Thermal Stresses in the Oceanic Lithosphere' Evidence From Geoid Anomalies at Fracture Zones

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 91, NO. B7, PAGES , JUNE 10, 1986 Thermal Stresses in the Oceanic Lithosphere' Evidence From Geoid Anomalies at Fracture Zones E. M. PARMENTIER Department of Geolo 7ical Sciences, Brown University, Providence, Rhode Island W. F. HAXBY Lamont-Doherty Geolo Iical Observatory of Columbia University, Palisades, New York Models for the thermal and mechanical evolution of the oceanic lithosphere predicthe progressive development of large thermal stresses in the thickening plate. However, there has so far been little direct evidence for the magnitude and distribution of thermal stresses. We presentheoretical models which examine the effect of thermal stresses at fracture zones and show that an anomaly of the predicted form can be observed in geoid profiles which cross fracture zones. Specifically, our models predicthe development of thermal bending moments which depend on lithosphere thickness or age and therefore change across fracture zones. Including the effect of varying thermal bending moments, thin plate theory predicts vertical, nonisostatic displacements of the lithosphere by plate flexure. The predicted amplitude of the resultin geoid anomaly is large enough to be observed in Seasat altimeter profiles. Furthermore, the general form of this anomaly differ sufficiently from other predicted components of the geoid anomaly at fracture zones to be discernable. The anomaly due to thermal stresses has been clearly identified in geoid profiles across the Clarion and the Udintsev fracture zones. The amplitude of this observed anomaly is well predicted if cooling lithosphere begins to accumulatelastic stresses at a temperature of 700øC, consistent with the maximum depth of seismicity in the oceanic lithosphere. The distribution of thermal stresses with depth is also consistent with focal mechanisms of intraplate earthquakes. INTRODUCTION Cooling and thermal contraction should be an important source of stress in the oceanic lithosphere. Failure of the lithosphere due to thermal stresses has been suggested as a mechanism for the formation of island and seamount chains [Turcotte and Oxbur ih, 1973] and fracture zones along mid-ocean ridges [Turcotte, 1974; Collette, 1974]. Sykes and Sbar [1973] have also suggested that thrust and strike-slip faulting in old oceanic lithosphere may be due to thermal stresses. It is imstresses in the oceanic lithosphere. Turcotte [1974] pointed out that thermal stresses may cause bending of the lithosphere and proposed thermal stresses as an explanation for the formation and spacing of fracture zones along mid-ocean ridges. While this explanation for the origin of fracture zones remains controversial, we show that thermal stresses may cause significant flexure of the lithosphere at fracture zones and that this flexure produces an identifiable geoid anomaly. The form and amplitude of this anomaly may provide direct evidence for the portant to understand intraplate stresses because they may magnitude and depth distribution of thermal stresses. provide evidence on the forces driving and resisting plate mo- There are several reasons that geoid anomalies associated tions [Sykes and Sbar, 1974; Richardson et al., 1979; Fleitout with fracture zones need to be better understood. The geoid and Froidet;aux, 1983; Weins and Stein, 1983]. However, thermal stresses have not been included in the global models of intraplate stresses on which inferences about these forces have been based. Weins and Stein [1984] and Bratt et al. [1985] discuss the possible importance of thermal stresses to interpretations of forces acting on plates. Despite their possible importance, only a few quantitative studies of thermal stresses due to cooling of the oceanic lithosphere have been carried out, perhaps because there has been no direct evidence for their magnitude and distribution. Howheight change across fracture zones has been used to derive a geoid height-age relationship and hence a constraint on the thermal structure of the upper mantle beneath spreading plates [Crou.qh, 1979; Detrick, 1981; Sandwell and Schubert, 1982a; Cazanat)e et al., 1983]. The geoid anomaly created by flexure due to thermal stresses may affect estimates of the change in geoid height across fracture zones. Fracture zone trends are important to understanding relative plate motions and carrying out plate reconstructions. It is thus important to understand the geoid signature of fracture zones so that they ever, in several recent studies of intraplate seismicity in young may be properly identified on global geoid maps. oceanic lithosphere [Ber iman and Solomon, 1984; Weins and Geoid anomalies at fracture zones may arise from several Stein, 1984], focal depths of intraplate earthquakes were determined, and distributions of seismicity that may be related to thermal stresses were identified. These results show deep normal faulting (horizontal extension) and shallow thrust faulting (horizontal compression) events. At least the deep tensources. A change in geoid height across a fracture zone should result from age-dependent differences in mantle thermal structure and isostatic seafloor depth [Crou ih, 1979; Derrick, 1981; Sandwell and Schubert, 1982a; Cazanave et al., 1983]. This change in geoid height occurs over a distance sional events have been attributed to thermal stresses. perpendicular to the fracture zone that depends on both the In this study we examine additional evidence for thermal horizontal and vertical dimensions of the mantle thermal Copyright 1986 by the American Geophysical Union. structure beneath the fracture zone. If the elastic lithosphere is continuous across the fracture zone, differing rates of subsidence on either side of the fracture zone result in flexure and Paper number 5B /86/005B-5751 $ departures from local isostasy that may also be reflected in the

2 7194 PARMENTIER AND HAXBY' THERMAL STRESSES IN THE OCEANIC LITHOSPHERE I I I ' o

3 ß PARMENTIER AND HAXBY: THERMAL STRESSES IN THE OCEANIC LITHOSPHERE Brittle-elastic layer thickness (km) MT/MTelo tic Fig. 2. Thermal stress bending moment as a function of brittleelastic layer thickness for free horizontal contraction (upper solid curve) with stress distributions like those in Figure lb and no horizontal contraction (lower solid curve) with stress distributions like those in Figure lc. Thermal stress bending moments, which include failure of the lithosphere, are normalized by their elastic values given in the text. The flexural rigidity (dashed curve) is shown for the case of free horizontal contraction. geoid anomaly [Sandwell and Schubert, 1982b; Sandwell, 1984]. The form of the geoid anomaly due to these effects is significantly different from that which we predict for bending due to thermal stresses. To demonstrate that thermal stresses may cause significant geoid anomalies, we first outline a theoretical formulation for thermal stresses in thin plates that is more general than previous treatments. We then formulate a simple, idealized model for flexure of the lithosphere at fracture zones due to thermal stresses and estimate the resulting geoid anomaly. Finally, we show examples of satellite-altimetry derived geoid profiles across fracture zones (FZs) in which this predicted anomaly can be easily recognized. This supports the existence of thermal stresses with a magnitude and depth distribution like that predicted by our model. THERMAL STRESSES IN THIN PLATES Thermal stresses in the elastic lithosphere will accumulate gradually as a plate cools and thickens away from a midocean ridge. To examine the effect of stress accumulation, we will first consider a lithosphere which is free to contract horizontally so that the horizontal thermal stress integrated over the lithosphere thickness, that is, the net horizontal force due to these stresses, vanishes. We will assume that rock behaves elastically for temperatures less than some prescribed value T/ but that viscous creep does not allow elastic stress to accumulate at higher temperature [Turcotte, 1974, Finally, we assume, for the sake of algebraic simplicity, that the temperature T varies linearly with depth z in a brittle-elastic layer of thickness h: T(z) = Tlz/h. This will be a good approximation if the elastic layer is relatively thin compared to the thermal boundary layer. The increment of thermal stress 5a,,,,(z) due to an increment of thickening 5h and cooling fit(z) is lus and v is Poisson's ratio. Expressing 5T in terms of 5h and allowing stresses to accumulate as the lithosphere thickens from zero to h gives a,,,, = o E*Tt[1 - z/h + In (z/h)/2] (2) As shown in Figure la, this predicts tensional stresses at depth and large, logarithmically singular compressional stresses near the surface (z = 0). The elastic stresses are large enough that the lithosphere will fail in compression near the surface and, if it is thin enough, in tension at depth. Using a standard criterion for brittle failure [cf. Brace and Kohlstedt, 1980], the accumulated stresses as a function of depth are shown in Figure lb for several layer thicknesses with = 10-5/øC, E = 100 GPa, v = 0.25, and T = 500øC. As in the purely elastic case, integrated over the thickness of the lithosphere must vanish. In regions at failure, 5axx = 0, and in the elastic region, 5a,,x is given by equation (1), where the integral on the right-hand side is taken over the depth interval where the stress increment is elastic. The results of Figure lb were calculated numerically for small, but finite, increments of layer thickening. The increment of layer thickness used was 0.03 km. Smaller increments would change the calculated stresses by less than 1%. With brittle failure, the stress in the elastic region for any particular layer thickness differs significantly from the stress at the same depth in the purely elastic layer: compressional failure near the surface reduces the tensional elastic stress at greater depth. As the layer thickens, the nearsurface region that is in compressional failure also thickens. However, tensional failure at depth occurs only if the layer is thin, less than about 3 km for the conditions shown in Figure lb. An additional applied horizontal tensional stress would be required to cause failure at the depths inferred from intraplate seismicity in some young oceanic lithosphere. The depth distribution of thermal stresses that develops depends significantly on how the brittle-elastic layer is horizontally constrained. If the lithosphere is treated as a plate with fixed edges, so that no horizontal contraction occurs at any depth, the elastic stress is a,,,, - E*T/(1 - z/h) with tensional stresses at all depths z < h. Tensional failure will occur near the surface, resulting in stress distributions shown in Figure lc for several brittle-elastic layer thicknesses. This stress distribution is qualitatively similar to that predicted by Bratt et al. [1985]. In that study, stresses due to cooling of lithosphere moving away from an infinitely long mid-ocean ridge were modeled as thermal stresses in an elastic half-space with no contraction parallel to the ridge axis. To produce horizontal compression and thrust faulting at shallow depths, either a surface layer initially cooled by hydrothermal circulation or horizontal gravity sliding forces were introduced. In the ab- M T h 2 M T where the stress increment averaged over the thickness of the elastic lithosphere vanishes. Here is the linear coefficient of thermal expansion, E* - El(1 - v), where E is Young's modu- Fig. 3. Idealized model of a fracture zone across which the brittleelastic lithosphere thickness h changes discontinuously. Moments M r due to thermal stresses act on each plate at the fracture zone. The net moment is the difference of the thermal moment in each plate.

4 7196 PARMENTIER AND HAXBY: THERMAL STRESSES IN THE OCEANIC LITHOSPHERE OMa 20 Ma 400 km 200km Fig. 4. Accumulation of thermal flexure along the transform portion of the FZ for an age offset of 20 m.y. Complete mechanical decoupling of the lithosphere across the transform is assumed in this model. Profiles of vertical displacements as a function of distance from the transform are shown for equal age intervals along it. sence of ridge-push or gravity sliding forces, thrust faulting was restricted to young lithosphere less than about 15 m.y. old. With free horizontal contraction, horizontal compression at shallow depth persists for all ages, consistent with studies of intraplate seismicity [e.g., Sykes and Sbar, 1974; Weins and Stein, 1983]. In modeling thermal stresses and their effect on geoid anomalies at FZs, we will assume that the lithosphere is free to contract horizontally. Since plate boundaries can be represented as forces acting on the edges of a plate [e.g., Forsyth and Uyeda, 1975; Chapple and Tullis, 1977] which cause intraplate stress [e.g., Richardson et al., 1979], free horizontal contraction implies that intraplate stresses due to plate boundary forces are small compared to thermal stresses resulting from temperature variation with depth. The principal effect of intraplate stresses, such as those arising from plate boundary forces, will be to influence the depth to which brittle failure extends. I km fraction increases with increasing h because the failure strength increases with depth. For no horizontal contraction the moment is reduced significantly from its fully elastic value and changes sign as the lithosphere thickens. Equation (3) has interesting consequences for vertical deflections of the lithosphere due to thermal stresses. If the lithosphere thickens with the square root of seafloor age or distance from a mid-ocean ridge, as inferred from seafloor subsidence, and if M T is proportional to h 2, then PT = 0. With brittle failure, Mr is not exactly proportional to h 2 as for a completely elastic lithosphere. However, for free horizontal contraction, Mr is a relatively constant fraction of its elastic value and therefore approximately proportional to h 2 for a brittle-elastic layer thicker than about km. The thermal structure of the lithosphere near the ridge axis will also be more complicated than that for simple vertical conductive cooling. Nevertheless, this result suggests that thermal stresses in a continuous lithosphere that is free to contract horizontally will not produce significant nonisostatic topography or a correspondin geoid anomaly due to cooling and seafloor subsidence away from a ridge. GEOID ANOMALY AT FRACTURE ZONES DUE TO THERMAL STRESSES Variations in thermal structure and lithosphere thickness across a fracture zone (FZ) can result in significant variations of M T and, therefore, nonisostatically compensated topography. The variation in h across a FZ and with age along it can be estimated using the thermal structure resulting from con- ductive heat transfer [Louden and Forsyth, 1976]. This can be used to calculate the thermal stress loading PT and the flexural TOPOGRAPHY Since the magnitude of thermal stress varies with depth, the lithosphere, unconstrained by gravity, would bend to relieve these stresses [cf. Timoshenko and Goodier, 1970, p. 433 ff.]. To include the effect of gravity and other forces, thin plate flexure theory [cf. Turcotte, 1979] can be modified by including a thermal bending moment M T, the moment of the horizontal thermal stresses about the center plane of the plate z = hi2. The moment balance on a section of plate of length dx then becomes d(m + MT)/dx = F, where F is the shear force in the plate and M = D d2w/dx 2 is the bending moment due to flexural stresses in a plate of flexural rigidity D deflected vertically o.5 by an amount w(x). If the plate contracts freely in the vertical direction, thermal stresses cause no vertical force on a section of the plate so that df/dx = Apgw, where Ap = p, - Pw, the difference between mantle and water densities. Combining these equations gives d2(d d2w/dx2)/dx 2 + Ap iw = PT (3) where PT = -d2mt/dx2 can be regarded as a verticaloading induced by the thermal bending moment. The thermal bending moment for completely elastic stresses can be directly determined from the stress distributions given above. For free horizontal contraction, Mr = ye*t h2/24, and for no horizontal contraction, Mr = -ye*t h2/12. The thermal bending moment including failure, shown in Figure 2 as a function of the brittle-elastic layer thickness, was calculated from stress distributions like those shown in Figure 1. For the case of free horizontal contraction the moment with failure remains a significant fraction of its fully elastic value. This (km) 0.25 I I I I. I I I km -.o Fig. 5. Flexural topography and resulting geoid anomaly across a FZ at a ridge-transform intersection. The young (left) side corresponds to the spreading axis where no thermal stress flexure due to cooling has yet developed. The topography on the old side (right) is that which has accumulated along the transform in Figure 4 for an age offset of At = 20 m.y. The geoid anomaly shown is due solely to the mass distribution represented by the above topography. For the idealized model discussed in the test, this geoid anomaly does not change with age along the inactive portion of the FZ.

5 PARMENTIER AND HAXBY' THERMAL STRESSES IN THE OCEANIC LITHOSPHERE 7197 rigidity, both of which vary with distance x perpendicular to the FZ. The solution of equation (3) would then predict the resulting vertical deflection of the lithosphere. Since D varies with x, a fully numerical solution would be required. Both the loading and the plate thickness will change simultaneously with age along a FZ, and therefore the development of plate flexure must be considered an incremental process. In any small increment of age gt, an increment of loading gpr will be applied to the plate producing and increment gw of deflection. The increment of deflection satisfies equation (3) where the flexural rigidity D is calculated for the age at which the increment of loading is applied. The increment of vertical.deflection produced by a given increment of loading will decrease as the flexural rigidity increases. The total deflection at any age will be the accumulation of increments over a range of ages. To estimate the magnitude of the deflection and geoid anomaly across a FZ, we consider a simple model in which the lithosphere thickness changes abruptly across the FZ, as shown in Figure 3. The lithosphere on each side of the FZ is treated as a half-infinite plate of uniform thickness. This idealization has been previously used to calculate the flexure at a FZ due to differential subsidence [Sandwell and Schubert, 1982b]. Uniform plate thickness on each side of the FZ will be a good approximation because the flexural length of the plates is greater than the width of the FZ thermal structure, except at very old ages along the FZ. Plate flexure cannot accurately represent deformation on a scale much smaller than the flexural length so that flexural models will not adequately describe small-scale features in the immediate vicinity of the FZ. The thermal flexure that accumulates along the transform will depend on the mechanical coupling across this active portion of the FZ. Previous studies of flexure due to differential subsidence [Sandwell and Schubert, 1982b] have assumed free GEOID ANOMALY (m) T I = 500 C I ß I Ti= 600 C GEOID ANOMALY (111) _L._ ' 0.5 i i I I '1 400 km 4 0 km Fig. 7. Geoid profiles across a FZ, as in Figure 5, for three values of T/, the temperature at which elastic stresses begin to accumulate as the lithosphere cools. Note the sensitivity of the anomaly amplitude to this temperature. All three profiles are for a FZ age offset of 20 m.y Fig. 6. Geoid profiles across a FZ, as in Figure 5, for age offsets of 10 and 20 m.y. The temperature at which elastic stresses begin to accumulate on cooling is 700 C. The amplitude of the geoid anomaly is approximately proportional to the age offset due to differential subsidence. vertical slip across the transform. We will examine models in which the plates are also horizontally decoupled so that no bending moment is transmitted across the transform. With no mechanical coupling, each plate must support its own thermal moment. Since the horizontal stresses must vanish at the end of a plate, flexure due to a thermal moment M r can be obtained by applying a moment -Mr to the free end of a plate with no internal thermal moment. The progressive accumulation of flexure along the transform predicted by this model is shown in Figure 4 for a 20- m.y. transform age offset. The thermal moment shown in Figure 2 is applied in small increments as the plate thickens with age along the transform. The flexural rigidity for each increment of loading is determined by the thickness of plate that remains elastic. The ratio of D to its full elastic value is shown in Figure 2. Failure of the lithosphere reduces both M r and D from their elastic values. Since the magnitude of the deflection increment (Sw is approximately proportional to csmr /D 1/2, failure of lithosphere will have approximately compensating effects on the amplitude of the thermal flexure. However, the width of the flexure will be less than for the fully elastic D which will tend to both narrow and reduce the am- plitude of the resulting geoid anomaly. Seafloor near the transform is flexed downward by the thermal moment as required to reduce compressional thermal stresses near the seafloor and tensional thermal stresses at

6 7198 PARMENTIER AND HAXBY' THERMAL STRESSES IN THE OCEANIC LITHOSPHERE GEOID ANOMALY (m) TOPOGRAPHY (km) 0.5 5Mo I I i i i km i i I I I 0.5 IOMo I km I, I I I I km I i I i -0,5 -I Mo I, ' '."., r I I I I i I km i I i -0.5 / 250 ' 400kin Fig. 8. Topographic profiles across a FZ showing flexure at the FZ due to differential subsidence for three ages along the FZ. The initial elevation difference between the young side (left) and the old side (right) is frozen in at the spreading axis. As the two sides approach a common depth, the young side is flexed upward, and the old side is flexed downward near the FZ. The geoid anomalies shown are due solely to the flexural topography. greater depth. Downward flexing of the plate near the transform creates a peripheral high that grows wider as moment increments are applied to a progressively thickening plate. Topographic profiles, shown at equal age intervals, were calculated numerically for small but finite age increments of 0.1 m.y. The brittle-elastic lithosphere thickness was calculated from a simple square root of age cooling model which gives h - 2[ (t + to)] /2 T /Tm if h is small compared to the thermal boundary layer thickness, as discussed previously. As an initial condition, lithosphere at the ridge axis was assumed to be unflexed and free of thermal stress. At the ridge axis (t = 0 m.y.), to was chosen to give a plate thickness of 3 km with Tm = 200øc. The amplitude of this geoid anomaly depends primarily on the age offset along the transform and the temperature Tt at which elastic stresses due to cooling begin to accumulate. The predicted geoid anomaly with transform age offsets of At = 10 and 20 m.y, with Tt - 700øC are shown in Figure 6. The amplitude of the geoid anomaly is approximately proportional to At. Doubling At increases the amplitude by about a factor of 1.8. The amplitude of the geoid anomaly is particularly sensitive to the temperature Tt, as shown by the predicted anomalies in Figure 7. For At = 20 m.y., increasing T from 500 ø to 700øC more than doubles the amplitude of the anomaly. Complete mechanical coupling of plates is assumed along the inactive portion of the FZ. The vertical deflection w, the The vertical deflection of the seafloor due to thermal slope dw/dx, and the shear force F = D d3w/dx 3 must therestresses along a profile perpendicular to the transform at a ridge-transform intersection is shown in Figure 5 for a transform age offset of 20 m.y. The topography on the old (right) side of the FZ is that which has accumulated along the transform as shown in Figure 4. No thermal flexure has yet developed along the ridge axis on the young (left) side. The geoid anomaly due to this stress-supported topography was calculated by approximating the mass distribution due to seafloor topography as a mass sheet at the mean depth of the seafloor. Each Fourier component of the potential Uk is given by Uk = 2rcG(p m -- pw)h,/k, where H is the component of the seafloor topography with wave number k and Pm and Pw are mantle and water densities, respectively. A discrete (fast) Fourier transform with 512 points along the length of the profile was used. The geoid height anomaly is then given by the anomafore be continuous across this part of the FZ. The net moment Mr2 - Mr is applied at the FZ as shown in Figure 3. If Mr were proportional to h 2, as in a perfectly elastic plate, and h were proportional to t /2, the net moment MT2- Mr would be constant. The increment of loading with an increment of age would thus vanish. With no incremental change of the net moment, the thermal stress flexure and resulting geoid anomaly would not change along the inactive portion of the FZ. With failure, the thermal moment is a relatively constant fraction of the elastic thermal moment and therefore approximately proportional to h 2 for a plate thickness greater than about km. Although an age-varying net moment, or moment difference, along the inactive portion of the FZ would modify the deformation, our simple model, in which the plates thicken with the square root of age, predicts that all of the lous potential divided by the gravitational acceleration. flexural deformation due to thermal stresses accumulates

7 PARMENTIER AND HAXBY.' THERMAL STRESSES IN THE OCEANIC LITHOSPHERE 7199 Fig. 9. Shaded relief map of the marine geoid in the Pacific ocean based on Seasat altimeter measurements. Geoid heights computed from the GEM 10B earth model [Lerch et al., 1979] to degree and order 12 have been removed. Illumination is from the north so that the geoid slopes up to the south in bright areas. Note that many Pacific FZs have well-defined geoid anomalies. along the transform and is frozen-in at the ridge-transform intersection. It is important to note that if incrementaloading were not considered, the same net moment would be applied to plates of increasing thickness, incorrectly predicting a large decrease in the flexure with increasing age along the FZ. The independent treatment of thermal stresses and the stresses resulting from flexure is an oversimplification of this idealized model. If the lithosphere behaved as a linearly elastic material, this approach would be exact: the total stress would be simply the superposition of the thermal and induced flexural stresses. In a lithosphere that undergoes brittle failure, the accumulation of both stress contributions should be treated simultaneously. Flexure will reduce the level of thermal stress, thus changing the depth to which failure occurs. This will in turn affect the level of thermal stress and the resulting thermal bending moment. This nonlinear interaction between thermal and bending stresses may influence the predicted anomaly but is not considered in the present study. The geoid anomaly across a FZ will consist of three parts: (1) an isostatic thermal edge effect and contributions arising from flexural topography due to (2) thermal stresses and (3) differential subsidence across the FZ. In distinguishing the effect of thermal stresses, it is important to separate these other contributions to the geoid anomaly. The thermal edge effect anomaly will depend on the age offset across the FZ and may vary with age along it. This will be discussed in more detail later when we examine actual geoid profiles. Flexure due to differential subsidence has been modeled by Sandwell and Schubert [1982b] and more recently by Sandwell [1984]. In these more recent models, thermal subsidence is distributed with distance away from the FZ, as predicted by thermal models that account for horizontal heat conduction [Louden and Forsyth, 1976]. However, to examine this contribution to the geoid anomaly in a simple way, we consider again an idealized model with an abrupt change in lithosphere thickness at the FZ. This provides a basis for comparison with our model for thermal stresses. Following the formulation of Sandwell and Schubert [1982b], the flexure due to differential subsidence is predicted by assuming that the initial elevation difference between seafloor across the FZ at the ridge is frozen in. The flexural topography and geoid anomaly predicted by this model for a FZ age offset of 20 m.y. is shown in Figure 8 at several ages along the FZ. Because old lithosphere subsides more slowly than young lithosphere, the old lithosphere is flexed downward and the young lithosphere is flexed upward at the FZ. The amplitude of this flexure increases with age as both young and old seafloor approach a common depth. The geoid anomaly shown is due solely to flexural topography. Ages are given in terms of the seafloor age on the younger

8 7200 PARMENTIER AND HAXBY' THERMAL STRESSES IN THE OCEANIC LITHOSPHERE i I I I I I I I I I ] km ; Fig. 10. Seasat altimeter profile across the Pacific segment of the Udintsev FZ (upper solid curve). A regional geoid gradient (upper dashed line) and an isostatic edge effect (center dashed curve) were subtracted to give the residual anomaly at the bottom. Crustal ages of 44 Ma and 59 Ma were used to compute the isostatic edge effect. M side, and the profiles are arranged with the young side on the left for comparison with Figure 5. In comparing the predicted geoid anomaly due to thermal stresses (Figure 5) and differential subsidence flexure (Figure 8), several points should be noted. First, the form of the two model anomalies is significantly different. Although both model anomalies have geoid lows immediately adjacent to the FZ on the old side, the anomaly due to differential subsidence has a geoid high on the young side which is not present in the anomaly due to thermal stresses. The geoid high on the old side of the FZ in the two models differs substantially: the high due to thermal stresses is much larger in amplitude and is located nearer the FZ where the anomaly due to differential subsidence has a zero crossing. Below, we present geoid profiles across FZs showing a prominent positive anomaly on the old side of the FZ which cannot be explained by flexure due to differential subsidence but which is well predicted by bending due to thermal stresses. Second, the amplitude of the geoid anomaly due to differential subsidence increases with age while that due to thermal stress, at least in this idealized model, is independent of age. Therefore, at young ages the predicted amplitude of the thermal stress anomaly is greater than that due to flexure associated with differential subsidence. Finally, if vertical slip occurs on the FZ thus reducing the amplitude of the topographic step, the geoid anomaly due to flexure associated with differential subsidence would be substantially reduced. If the plates were horizontally decoupled along the FZ, the amplitude of the geoid anomaly due to Udintsev FZ - Pacific plate 4O 4.5 : :38 õ0 õ0 83 5,1 i i i I I I I I I I klti I I I I I I I I I I (a) Fig. 11. (a) Seasat altimeter profiles across the Pacific segment of the Udintsev FZ. Ages in million years on each side of the FZ are indicated on each profile. The x origin is taken to be the point of maximum geoid slope for each profile. (b) Residual geoid profiles after subtracting an isostatic edge effect and a regional slope. See text and caption of Figure 10 further discussion. (b)

9 PARMENTIER AND HAXBY; THERMAL STRESSES IN THE OCEANIC LITHOSPHERE 7201 Udintsev FZ Antarctic plate t i I I I t t t t i t km I I I I I I I I I I I kill (a) Fig. 12. (a) Seasat altimeter profiles across the Antarctic segment of the Udintsev FZ. Ages in million years on each side of the FZ are indicated on each profile. (b) Residual geoid profiles after subtracting an isostatic edge effect and a regional slope. See text and caption of Figure 10 further discussion. (b) thermal stresses would be increased. In this case, bending on the young side would result in a more symmetrical anomaly. GEOID PROFILES ACROSS FRACTURE ZONES A shaded relief map showing north-south slopes of the Seasat altimetric sea surface is shown in Figure 9. The labeled Udintsev and Clarion FZs, which we will later examine in detail, are clearly visible in Figure 9. A persistent characteristic of nearly all the FZs in Figure 9 is a geoid trough, indicated by adjacent dark and bright traces along the FZs. The darker trace, indicating downward slope to the south, is always immediately to the north of the brighter trace. The topographic ridge often observed on the young side of FZs is conspicuously absent in most Pacific FZ geoid signatures. This indicates that the ridge is either absent or too narrow to generate a discernible geoid anomaly. Unlike gravity anomalies, geoid anomaly amplitudes are highly sensitive to the width of topographic features. Topography or crustal thickness variations within km of the FZ will not contribute significantly to the geoid anomaly. To analyze quantitatively the geoid anomaly at FZs and to test our theoretical predictions, we examine individual Seasat altimeter profiles across the Clarion and Udintsev FZs. Figure 10 illustrates the procedure employed to reduce the observed geoid profile (upper, solid curve) to a residual profile (lower curve) which may be directly compared with model predic- tions (Figures 5 and 8). The profile in Figure 10 crosses the Pacific segment of the Udintsev FZ where 44 Ma oceanic crust is juxtaposed against 59 Ma crust. The part of the profile over younger crust, south of the FZ, is to the left of the origin in Figure 10. The residual profile is obtained by first subtracting a theoretical estimate of the isostatic edge effect (central, dashed line) and then removing a computed least squares geoid slope from this result. The isostatic edge effect, calculated following Sandwell [1984], accounts for the thermal structure, including horizontal heat conduction and the associated isostatic seafloor topography across the FZ. The thermal structure is based on a half-space cooling model at a large distance from the FZ. The shape of the residual geoid profile in the immediate vicinity of the FZ age offset is most sensitive to the position assumed for the origin of the isostatic edge effect. The amplitude of the residual geoid low centered over the FZ and the geoid gradient on the young (left) side of the low may change by as much as 25% with a 20-km shift in edge effect origin. Our model results indicate that the position of maximum geoid slope should accurately coincide with the position of the age offset. Each of the three potentially important components of the FZ geoid anomaly (Figures 5, 8, and 10) shows a geoid slope maximum over the age offset. We therefore chose the origin of the isostatic edge effect to coincide with point of maximum observed geoid slope. This point can be identified

10 7202 PARMENTIER AND HAXBY: THERMAL STRESSES IN THE OCEANIC LITHOSPHERE Clarion FZ I I I I I I I I I I I km I I I I I I I I I I I km (a) Fig. 13. (a) Seasat altimeter profiles across the Clarion FZ. Ages in million years on each side of the FZ are indicated on each profile. (b) Residual geoid profiles after subtracting an isostatic edge effect and a regional slope. See text and caption of Figure 10 further discussion. on individual Seasat profiles to an estimated accuracy of 10 tained following the procedure described above. Unlike recent km. We note that the broad residual geoid high on the old studies by Detrick [1981] and Cazanave et al. [1983], which side of the FZ is not sensitive to shifts in the estimated origin attempted to recover the amplitude of the isostatic edge effect of the edge effect. directly from altimeter profiles, we removed an edge effect Geoid profiles crossing the Pacific and Antarctic segments based solely on the indicated ages of either side of the FZ. of the Udintsev FZ and the Clarion FZ are shown in Figures These previous studies found that a vertical thermal structure Crustal ages shown on each profile were obtained by based solely on conductive cooling overestimates the geoid plotting Seasat tracks on the Larsen et al. [1985] map of offset by an amount that increases with age and concluded crustal age and interpolating linearly between indicated age that heat must be input at the base of the lithosphere. In boundaries. An isostatic edge effect is observed in all profiles Figures l lb, 12b, and 13b our theoretical model overestimates (Figures 1 la, 12a, and 13a) as a change in geoid height across the geoid step across the Antarctic segment of the Udintsev the FZs. Regional geoid gradients, unrelated to the FZ, are FZ, correctly estimates the geoid step across the Pacific segalso clearly visible in the profiles. A positive anomaly which ment of the Udintsev FZ, and underestimates, by as much as we attribute to thermal stresses can be seen on the old side of 50%, the geoid step across the Clarion FZ. The residual geoid the FZ on each of the profiles. A geoid high on the old side of high on the old side of the FZ cannot be the result of misesti- FZs appears to associated with the Mendocino FZ [Detrick, mation of the isostatic geoid height offset. This isostatic edge 1981, Figure 9] and the Heezen FZ [Cazanave et al., 1983, effect is confined to a narrow region centered about the FZ Figure 7]. Furthermore, global maps of geoid height recov- that does not extend to distances comparable to that of the ered from Seasat altimeter data, like that in Figure 9, show a residual geoid high. similar characteristic associated with numerous other FZs. We The residual geoid anomalies are remarkably similar to one have chosen the Clarion and Udintsev FZs for this study another and to the predicted anomaly due to thermal stresses because the age offsets across them are large enough to gener- as shown in Figure 14a for the Udintsev FZ. The prominent ate anomaly amplitudes which should be discernible and be- geoid low centered on the FZ and the somewhat broader high cause they are relatively isolated from other FZs. For closely on the old side of the FZ are nearly identical in form to the spaced FZs, such as those along the Mid-Atlantic Ridge, ther- predicted anomaly. Furthermore, the amplitude of the geoid mal bending may contribute to the symmetrical deepening of anomaly appears to be relatively independent of age as predicthe seafloor parallel to the ridge axis away from the center of a ted by our idealized model. Figure 14b compares the residual ridge segment [e.g., Parrnentier and Forsyth, 1985]. anomalies with the predicted anomaly due to differential sub- The residual profiles in Figures llb, 12b, and 13b were ob- sidence flexure. This model anomaly can explain the residual (b)

11 PARMENTIER AND HAXBY: THERMAL STRESSES IN THE OCEANIC LITHOSPHERE 7203 Udintsev FZ - Pacific plate I I I I i I i I I I kna 4O )0-4O0 Fig. 14a. Comparison between residual geoid profiles across the Pacific segment of the Udintsev FZ and predicted geoid anomalies due to thermal bending moments for At = 15 m.y. and T = 700øC. Udintsev FZ - Pacific plate 4O geoid low at the FZ, at least for the older ages shown, but does not predict the geoid high on the old side of the FZ. The predicted geoid high on the young side of the FZ is not visible in the residual anomalies. This may be explained by vertical slip along the inactive part of the FZ. Neither model predicts the observed broad geoid low on the old side centered about 200 km from the FZ. This feature is observed on all the profiles in Figure 14a and is located too far from the FZ to be explained by flexure due to forces or moments acting on the lithosphere near the FZ. Convection beneath the fracture zone may be a possible mechanism producing this anomaly. Cold descending mantle beneath the older plate may depress the seafloor resulting in the observed geoid low. Convection may also explain the anomalously large geoid step across the Clarion fracture zone. The observed residual anomaly is much better predicted by the model anomaly due to thermal stresses than by that due to flexure due to differential subsidence. The thermal stress anomaly in Figure 14a was calculated for Tt = 700øC. If Tt were reduced by only 100øC, the amplitude of the predicted anomaly would be much smaller than that observed. This value of Tt is remarkably consistent with the maximum temperature at which earthquakes occur in the oceanic lithosphere as inferred on the basis of thermal models and intraplate earthquake focal depths [Bergman and Solomon, 1984; Weins and Stein, 1984]. CONCLUSIONS The principal conclusions of this study are (1) large deviatoric thermal stresses develop in the oceanic lithosphere due to the progressive cooling and thickening of the plate with age, (2) if the lithosphere is free to contract during cooling, the thermal stresses will be compressive near the surface and tensional at depth resulting in a large thermal bending moment, and (3) the differential bending moment at fracture zones due to the juxtaposition of seafloor of different ages causes lithospheric flexure and a distinctive geoid high on the old side of the FZ which is observed in Seasat altimeter profiles across both the Udintsev and Clarion as well as other fracture zones. The observed geoid anomaly at the Udintsev and Clarion fracture zones is well predicted only when the effect of flexure due to thermal stresses is included in the model anomaly. The depth distribution of thermal stresses which predict this geoid anomaly is also consistent with studies of intraplate seismicity which show widespread horizontal compression at shallow depths in the oceanic lithosphere. The amplitude of the anomaly due to thermal stresses depends strongly on the temperature at which elastic stresses due to cooling begin to accumulate. The temperature inferred from the observed geoid anomaly agrees remarkably well with that based on the depth to which seismicity extends in the oceanic lithosphere. Acknowledgments. This research was supported by National Science Foundation grant OCE Helpful reviews were provided by David Sandwell and Seth Stein. REFERENCES I I I i i I I i I I 4OO 2OO 0-1o -40o Fig. 14b. Comparison between the same residual geoid profiles and predicted geoid anomalies due to differential subsidence flexure. The model anomaly due to thermal stresses predicts the observed anomaly much better than the model anomaly due to differential subsidence flexure. Bergman, E. A., and S.C. Solomon, Source mechanisms of earthquakes near mid-ocean ridges for body waveform inversion: Implications for the early evolution of the oceanic lithosphere, J. Geophys. Res., 89, 11,415-11,441, Bergman, E. A., J. L. Nabelek, and S.C. Solomon, An extensive region of off-ridge normal-faulting earthquakes in the southern Indian Ocean, J. Geophys. Res., 89, , Brace, W. F., and D. L. Kohlstedt, Limits on lithospheric stress im-

12 7204 PARMENTIER AND HAXBY: THERMAL STRESSES IN THE OCEANIC LITHOSPHERE posed by laboratory experiments, d. Geophys. Res., 85, , Bratt, S. R., E. A. Bergman, and S.C. Solomon, Thermoelastic stress: How important as a cause of earthquakes in young oceanic lithosphere?, d. Geophys. Res., 90, 10,249-10,260, Cazanave, A., B. Lago, and K. Dominh, Thermal parameters of the oceanic lithosphere estimated from geoid height data, d. Geophys. Res.,88, , Chapple, W. M., and T. E. Tullis, Evaluation of the forces that drive the plates, d. Geophys. Res., 82, , Collette, B. J., Thermal contraction joints in a spreading seafloor as origin of fracture zones, Nature, 251, , Crough, S. T., Geoid anomalies across fracture zones and the thickness of the lithosphere, Earth Planet. Sci. Lett., 44, , Detrick, R. S., An analysis of geoid anomalies across the Mendocino fracture zone: Implications for thermal models of the lithosphere, 0r. Geophys. Res., 86, 11,751-11,762, Fleitout, L., and C. Froidevaux, Tectonic stresses in the lithosphere, Tectonics, 2, , Forsyth, D. W., and S. Uyeda, On the relative importance of the driving forces of plate motion, Geophys. d. R. Astron. Soc., 43, , Larsen, R. L., W. C. Pitman III, X. Golovchenko, S.C. Cande, J. F. Sandwell, D., and G. Schubert, Geoid height-age relation from Seasat altimeter profiles across the Mendocino fracture zone, d. Geophys. Res., 87, , 1982a. Sandwell, D., and G. Schubert, Lithospheric flexure at fracture zones, d. Geophys. Res., 87, , 1982b. Sykes, L. R., and M. L. Sbar, Intraplate earthquakes, lithospheric stresses, and the driving mechanism of plate tectonics, Nature, 245, , Sykes, L. R., and M. L. Sbar, Focal mechanism solutions of intraplate earthquakes and stresses in the lithosphere, in Geodynamics of Iceland and the North Atlantic Area, edited by L. Kristjansson, pp , D. Reidel, Hingham, Mass., Timoshenko, S. P., and J. N. Goodier, Theory of Elasticity, McGraw- Hill, New York, Turcotte, D. L., Are transform faults thermal contraction cracks?, d. Geophys. Res., 79, , Turcotte, D. L., Flexure, Adt;. Gephys., 21, 51-86, Turcotte, D. L., Thermal stresses in planetary elastic lithospheres, Prac. Lunar Planet. Sci. Conf. 13th, Part 2, d. Geophys. Res., 88, suppl., A585-A587, Turcotte, D. L., and E. R. Oxburgh, Mid-plate tectonics, Nature, 244, , Weins, D. A., and S. Stein, Age dependence of oceanic intraplate seismicity and implications for lithospheric evolution, d. Geophys. Res., 88, , Dewey, W. F. Haxby, and J. L. LaBrecque, The Bedrock Geolo 7y of the World, W. H. Freeman, New York, Lerch, F. J., S. M. Klosko, R. E. Laubscher, and C. A. Wagner, Gravity model improvement using GEOS 3 (GEM 9 and 10), 0r. Weins, D. A., and S. Stein, Intraplate seismicity and stresses in young oceanic lithosphere, d. Geophys. Res., 89, 11,442-11,464, Geophys. Res., 84, , Louden, K. E., and D. W. Forsyth, Thermal conduction across frac- W. F. Haxby, Lamont-Doherty Geological Observatory, Palisades, ture zones and the gravitational edge effect, d. Geophys. Res., 81, NY , Parmentier, E. M., and D. W. Forsyth, Three-dimensional flow be- E. M. Parmentier, Department of Geological Sciences, Brown University, Providence, RI neath a slow spreading ridge axis: A dynamic contribution to the deepening of the median valley toward fracture zones, d. Geophys. Res., 90, , Richardson, R. M., S.C. Solomon, and N.H. Sleep, Tectonic stresses in the plates, Rev. Geophys., 17, , Sandwell, D., Thermomechanical evolution of oceanic fracture zones, d. Geophys. Res.,89, 11,401-11,413, (Received July 31, 1985; revised January 13, 1986; accepted January 30, 1986.)