eprintid: 1724
rev_number: 10
eprint_status: archive
userid: 6
dir: disk0/00/00/17/24
datestamp: 2016-09-15 11:26:45
lastmod: 2019-03-07 13:54:56
status_changed: 2016-09-15 11:26:45
type: article
metadata_visibility: show
creators_name: Lasocki, Stanislaw
creators_id: lasocki@igf.edu.pl
corp_creators: Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland
title: Transformation to equivalent dimensions--a new methodology to study earthquake clustering
subjects: MP2_1
subjects: MP2_3
full_text_status: none
keywords: Persistence, memory, correlations, clustering
abstract: A seismic event is represented by a point in a parameter space, quantified by the vector of parameter values. Studies of earthquake clustering involve considering distances between such points in multidimensional spaces. However, the metrics of earthquake parameters are different, hence the metric in a multidimensional parameter space cannot be readily defined. The present paper proposes a solution of this metric problem based on a concept of probabilistic equivalence of earthquake parameters. Under this concept the lengths of parameter intervals are equivalent if the probability for earthquakes to take values from either interval is the same. Earthquake clustering is studied in an equivalent rather than the original dimensions space, where the equivalent dimension (ED) of a parameter is its cumulative distribution function. All transformed parameters are of linear scale in [0, 1] interval and the distance between earthquakes represented by vectors in any ED space is Euclidean. The unknown, in general, cumulative distributions of earthquake parameters are estimated from earthquake catalogues by means of the model-free non-parametric kernel estimation method. Potential of the transformation to EDs is illustrated by two examples of use: to find hierarchically closest neighbours in time–space and to assess temporal variations of earthquake clustering in a specific 4-D phase space.
date: 2014-02
date_type: published
publication: Geophysical Journal International
volume: 197
number: 2
publisher: Oxford University Press
pagerange: 1224-1235
id_number: doi:10.1093/gji/ggu062
issn: 0956-540X
official_url: http://doi.org/10.1093/gji/ggu062
access_IS-EPOS: limited
software_references: Transformation_to_Equivalent_Dimensions
owner: Publisher
citation:   Lasocki, Stanislaw  (2014) Transformation to equivalent dimensions--a new methodology to study earthquake clustering.  Geophysical Journal International, 197 (2).  pp. 1224-1235. DOI: https://doi.org/10.1093/gji/ggu062 <https://doi.org/10.1093/gji/ggu062>