Aug 6, 1993 - anelasticity will also be important in the deep mantle where Q is larger, if temperature ... al., 1985; Forte et al., 1993]. Important material ...
GEOPHYSICAL RESEARCH LETTERS, VOL. 20, NO. 15, PAGES 1623-1626, AUGUST 6, 1993
IMPORTANCE OF ANELASTIC1TY IN THE INTERPRETATION OF SEISMIC TOMOGRAPHY Shun-ichiro Karato
Department of Geology andGeophysics, University of Minnesota, Minneapolis, MN 55455 Abstract. Temperature dependenceof seismic wave velocitiescomesboth from anharmonicityand anelasticity. The conu'ibution from anelasticityis shownto be important in theEarth'smantleparticularlyfor shearwaves.In the low
Q (Qla ~100)regions in theuppermantle, thecorrection due
lateralheterogeneity in seismicwavevelocitieshasnotbeen wellappreciated. Thepurpose of thispaperis to evaluate the effects of anelasticityon the temperaturederivative of seismicwave velocitiesand discussits importancein the interpretation of seismictomography.
to anelasticity will roughly double the temperature derivativesdue to anharmonicityalone.The correctionfor anelasticity will alsobeimportant in thedeepmantlewhereQ is larger,if temperature derivatives dueto anharmonicity will decrease significantly withpressure. Theseresultsimplythat the temperatureanomaliesassociatedwith low velocity anomaliesin the mantlewill be significantlysmallerthan previouslyconsideredon the basisof anharmoniceffect aloneand that the amplitudeof velocity anomalieswill be significantlylargerfor shearwavesthanfor compressional waves.
The interpretation of seismictomography requiresa sound understanding of the possiblecausesof lateralvariationof seismicwavevelocities.Whentheeffectsof heterogeneity in chemicalcomposition canbe neglected,the mainsourcefor variation
in velocities
Derivatives
Anharmoniceffectsareaccompanied with no energyloss andinsensitiveto thefrequencyof elasticwaves.In contrast, anelastic(includingviscoelastic) effectsareassociated with
energylossandhencearedependent on frequency.When thefrequency of anelasticwaveis comparable to or shorter than the characteristicfrequencyof relaxation, then a significant relaxationwill occurthatwill affectelasticwave velocities.Most of the relaxationprocessesare thermally activatedandthereforethecharacteristic frequencies increase
Introduction
lateral
Anelasticity, VelocityDispersion andTemperature
is the lateral
variation
significantly with temperature leadingto anothersourceof temperature derivatives of elasticwavevelocities. Thus the temperaturedependenceof seismicwave velocities will include both anharmonic and anelastic effects
and the measurementsof the latter effects will only be
in
possibleat high temperaturesand low frequencies. of elasticproperties at low frequencies require temperatures.Velocity anomalies ISV, in this case, are Measurements proportionalto temperatureanomalies1STand henceto highprecision measurements of displacements, anddefinite densityanomalieslSp.The densityanomaliesthusestimated resultshavenotbeenobtainedalthoughsignificantprogress have been usedin geodynamicalmodellingof convective has been made toward this goal [Getting et al., 1990; Jacksonet al., 1992; Jackson,1993]. processes andthe resultantgeoidanomalies[e.g., Hageret The mannerin which seismicwave velocitieschangewith
al., 1985; Forte et al., 1993].
Important materialparameters to estimate õT andõpfrom frequencyand temperaturedependson the frequency of Q. Previous studies suggest nearlyfrequency õV are •}V/i}T and •}p/i}T (i.e. thermal expansion) dependence respectively. Althoughsignificant progress hasrecentlybeen independent Q [KanamoriandAnderson, 1977]or a weak made in the measurementsof thermal expansion[e.g., dependence of Q onfrequency (•o)as[KaratoandSpetzler, ChopelasandBoehler,1989], not muchprogresshasbeen made in the measurements of temperaturederivativesof seismic
wave
velocities.
In
most
of
the
studies
on
1990],
Q~r.oa
(1)
geodynamics, the temperaturederivativesof seismicwave velocitiesdeterminedat high frequencies(~1 MHz, e.g.,
where {x~ 0.1-0.3forthefrequencies ranging from10-8to 1
Kumazawa and Anderson, 1969; Isaak, 1992) have been
invokea distributionof relaxationtimesin an anelasticbody (standard linearsolid;e.g.,MinsterandAnderson,1981).In eithercase,the dependence of velocitieson frequencyand temperature will besignificantly smallerthanin simplecases with onlyonerelaxationtime. For a frequencyindependent Q, theseismicwavevelocity
used, which are due mostly to anharmonic effects. However,mostof the seismological observations are made at low frequencies(•o < 1 Hz) and contributionsfrom anelastic(includingviscoelastic) effectsbecomeimportant,
particularly for shearwaves,whentemperature is high. Althoughthe importance of anelasticeffectsin velocity dispersionhas long been recognized[Kanamori and Anderson,1977], its importancein the interpretationof
Hz. A mechanism to account for these observations is to
will dependonfrequency andtemperature (T) as[Kanamori and Anderson, 1977],
V(•o,T)= Vo(T){1 + (Q-1/x)lnroxCr)}
(2)
where Vo is a referencevelocity correspondingto the unrelaxed state, and x(T) is the relaxation time which dependson temperatureas,
Copyright1993 by the AmericanGeophysical Union. Paper Number 93GL01767
•:(T)= Xoexp(H*/RT)
0094-8534/93/93 GL-01767503.00 1623
(3)
1624
Karato:Effectsof Anelasticityon SeismicTomography
where •o is the pre-exponentialfactor,H* the activation enthalpyandR the gasconstant. Takingderivativeof equation(2), onegets,
i}lnVfdT= i}lnVo/i}T - (Q-1/a;)(H*/RT2)
(4)
whereI assumed a smallanelasticity (Q-I
