.org/euclid.bj/1161614948
 date added to LUP
 20160401 15:20:42
 date last changed
 20200112 18:25:14
@article{14b71a3dad8842f1956f915de9ccd0d8, 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) constantvelocity process. Such a problem arises in connection with the study of seismic data, where L represents a faultline and the constantvelocity process there results from the steady diffusion of stress. We suggest methodology for solving this needleinahaystack 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 = {13507265}, language = {eng}, number = {5}, pages = {821839}, publisher = {Chapman and Hall}, series = {Bernoulli}, title = {Locating lines among scattered points}, url = {http://projecteuclid.org/euclid.bj/1161614948}, volume = {12}, year = {2006}, }