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Revisiting the 1894 Omori aftershock dataset with the stretched exponential function; reply

Arnaud Mignan
Revisiting the 1894 Omori aftershock dataset with the stretched exponential function; reply
Seismological Research Letters (July 2016) Pre-Issue Publication

Abstract

Hainzl and Christophersen (2016) recently suggested that the approach used by Mignan (2016) to visualize the Omori law in a log-log plot using the complementary cumulative density function (CCDF) was misleading. They showed that one should use a temporal upper bound t (sub max) =max(t (sub obs) ), with t (sub obs) the occurrence time of a set of observed aftershocks, instead of t (sub max) -->infinity, as used by Mignan. They found that both the Omori law and stretched exponential function (SEF) are undistinguishable on a corrected CCDF log-log plot but that the Omori law is preferred based on maximum-likelihood estimations (MLEs). I first clarify the rationale for using the CCDF log-log plot for comparison of the SEF with a power law but verify that the comparison indeed becomes misleading when the data sequence is incomplete. However, I then show that MLEs obtained for the Omori law are ambiguous, because this function may win versus the SEF, even if the true relaxation process follows an SEF (subject to early data incompleteness). This debate highlights that statistics alone may not be enough to choose between the stretched exponential and the Omori law and that physical considerations should be added to the discussion.


ISSN: 0895-0695
EISSN: 1938-2057
Serial Title: Seismological Research Letters
Serial Volume: Pre-Issue Publication
Title: Revisiting the 1894 Omori aftershock dataset with the stretched exponential function; reply
Author(s): Mignan, Arnaud
Affiliation: Swiss Federal Institute of Technology, Institute of Geophysics, Zurich, Switzerland
Published: 20160713
Text Language: English
Publisher: Seismological Society of America, El Cerrito, CA, United States
Number of pages: 4
References: 19
Accession Number: 2016-073001
Categories: Seismology
Document Type: Serial
Bibliographic Level: Analytic
Annotation: For reference to discussion see Hainzl, A. and Christophersen, A., Seismological Research Letters, Vol. 87. No. 5, p. 1-4, 2016; for reference to original see Mignan, A., Seismological Research Letters, Vol. 87, No. 3, p. 685-689, 2016
Illustration Description: illus. incl. 2 tables
N30°00'00" - N45°00'00", E129°00'00" - E147°00'00"
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Abstract, Copyright, Seismological Society of America. Reference includes data from GeoScienceWorld, Alexandria, VA, United States
Update Code: 201635
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