JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. B6,PAGES 13,581-13,594, JUNE 10,1996 Horizontal viscoelastic-gravitational displacement due to a rectangular dippingthrust fault in a layered Earth model Jos6 Femfindez Insfituto de Astronomia y Geodesia, Faeultad de Cieneias Matem,•tieas, Ciudad Universitaria, Madrid, Spain Ting-To Yu • and John B.Rundle Cooperative Institute forResearch in Environmental Sciences, University of Colorado, Boulder Abstract.Calculations ofhorizontal displ•ents due to a rec•ar finite thrust fault in a viseoelasfic-gravitational layered Earth model are presented. The Earth model consists of a single elastic-gravitational layer overlying a viseoelasfi½-gravitafional hoW-space. A review ofthe fullthree- dimensional theoretical solutions ispresented along with the explicit solutions forhorizontal displacgments. Several examples ofcomputations for dipping faults with various angles, and 1oea• atdifferent depths, are shown. The results indicate that viseoelastieity introduces a long-wavelength eom•n•t into the interseismic deformation field which is not present inpublished elastic techniques and also that a proper consideration ofgravity isnec•sary only for near-field computations atlonger periods oftime. A pattern isfound inthe cumulative displacgment ofcycled earthquakes, which indicates that the viscoelasfic displacgments are visible forlonger recurrence time events and that these may serve as a time index for the various stages between cycles. Introduction One im•t goal in crustal deformation research is to under- stand thepostseismic deformation following large earth•es. High-precision data obtained by modem land- andspace-based insmanentation provide a feasible monitoring technique for such deformation processes, especially for horizontal movements. Nur andMavko [1974], Smith [1974], Bischke [1974], Rundle [1978], Thatcher and Rtmdle [1979], Thatcher et al., [1980] and Matsu'ura and Tanimoto [1980]focused on explaining crustal motions in areas of thrust faulting. In most of the previous work theomission of gravitational effects is justified [Rundle, 1982a] beea• onlydeformation for the short timeperiods following earthquakes was modeled. The gravitational effect must be included for deformations that involve longer periods of time, for the reason that gravity will affect both the magnitude and pattern atlonger periods of time, as shown inthe following plots. Thatcher and Rund/e [1979] and Rund/e and Thatcher [1980] have made use of inelastic displacement models to explain patterns of • deformation based on a numerical technique developed by Rundle [1978]. This method enables one tocalculate surface displacements oce• after the insertion of a displa- cement into a medium consisting of anelastic layer over a linear, visc, oelasfic half-space. The two principal defects in the work cited above were the lack deformation in thenear-source region However, this is notthe case for viscoelastic calculations [Rundle, 1981a, b], and for viscoelasfic-gravitafional deformation the inclusion ofgravity will affect the postseismic displacement field even inthe vicinity of the fault [Yu, 1995]. A series ofrec• calculations have examined various aspects of this problem. Ma and Kusznir [1992, 1993, 1994] simulate multilayered relaxed viscoelastic gravitational models by setting the elastic l_ame parameters inone or more layers to zero. Notime dependence is examiner[ Cohen [1994] models theearthquake cycle in thrust domains using a plane-strain finiteelement calculation_ Our present calculations extend these results to a systematic examination of three4•ensional thnmfaulting in viseoelastic-gravitafional models using the techniques developed byaund•e [• 98•a]. Rtmdle [1980] explicitlysolved the coupled elastic- gravitational field equations and derived the displacements resulting from theinsertion of point sources in a layered half- space. Rundle [1981a] obtained the solution of the coupled viscxxflastie-gravitational problem. These solutions generally proceed in three steps. First, theGreen's functions fortheelastic- gravitational field equations are compute& Next, the corres- pondence principle that relates the elastic-gravitational solutions to the Laplace-tmmfonned viseoelasfic-gravitational solutions is ofinclusion ofgravitational effects inthe calculations and the applied. Upon completion of the inverse transform into the time inability to calculate viscx•lastic displacements for long periods of domain, the Green's function is integrated over the finite source time •ard (tens to hundreds of Maxwell times). For purely region toobtain the time-dependent near-field displacements. elastic calculations, gravitational effects manifest themselves over distaac•greater than1000 km and thus have little relevance to •Now at Institute of Earth Sciences, Academia Sinica, Taipei, Taiwan. Copyright 1996 by the American Geophysical Union. Paper number 96JB00525. 0148-0227/96/96JB4)0525509.00 Rund/e [198 l a] collected the neces• numefi• techniques and produexxt calculations ofthe elastic dip-slip Green's functions for vertical deformation He found that asIx, the half-space rigidity, decreases in magnitude, theabsolute effects of gravity bernroe more important This property implies that for the time-dependent displacements which are theresult of faulting in a viscoelasfic medium, the effects of gravity will only become important over sufficiently long time intervals, e.g., when g has relaxed to some small value. 13,581