Earthquakes : models, statistics, testable forecasts

307 Pages·2014·13.616 MB·English

by  Kagan, Yan K

Earthquakes
BookSeries:StatisticalPhysicsofFractureandBreakdown
Editors:BikasK.ChakrabartiandPurusattamRay
Whydoesabridgecollapse,anaircraftorashipbreakapart?Whendoesadielec-
tricinsulationfailoracircuitfuse,eveninmicroelectronicsystems?Howdoesan
earthquakeoccur?Arethereprecursorstothesefailures?Theseremainimpor-
tant questions, even more so as our civilization depends increasingly on struc-
turesandserviceswheresuchfailurecanbecatastrophic.Howcanwepredict
andpreventsuchfailures?Canweanalyzetheprecursorysignalssufficientlyin
advancetotakeappropriatemeasures,suchasthetimelyevacuationofstructures
orlocalities,ortheshutdownoffacilitiessuchasnuclearpowerplants?
Whilst these questions have long been the subject of research, the study of
fractureandbreakdownprocesseshasnowgonebeyondsimplydesigningsafe
andreliablemachines,vehiclesandstructures.Fromthefractureofawoodblock
orthetearingofasheetofpaperinthelaboratory,thebreakdownofanelectrical
network on an engineering scale, to an earthquake on a geological scale, one
findscommonthreadsanduniversalfeaturesinfailureprocesses.Theideasand
observationsofmaterialscientists,engineers,technologists,geologists,chemists
andphysicistshaveallplayedapivotalroleinthedevelopmentofmodernfracture
science.
Overthelastthreedecades,considerableprogresshasbeenmadeinmodeling
andanalyzingfailureandfractureprocesses.Thephysicsofnonlinear,dynamic,
many-bodiedandnon-equilibriumstatistical,mechanicalsystems,theexactsolu-
tionsoffibrebundlemodels,solutionsofearthquakemodels,numericalstudies
of random resistor and random spring networks, and laboratory-scale innova-
tiveexperimentalverificationshaveallopenedupbroadvistasoftheprocesses
underlyingfracture.Thesehaveprovidedaunifyingpictureoffailureoverawide
rangeoflength,energyandtimescales.
Thisseriesofbooksintroducesreaders – inparticular,graduatestudentsand
researchers in mechanical and electrical engineering, earth sciences, material
science, and statistical physics – to these exciting recent developments in our
understandingofthedynamicsoffracture,breakdownandearthquakes.
Earthquakes
Models, Statistics, Testable Forecasts
Yan Y. Kagan
DepartmentofEarthandSpaceSciences,UniversityofCalifornia,LosAngeles,USA
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LibraryofCongressCataloging-in-PublicationData
Kagan,YanY.,author.
Earthquakes:models,statistics,testableforecasts/YanY.Kagan.
pagescm–(Statisticalphysicsoffractureandbreakdown)
Includesbibliographicalreferencesandindex.
ISBN978-1-118-63792-0(hardback)
1. Earthquakeprediction.2. Earthquakehazardanalysis. I.Title.
QE538.8.K322014
551.2201′12–dc23
2013033255
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay
notbeavailableinelectronicbooks.
Coverimage:Earthquake.Menlookingatcracksinthegroundcausedbyamagnitude7.1earthquake
thatstrucknearthecityofVan,Turkey,on23rdOctober2011.Photographedinnear
Alakoy,Turkey,on30thNovember2011.RiaNovosti/SciencePhotoLibrary.
StructuraldamageonanapartmentbuildingduringtheearthquakeofFebruary27,2010in
Chile(Santiago).©iStockphoto.com/erlucho(Frontcover).
LocationofshallowearthquakesintheGlobalCentroidMomentTensor(GCMT)catalog,
1976/1/1–2012/12/31.CourtesyofGöranEkströmandtheGCMTproject(Backcover).
CoverdesignbySteveThompson
Setin10.5/12.5ptDanteMTbyLaserwordsPrivateLimited,Chennai,India
12014
TomywifeOlga,alwaysmyfirstreader,editorandcritic

Contents
Preface xiii
Acknowledgments xvii
ListofAbbreviations xix
ListofMathematicalSymbols xxi
PARTI MODELS 1
1 Motivation:Earthquakesciencechallenges 3
2 Seismologicalbackground 6
2.1 Earthquakes 6
2.2 Earthquakecatalogs 8
2.3 Descriptionofmodernearthquakecatalogs 11
2.4 Earthquaketemporaloccurrence:quasi-periodic,Poisson,or
clustered? 14
2.5 Earthquakefaults:onefault,severalfaults,oraninfinite
numberoffaults? 16
2.6 Statisticalandphysicalmodelsofseismicity 18
2.7 Laboratoryandtheoreticalstudiesoffracture 19
3 Stochasticprocessesandearthquakeoccurrencemodels 21
3.1 Earthquakeclusteringandbranchingprocesses 21
3.2 Severalproblemsandchallenges 24
3.3 Criticalcontinuum-statebranchingmodelofearthquake
rupture 26
3.3.1 Time-magnitudesimulation 26
3.3.2 Space-focalmechanismsimulation 28
PARTII STATISTICS 31
4 Statisticaldistributionsofearthquakenumbers:Consequenceof
branchingprocess 33
4.1 Theoreticalconsiderations 34
4.1.1 Generatingfunctionforthenegativebinomial
distribution(NBD) 34
viii CONTENTS
4.1.2 NBDdistributionexpressions 39
4.1.3 Statisticalparameterestimation 41
4.2 Observedearthquakenumbersdistribution 43
4.2.1 Statisticalanalysisofearthquakecatalogs 43
4.2.2 Observedearthquakenumbersdistributions 43
4.2.3 Likelihoodanalysis 46
4.2.4 Tablesofparameters 49
5 Earthquakesizedistribution 54
5.1 Magnitudeversusseismicmoment 54
5.2 Seismicmomentdistribution 56
5.3 Is𝛽 ≡1∕2? 60
5.3.1 Preamble 60
5.3.2 Cataloganalysisandearthquakesizedistribution 62
5.3.3 Systematicandrandomeffectsindetermining
earthquakesize 63
5.3.4 Dislocationavalanchestatistics 77
5.3.5 Whatare𝛽 ≡1∕2consequences? 79
5.4 Seismicmomentsumdistribution 80
5.4.1 Simulationandanalyticalresults 80
5.4.2 Applicationstoseismicityanalysis 83
5.5 Lengthofaftershockzone(earthquakespatialscaling) 86
5.6 Maximumorcornermagnitude:2004Sumatraand2011
Tohokumega-earthquakes 90
5.6.1 Maximummomentforsubductionzones 90
5.6.2 Seismicmomentconservationprinciple 90
6 Temporalearthquakedistribution 96
6.1 Omori’slaw 96
6.2 Seismicmomentreleaseinearthquakesandaftershocks 97
6.2.1 Temporaldistributionofaftershocks 97
6.2.2 SouthernCaliforniaearthquakesandtheir
aftershocks 99
6.2.3 Globalshallowearthquakes 103
6.2.4 Comparisonofsource-timefunctionsand
aftershockmomentrelease 105
6.3 RandomshearstressandOmori’slaw 107
6.4 Aftershocktemporaldistribution,theoreticalanalysis 110
6.4.1 Lévydistribution 110
6.4.2 InverseGaussiandistribution(IGD) 112
6.5 Temporaldistributionofaftershocks:Observations 116
6.5.1 Aftershocksequences 116
6.5.2 Temporaldistributionforearthquakepairs 116
6.6 Example:TheNewMadridearthquakesequenceof1811–12 121
6.7 Conclusion 123