简介：TheorderofmagnitudeofmultipleFouriercoefficientsofcomplexvaluedfunctionsofgeneralizedboundedvariationslike(Λ1,,ΛN)BV(p)andr-BV,over[0,2π]N,areestimated.

简介：Inthisarticle,theseismicrecordsofJapan’sKik-netareselectedtomeasuretheacceleration,displacement,andeffectivepeakaccelerationofeachseismicrecordwithinacertaintimeafterPwave,thenacontinuousestimationisgivenonearthquakeearlywarningmagnitudethroughstatisticalanalysismethod,andWenchuanearthquakerecordisutilizedtocheckthemethod.Theresultsshowthatthereliabilityofearthquakeearlywarningmagnitudecontinuouslyincreaseswiththeincreaseoftheseismicinformation,thebiggestresidualhappensiftheaccelerationisadoptedtofitearthquakemagnitude,whichmaybecausedbyrichhigh-frequencycomponentsandlargedispersionofpeakvalueinaccelerationrecord,theinfluencecausedbythehigh-frequencycomponentscanbeeffectivelyreducediftheeffectivepeakaccelerationandpeakdisplacementisadopted,itisestimatedthatthedispersionofearthquakemagnitudeobviouslyreduces,butitiseasyforpeakdisplacementtobeaffectedbylong-perioddrifting.Invariouscomponents,theresidualenlargementphenomenonatverticaldirectionisalmostunobvious,thusitisrecommendedinthisarticlethattheeffectivepeakaccelerationatverticaldirectionispreferredtoestimateearthquakeearlywarningmagnitude.ThroughadoptingWenchuanstrongearthquakerecordtocheckthemethodmentionedinthisarticle,itisfoundthatthismethodcanbeusedtoquickly,stably,andaccuratelyestimatetheearlywarningmagnitudeofthisearthquake,whichshowsthatthismethodiscompletelyapplicableforearthquakeearlywarning.

简介：SeismicityoftheEarth(MC4.5)wascompiledfromNEIC,IRISandISCcataloguesandusedtocomputeb-valuebasedonvarioustimewindows.Itisfoundthatcontinuouscyclicb-variationsoccuronbothlongandshorttimescales,thelatterbeingofmuchhighervalueandsometimesinexcessof0.7oftheabsoluteb-value.Thesevariationsoccurnotonlyyearlyormonthly,butalsodaily.Beforetheoccurrenceoflargeearthquakes,b-valuesstartincreasingwithvariablegradientsthatareaffectedbyforeshocks.Insomecases,thegradientisreducedtozeroortoanegativevalueafewdaysbeforetheearthquakeoccurrence.Ingeneral,calculatedb-valuesattainmaxima1daybeforelargeearthquakesandminimasoonaftertheiroccurrence.Bothlinearregressionandmaximumlikelihoodmethodsgivecorrelatable,butvariableresults.Itisfoundthatanexpandingtimewindowtechniquefromafixedstartingpointismoreeffectiveinthestudyofb-variations.Thecalculatedb-variationsforthewholeEarth,itshemispheres,quadrantsandtheepicentralregionsofsomelargeearthquakesareofbothlocalandregionalcharacter,whichmayindicatethatinsuchcases,thegeodynamicprocessesactingwithinacertainregionhaveamuchregionaleffectwithintheEarth.Theb-variationshavelongbeenknowntovarywithanumberoflocalandregionalfactorsincludingtectonicstresses.Theresultsreportedhereindicatethatgeotectonicstressremainsthemostsignificantfactorthatcontrolsb-variations.ItisfoundthatforearthquakeswithMwC7,anincreaseofabout0.20intheb-valueimpliesastressincreasethatwillresultinanearthquakewithamagnitudeoneunithigher.

简介：Thecorrelationofthescaledenergy,e?=Es/M0,versusearthquakemagnitude,Ms,isstudiedbasedontwomodels:(1)Model1basedontheuseofthetimefunctionoftheaveragedisplacements,withax-2sourcespectrum,acrossafaultplane;and(2)Model2basedontheuseofthetimefunctionoftheaveragedisplacements,withax-3sourcespectrum,acrossafaultplane.Forthesecondmodel,therearetwocases:(a)Ass*T,wheresistherisetimeandTtherupturetime,lg(e?)*-Ms;and(b)AssT,lg(e?)*-(1/2)Ms.Thesecondmodelleadstoanegativevalueofe?.ThismeansthatModel2cannotworkforstudyingthepresentproblem.TheresultsobtainedfromModel1suggestthatthesourcemodelisafactor,yetnotauniqueone,incontrollingthecorrelationofe?versusMs.