Correction to Horizontal viscoelasticgravitational ... - CSIC Digital

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. B12, PAGES 30,283-30,286,DECEMBER 10, 1998

Correction to "Horizontal viscoelastic-gravitational displacement due to a rectangular dipping thrust fault in a layered Earth model" by Jos6 Fernandez, Ting-To Yu and John B. Rundle In the paper "Horizontal viscoelastic-gravitational displacementdue to a rectangulardipping thrustfault in a layeredEarthmodel"by JosdFernfindez,Ting-To Yu andJohnB. Rundle(Journal of GeophysicalResearch,101(B6), 13,581-13,594, 1996) we have found two mistakeswhile using the methodfor calculatinghorizontaldeformationsproducedby thrust faulting in viscoelasticgravitational layeredEarth models. The first is that equations(5), (6), and (7) containsomeminor misprintsand shouldbe replacedby equations(1), (2), and (3) respectively,

(• 2 - +•I(0) Jo(kr)+J2(kr))sinO, 2 / I J0(kr)-Jo(kr) ) e3=(y2(0) 2 -z2(0) ,• sin20,(2) i Jl(kr)+J3(kr) i Ji(kr)-j3(kr)) + zl(0) cos0. (3) 84=/•(0) Y• J0(kr) 2 J2 5J:(kr)) + (kr) J0(kr)-

e2= y•(0)

Z --- -d

ß

The second mistake is rather more notable. Ferndndez et al.

[1996] calculatethe coseismicdisplacementsusingthe formulae described by Okada [1985]. Ferndndez et al. [1996] use a referencesystem(Figure 1) differentfrom the one usedby Okada [1985] (Figure 2). The transformationbetweenboth systemsis easy to obtain. Using the subscriptO to refer to Okada's [1985] referencesystem, and the subscriptR for the system used by Ferndndezet al. [1996], which is the same as the one used by Rundle [1982], we get

Figure 2. Geometryof the sourcemodeland coordinatesystem definedby Okada [1985].

The calculationsdescribedby Ferndndez et al. [1996] mistakenly showed YR=Yo. This meant that in their figures the coseismicdisplacements(and only the coseismicones)have the sign changedand, if dip angle is different from 90ø, displacedon the Y axis. This mistakedoesnot have any effect on their paper's results and conclusions, which are based on the viscoelastic

X O = X R, Yo =--YR +(W +D/sing/)cosg/, Z o = - Z R.

(4)

displacements,becausethe latter are calculateddirectly with the referencesystemusedby Fernandez et al. [1996] and are thusnot affected by this incorrect transformation. The coseismic displacementsshown in the figures should be changed, and henceforth the figures shown in this correction should be considered

l-ta!œspace

correct.

Acknowledgments. The researchof J.F. have been supportedby contractAMB96-0498-C04-04to Instituteof AstronomyandGeodesy,Madrid, and DE-FG03-95ER14499 to CIRES. Researchby T.-T.Y. have been supportedby the postdoctoralresearchfellow grant of Institute of Earth Sciences,Academia Sinica.The researchof J.B.R. has been supported under US Department of Energy grant DE-FG03-95ER14499 to the CooperativeInstitute for Researchin EnvironmentalSciences(CIRES) at the University of Colorado at Boulder.

References Fem•dez, J.,T.-T. Yu andJ.B.Rundle,Horizontalviscoelastic-gravitational displacement dueto a rectangular dippingthrustfaultin a layeredEarth

Figure 1. Geometryandcoordinate systemfor a rectangular, finite, model,J. Geophys. Res.,101, 13581-13594, 1996. dipping fault in elastic-gravitational layer over a viscoelasticdueto shearandtensilefaultsin a half-space, gravitational half-space. D is depth,W is fault planewidth,2L is Okada,Y., Surfacedeformation Bull. Seismol.Soc.Am., 75, 1135-1154, 1985. lengthalongstrike, g"is dip angle,andH is layer thickness[after Rundle,1982;Ferndndezet al., 1996]. Rundle,J.B.,Viscoelastic-gravitational deformation by a rectangular thrust faultin a layeredEarth,J. Geophys. Res.,87, 7787-7796,1982. Copyright1998by theAmericanGeophysical Union. Papernumber98JB02765. 0148 -0227/98/98JB -02765509.00

(ReceivedAugust13, 1998.)

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