JOURNAL OF GFOPHYSTCAL RESEARCH. VOL. 103, NO. E7, PAGES 16,841-16,853, JULY 25, 1998 Tectonic evolution of Bell Regio, Venus: Regional stress, lithospheric flexure, and edifice stresses Patricia G. Rogers' RAND, Washington, D, C. Maria T. Zuber Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge Abstract. In order to understand the relationship between volcanic and tectonic processes and the stress state in the lithosph?re of Venus, we analyzed the stress environments and resulting tectonic features as'sociated with the major volcanic edifices in Bell Regio, using Magellan synthetic aper- ture radar (SAR) images and altimeter measurements of topography. The major volcanoes of Bell Regio, Tepev Mons and Nyx Mons, exhibit tectonic characteristics that are unique relative to other volcanic edifices on Venus. The most prominent distinction is the lack of large rift zones within the overall highland uplift, which characterize many other highland rises on Venus. Also, previous studies have determined that many large Venus volcanoes exhibit radial tectonic struc- tures on their flanks but generally lack the circumferential graben which surround volcanoes on Earlh and Mars. Tepev and Nyx Montes exhibit both the radial tectonic features associated with other Venusian edifices and numerous concentric graben. Nyx Mons implies a more distributed magmatic system by its broad shape, radial chains of pit craters, and expansive flow fields, whereas Tepev Mons is a more centralized volcanic system, with limited associated long flows. We investigate the regional stresses associated with Bell Regio and structural features believed to be a consequence of lithospheric flexure due to volcanic loading, modeling both Nyx Mons and I'epev Mons as axisymmetric loads with Gaussian mass distributions on an elastic plate. The re- lationship between the tectonic features surrounding Tcpcv Mons and stresses associated with magma chamber inflation are also examined through finite element analysis. Using topography data to model the shape of the volcano, we determine that a horizontally ellipsoidal or tabular res- ervoir at a range of depths from approximately 20 to 40 km can satisly the locations of graben formation observed in Magellan images. These results imply a shift ?n volcanic style within Bei! Regio from an early phase of broad, low shield formation to later steep-sided, more centralized edifice development. Such changes are consistent with an increase in the thickness of the litho- sph?re over time. 1, Introductiun lithospheric flexure [Comer et al, 19S5; McGovern and Solomon, 1992]. Tepev Mons and Nyx Mon.^i (provisional Geophysical analyses of the tectonic features associated name) exhibit both the radial tectonic features associated with with the Venus highlands and major volcanoes provide impor- other venusian edifices and numerous distinct concentric gra- tant insight into the relationship between volcanic and ben ?Campbell and Rogers, 1994|. tectonic processes and the stress state of die venusian crust To understand the geophysical evolution of Bell Regio, overtime. Bell Regio is unique relative to many of the other this study examines the structural features associated with the volcanic highland regions on Venus, such as Western Eistla major volcanoes using Magellan synthetic aperture radar or Dione Regiones [Senske et al.. 1992], in its apparent lack of (SAR) images and ahimeter measurements of topography. First, rift zones dissecting the topographic swell. Most large Venus wc analyze the regional stress field in Bell Regio based on the volcanoes also exhibit radial tectonic structures on their style and distribution of tectonic features in the region. Next flanks, and typically lack the circumferential graben which we examine structural features we believe to be a consequence surround volcanoes on Earth and Mars, indicating of lithospheric flexure due to volcanic loading. Analytical models for the formation of similar features on Earth and other planetary surfaces are examined, and a model for the stress re- ' Currently at Center for Earth and Planetary Studies, Smithsonian gime and formation of tectonic struciures within Bell Reglo is Institution, Washington, D.C. developed. This analysis of lithospheric flexure and associ- ated deformation models the volcano as an axisymmetric load Copyright 1998 by the American Geophysical Union, ^?^j^ ^ Q^^^^?^? ^^^^ distribution on an elastic plate of vari- Paper Number 98JE?0585 ^'^'^ thickness, and incorporates criteria for tensile and shear ?148-?227/98/98JE-??58; S09.0? failure. Finally, the relationship between the tectonic features 16,841 16,842 ROGERS AND ZUBER: TECTOXiC EVOLUTION OF BELL REG?O, VEX?S vr.: ^--^?5%4 L':;;;!:_.^!?:-aafl%?t^l^ Figure 1. Magellan SAR image of Bell Regio. Resolution is approximately 1.2 km. For scale, the large caldera on Tepev Mons, the prominent central edifice in the image, is approximately 30 km. associated with the Tepev Mons edifice and stresses associ- ated with magma chamber inflation is examined throiigh finite element analysis. 2. Regional Stress Regime Analysis of regional stresses provides a framework, for un- derstanding smaller-scale tectonic features within the highland. As indicated above, this region iacks rift zones; however, large-scale tectonic deformation is exhibited by tessera blocks which surround the major volcanic edifices (Figure I) {Campbell and Rogers, 1994]. Tessera arc gener- ally the stratigraphicaily oldest units in this region and preserve a record of periods of intense tectonic deformation. The fractures within some blocks are irregularly oriented, but the prevailing -fracture patterns within the tessera regions trend SW-NE. The preexisting tes.sera plateaus are thought_ to be regions of thickened crust [Bindschadler and Head, 1991] and may have inhibited lateral spreading and the formation of major rift zones during the early period of highland formation. If the stresses that governed the formation of the SW-NE tessera blocks still existed at the time the volcanic edifices formed, similar trends in the subsequent volcanic and tectonic features might be observed. However, although some of the Nyx Mons iava flows trend SW-NE, little direct evidence of significant SW-NR fracture patterns exists. This implies that the formation of Tepev Mons and Nyx Mons postdate the re- gional stress regime which produced the tessera or that stresses in the regions that lack fractures did not exceed the lithospheric failure criteria. Plains regions surrounding Bell Regio are next in the stratigraphie sequence after the tessera and may be divided ROGERS AND ZUBER: TECTON?C EVOLUTION OF BELL REGIO, VENUS 16,843 ??^^S;?fe,;.^:;?^?,..;^,,^.A^^-??vJ Figure 2. Magel?an SAR image of Myx Mons with concentric fracture map overlay, centered at approximately 29.9"^, 48.5?E. Note the radial chains of pit craters and concentric fractures surrounding the edifice outlined in the image. into at least three distinct units; bright plains, dark plains, and ridged plains [Campbell and Rogers, 1994J. The ridged plains arc the oldest of these units and record an intense pe- riod of deformation with ridges and graben oriented SE-NW and SW-NE. The bright and dark plains are less deformed than the ridged plains or the tessera, with deformation primarily represented by SE-NW trending fractures. Since Ihe lava flows from the major volcanic edifices in this region embay the tessera, superpose most of the plains units, and do not contain major deformation patterns, it is reasonable to conclude that the last large volcanic events in this region postdate the re- gional stress regime which produced the tessera and ridged plains. These volcanic units thus record more recent localized stresses in the region and are the subject of the next sections. 3. Lithospheric Flexure and Nyx Mons The oldest volcanic edifice within Bell Regio is Nyx Mons, a feature characterized by a wishbone pattern of ridges and gentie flank slopes. The inner region contains a central bulge and radial chains of pit craters [Campbell and Rogers, 1994]. Surrounding the edifice to the east, south, and north- west arc large sets of circumferential fractures, which are the main focus of this section (Figure 2). Figure 3 illustrates the topography of Nyx Mons and surrounding regions. This edi- fice rises approximately 1 km above the surrounding apron of flows; the central bulge and wishbone ridges contain the highest elevations of the feature at approximately 6053.5 km. Slopes on the southern flanks of the edifice are generally 1 - 2", grading into slopes less than 0.5" continuing southward, corresponding to the flow apron that typically surrounds vol- canoes on Venus [McGovern and Solomon, 1995], It is in this gently sloping region that the most prominent concentric graben occur. Detailed structural mapping of these features indicates that the innermost concentric graben occur at a radial distance of approximately 280 km from the center of the edifice, while the outer radius of these features lies at approximately 470 km. A 500-m change in elevation occurs between these two radii. The most prominent volcanic flow fields in the re- gion (the youngest flows of Nyx Mons) emanate from these concentric fractures [Campbell and Rogers, 1994]. 3.1. Models of Lithospheric Flexure The distribution of fractures around large volcanic loads is an ?inportant indicatoi' of the stress state and effective thick- ness of the elastic lithosph?re. Comparing the tectonic features formed in response to large volcanic loads on various 16,844 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 6055 6054 6053 6052 T?I?I?I?I?I?I?I?I?I?I?I?I?[?I?I?I?I?I?r~i?I?r I I I I I I I J I I L J i I L _L_J L 100 200 300 DISTANCE (KM) 400 Figure 3. Topographic profile through Nyx Mon.s trending approximately west to east. Note the higher ele- vated ridges and central regions. planetary surfaces has provided important constraints on the relative ?thospheric thicknesses on Venus, Earth, Mars, and the Moon [e.g., Melosh, 1976, 1978; Comer et al.. 1985; Hall et ai, 1986; McGovern and Solomon, 1993J. In these analy- ses, grahen form concentric to a load as a resuh of surficial extensional bending stresses associated with lithospheric flexure. If the lithosph?re is extremely thick or rigid, then the stress field is dominated by compressional forces, due to the volcano [Artyushkov, 1973; Fleitout and Froidevaux, 1983]. This analysis of lithospheric flexure and associated defor- mation models the two major volcanoes within Bell Regio as axisyrametric loads with Gaussian mass distributions on an elastic plate, following the analysis o?Metosh [1978] of the mechanics of lunar masc?n loading. Deviations of the actual load from axisymmetry are a second-order effect [Comer et al., 1985]. Melosh [1978] analyzed load-related stresses and de- formation and determined that the tectonic pattern predicted by this model, with increasing radial distance from the center of the load, included a proximal zone of radial thrust faults fol- lowed by strike-siip faults, all surrounded by concentric normal faults. Although the zone of strike-slip faulting is not readily observed surrounding the lunar mascons, they sug- gested that some of the ridges surrounding lunar maria might be evidence of strike-slip motion. Golombek [\9^5] proposed that the lack of observed strike-slip faults can be explained by the fact that fault nucleation occurs at subsurface interfaces, though this does not account for the absence of such features in regions that most likely lack discrete subsurface layering. In an analysis of the formation of large volcanic loads on Mars by McGovern and Solomon [1993], time-dependent ef- fects on the predicted failure mechanisms of the growing load were considered. They determined that the 7one of strike-slip faulting is not observed because it either occurs in a region that had previously formed normal faults (the normal faults are reactivated), or that they form and are buried by subsequent deposits. The fractm-es considered in our analysis occur on the youngest volcanic flows; therefore this analysis considers their formation as a late stage event and is not concerned with the growing load. However, our treatment of the lithosph?re as an elastic plate inherently supposes that stresses due to the growing edifice did not pervasively fracture the lithosph?re. In a more recent analysis, McGovern and Solomon [1997] at- tribute the absence of topographic moats and concentric normal faulting surrounding large Venus volcanoes to mask- ing by lava flows from the central edifice. In their model, the stresses in this moat fill arc too low to induce failure. Schultz and J.uhe.r [1994] addressed the paradox of the ex- istence of an annular zone of strike-slip faults around prominent loads predicted in previous models, evidence for which is rarely found on planetary surfaces. In their model, the discrepancies between the observations and the model predic- tions result from other considerations significant in fault analysis: the neglect of stress magnitudes and reliance only on stress trajectories, and the identification of first failure. When rock strength, stress differences, stress geometries or stress state at the onset of failure and load evolution are taken into account, their model predicts that concentric normal faults and joints (as opposed to strike-slip faults) occur at or near the surface surrounding loads. Rock strength is significant in determining the stress level when the first fractures occur. Their model, which examines the importance of failure mecha- nisms such as tensile cracking near surface regions and varying values of Young's modulus, was experimentally veri- fied by Williams and Zuber [1995]. The analysis below uses the general solutions described in the Melosh [I978J model but also incorporates these failure criteria. 3.2 Modeling Volcanic Loads This study analyzes the volcanic edifices and associated stresses in Bell Regio by modeling the two major loads as Gaussian distributions on an elastic plate following Melosh [1978]. The general solution to the stress field is given by Melo'ih [1978] as arc Bessel functions, Ozz is the vertical stress, On- is the radial stress, OM is the hoop (tangential) stress, Orz is the shear stress, On is the normal stress, r is the radius from the center of the load, z is the depth in the plate, k is the wave number, and v is Poisson's ratio. Because the total stress is sought in this analysis, a term for the confining pres- sure (Kpcgz) is added to the above stresses where K is the ratio of horizontal to vertical overburden [Banerdt, 1988]. The vertical stress at the surface, and the lack of shear stress at the surface or base are indicated by the following boundary conditions: a^(z = 0,r) = bJo(kr) (6) O^(z = 0,r) = o^(z=H,r) = c?(z = H,r) = 0 (7) In this analysis, the vertical load is represented by w^p^gT (8) e/i ? -50 -100 Figure 4. Plot of elastic surface stresses resulting from the Nyx Mons load with a lithospheric thickness of 50 km. Nega- tive stresses are compressional and positive stresses are extensional. The bar represents the zone of fracturing observed in the images and corresponds well to the R/A range of 1.5-2.7 resulting from the model. where Pm is equal to its density, T is its height at r = 0, and g is gravitational acceleration. According to Anderson [1951], concentric normal faulting will occur in the region defined by positive Cfrr and CJij^ and maximum ?rr. In order to distinguish the likely mechanism for initial lithospheric failure, we have incorporated into this formalism the following rock failure criteria: a Griffith criterion for ten- sile failure and the Byerlee criterion for shear failure [Schultz and Zuber, 1994]. Specifically, applying stress to a fractured rock will cause frictional sliding along the fractures prior to reaching the level required to cause brittle failure of the rock mass. This relationship, referred to as Byerlee's law, is given by {Brace and Kohlstedt, 1980] t = 0.85 o? 3 < o? < 200 MPa T = 60 i 10 + 0.6 a? 0? > 200 Mpa (9) The Griffith criteria for brittle failure states that fracture occurs at a given stress according to a, = (2AE / TIC)" (10) where 2c is the length of the pre-existing crack, A is the sur- face energy, E is the Young's modulus, and a, is the applied tensile stress [Price and Cosgrove, 1990]. Table 1. Fixed Parameters Used in Modeling Nyx Mons Parameter Description Value g gravitational acceleration 8.6 m s'^ Pra load density 3000 kg m"^ r load height Ikm K horijjontal/verticai overburden 0.5 V Poisson's ratio 0.33 Pc lithosph?re density 3300 kg ni"^ 3.3. Nyx Mons ?Vlodeling Results In this analysis, an analytic model was used to determine the stress field and predict the spatial distribution of faulting on the lithosph?re surrounding Nyx Mons. The predictions were then compared to the observed fault distributions, thereby constraining the properties of the lithosph?re that supports the volcano. Fifteen cases, with varying lithospheric thickness and Young's modulus, were considered in this analysis of Nyx Mons to determine which most closely corre- sponds to the observed fracture patterns. The fixed parameters are given in Table I. In the first seven cases, the effects of varying the lithospheric thickness between 30 and 70 km were examined. The diameter of the feature was defined to be the distance at which the topography of the edifice merged with the surround- ing plateau. Since Nyx Mons is an irregularly shaped "wishbone" feature, minimum and maximumvalues for the load extent were also examined. The maximum diameter, correspond- ing to the feature's N-S extent, is 350 km, and the minimum diameter, corresponding to the edifice's E-W extent and an idealized circular shape for the feature, is 270 km. These di- ameters correspond to halfwidths of 175 and 135 km, respectively. The deviation of the load from a Gaussian shape is not significant. The next cases examined the effects of varying Young's modulus. In-situ measurements of elastic moduli can be up to an order of magnitude lower than laboratory measurements [Cullen et al., 1987], so we examined the effect of reducing Young's modulus by an order of magnitude (from 10^' to 10 " Pa) while varying the load halfwidth and the lithospheric thickness. Next we examined the e??ect of an increase in Young's modulus (to 10 Pa). This situation may represent the effective Young's modulus of a rock containing closed cracks [Jaeger and Cook, 1979] although it's uncertain that this effect would increase E by an order of magnitude. We consider this value to be an upper limit on E. The effect of increasing the lithospheric thickness shifts the range of concentric normal faulting to slightly higher val- 16,846 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REG?O, VENUS y^^'r.:^ ;^;....=->:.-? ?..?. ri? if. ?';&'?? :,'-X-" ? K-1 J I ???.i?'-^v...:>"': ?IM, .?.'.-? -? " '??'- v, ."= ;f, - :. :,-^ . ;. ?' ;.i.--N,--ri-:.,;.,.. -? '. :*'*='-? ?.. ?=-''l?"-i:-i' ?? .-??,:?? ' ' " .',&;???. ; ,",iv-. ;.!?.,' >?; ? ~Ji 4^ :i:.-;, >^?^,-^.?>5: ?;?-?'-?--=?'^; ,?--?? -'!*t. , .1. 1 ' i r-Jiffl" i^?![. ~^'' Figures. Magellan SAR image of Tepev Mons with fracture map overlay. Note the prominent fractures con- centric to the volcano. For scale, the largest caldera on Tepev Mons is approximately 30 km in diameter. ues of R/A (normalized radial position, where A is the halfwidth of the load), while decreasing the size of the load causes a small increase in the maximum Cfrr and the range of R/A for graben formation. Decreasing Young's modulus de- creases CT? and the R/A range for graben formation, while increasing E has the opposite effect. The inner and outer radii for the concentric faults (2Sfl and 470 km) correspond to an R/A range of approximately 2.0 - 3.5 if A = 135 km and an R/A range of 1.6 - 2.7 if A = 175 km. Fig- ure 4 illustrates the results of the best solution that produces concentric normal faulting in the range of 1.5 - 2.7. Total stress (MPa) is plotted against R/A. Individual points are plotted on the On curve. These results indicate that for the pa- rameters used in this analysis, a lithospheric thickness of 50 km, E=10 , and load halfwidth of 175 km best describes the conditions at Nyx Mons at the time of the formation of the con- centric graben. 4. Edifice Stresses and Tepev Mons Tepev Mons is a prominent volcanic shield within Bell Regio thought to be younger than the large volcano Nyx Mons discussed above [Campbell and Rogers, 1994J. It rises approximately 5 km above the surrounding plains and is char- acterized by relatively steep slopes (20? - 40?) near the summit region. The steepest slopes occur along the eastern flank of the volcano (Figure 5). Two large (11 and 31 km diameter) calderas superpose the summit region. The northern flank is characterized by prominent fractures and coalesced chains of pit craters concentrically distributed around the main peak and calderas. In this section we consider the origin of tectonic features on Tepev Mons, beginning with a test of the lithospheric flexure model used above and concluding with a comparison between terrestrial volcanic deformation patterns and the Venus observations. 4.1. Modeling of Tepev Mons Concentric Fractures In preliminary analyses by Solomon et a!. [1992] it was postulated that the concentric graben north of Tepev Mons may have resulted from lithospheric flexure due to the volcanic load. To test this liypothesis, an analysis similar to the one described above for the formation of the concentric graben sur- rounding Nyx Mons was performed for the Tepev Mons load. ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,847 d O? ;^ ""-200 Vi ^"-400 -600 _, 1 1 1 1 1 ly-i^ -4?JI 1 1 1 r / --C - / /" - -0-? / / - ? 1 / ? . // '_// 1?i --T 1 1 1 1 1 1 1 1 1 i lilil? 1 0 2 R/A Figure 6. Plot of elastic surface stresses resulting from model- ing the Tepev Mons load with a lithospheric thickness of 30 km. The bar represents the zone of fracturing observed in the images. Unlike the Nyx Mons case, this region does not cor- respond to the R/A range of 1.5-2.5 resulting from the mode!. Five cases were examined in which the lithospheric thickness varied from 20 to 60 km. The results of the model for the case of a 30-km-thick lithosph?re are illustrated in Figure 6. Structural mapping of concentric graben around Tepev Mons indicates that these features occur at inner and outer ra- dial distances of 65 and 90 km, respectively. With a halfwidth for the load of 80 km based on topographic profiles across the edifice (Figui'e 7), this corresponds to R/A values ranging from 0.8 to 1.1. Flowever, results of the model indicate that maxi- mum extensionat stress occurs at R/A of 1.5 to 2.5. This region corresponds to the approximate location of a possible topo- graphic moat north of Tepev Mons (R/A = 1.8) which has been discussed by several authors \Janle et al., \988; Solomon and Head, 1990; McGovern and Solomon, 1992; Campbell and Rogers, 1994] (Figure 8). The effective elastic thickness based on the location of this volcanically flooded moat yielded a preliminary value of approximately 10 km [McGovern and Solomon, 1992J. However, the lava tlow which fills this moat has a high surface roughness [Campbell and Rogers, 1994] which may have prevented the Magellan altimeter from acquir- ing an accurate surface response, which could result in spurious range measurements. Hence the minimum elevation of this potential moat is difficult to constrain. Assuming the flow is contained within the lowest region, the approximate center of the moat would correspond to an R/A value of 1,8, almost at the center of the range of maximumextension predicted in our models using a lithospheric thickness of 30 - 50 km. This re- sult is supported by recent studies of gravity-topography relationships which yield elastic thickness estimates for this region in the range of 30-50 km [Smrekar, 1994]. There is thus evidence for lithospheric bending associated with Tepev Mons, but the results of our model indicate that this flexure is not the likely cause of the prominent concentric graben which occur on the steep northern flanks, close to the center of the load. Similar features are observed on the flanks of Pa von is and Arsia Mons, two large shield volcanoes on Mars [Comer et ai, 1985]. Comer et al. studied the tectonic features associated with large volcanic loads on Mars and de- termined that the concentric graben on Pavonis and Arsia Which lie close to the center of the load may be concentric ex- tensional fractures formed during the evolution of the caldera rim as magma was withdrawn or solidified, producing an annu- lar ring of faults. Another cause may have been topographic stresses and gravitational spreading, which resulted in exten- sional faults on the flanks of the shield [McGovern and Solomon, 1993]. The concentric graben tiiay also reflect zones of weakness inherited from flexural stresses during an early stage of volcano growth. In the next section we examine some of these mechanisms in more detail and discuss possible terres- trial analogs to understand if stresses within the Tepev Mons edifice may have produced the observed circumferential frac- tures. 4.2. Models of Edifice Deformation As discussed above, the free surface of a volcanic edifice may undergo tectonic deformation as a result of several mecha- nisms: inflation and doming due to subsurface injection of magma, deflation associated with caldera collapse, and gravita- tional relaxation which may lead to slumping of material along the flanks. The mechanical behavior and overall morphology of a volcanic shield generally results from the interaction of all these processes. However, gravitational collapse and slump- 6056 ,6056 ? w R 6054 ? 6052 I I I I I I I I i I ! T~r T I -I T T 7?1 T ?.L,?I,.,J,-L JUJ_ 0 50 100 150 DISTANCE (KM) 200 250 300 Figure 7. Topographic profile through Tepev Mons trending approximately NW to SB. The two peaks cen- tered at approximately 200 and 250 km represent small, steep volcanoes on the SE flanks of Tepev Mons. 16,848 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS *??-'? J?- ? ???.r - 9f" .""."'ai-pi.i *?, Figure 8. Magellan SAR ?mage of lava flow north ofTepev Mons, thought to be confined within a topo- graphic moat, Tepev Mons is on" the image to the southeast. ing of the flanks may be less significant for venusian edifices due to their relatively gentle profiles and limited vertical ex- tent [Head and Wilson, 1992], Therefore the major forces affecting the overall morphology of Venus volcanoes may be related to stresses associated with the evolution of a magma reservoir and internal dike propagation. Several authors have examined the surface deformation associated with stresses that arise from the inflation and deflation of a subsurface magma chamber. A period of uplift and swelling of the edifice may oc- cur due to the inflation of such a magma chamber and the associated injection of dikes and sills. Deflation, which may lead to caldera collapse, results as rift eruptions occur along the flanks or as intrusions occur into new regions within the volcano [Dieterich and Decker, 1975; Marsh, 1984]. In early models of magma chamber deformation the chamber was represented by a point source in an elastic half space, or by magma reservoirs that were spherical and small in compari- son to their depth [Anderson, 1935, Mogi, 1958]. However, these point source models applied accurately only to stresses at large distances from the chamber. Later models represented the magma reservoir as a finite source and were able to more ac- curately determine near field (shallow source) stresses [Ryan, 1988], Dieterich and Decker [1975] determined that the early analytical approaches predicted generally similar surface de- formation, regardless of the actual model used and that these models did not predict the ratio of horizontal to vertical sur- face movements observed near summit regions. They were among the first to use a finite element method, enabling them to model summit deformations and rift zone intrusions using a va- riety of shapes and depths for the magma reservoir. Dieterich and Decker [1975] also observed a relationship between flank eruptions and the systematic inflation and deflation of the summit reservoir; flank eruptions occur as magma is trans- ported vertically to a shallow storage zone beneath the summit followed by lateral transport of magma from the summit reser- voir to the flanks by dikes. Znber and Mouginis-Mark [1992] examined the tectonic responses associated with the evolution of the caldera on Olympus Mons, Mars. They used a linear elastic finite element model to determine the range of magma chamber geometries and pressures that could produce the ob- served tectonic pattern. Specifically, the ridges and graben which formed from subsidence of the caldera floor during defla- tion of the magma chamber were used to provide constraints on the dimensions, depth and pressures associated with the sub- surface reservoir. They determined that the surface stress distribution is relatively insensitive to the details of the shape of the magma chamber and is very sensitive to its depth. 4.3. Numerical Modeling of Edifice Deformation In this section we examine whether the coneentric graben observed on the flanks of Tepev Mons could be due to stresses within the edifice. To understand the nature of the stress state of the edifice, we constructed an axisymmetric finite element model to calculate the elastic stresses within the volcano and to examine the relationship between these stresses and the ob- served tectonic features. Following a model previously employed in the study of caldera subsidence [Zuber and Mouginis-Mark, 1992] we analyzed the stresses associated with variations in a magma reservoir. However, while the Zuber and Mouginis-Mark [1992] analysis modeled the defla- tion of the magma chamber and the resulting caldera structures, this model Is concerned with the inflation of the magma cham- ber and the associated stresses on the flanks of the volcano. Deflation and resulting deformation within the Tepev Mons calderas may have also occurred during its history, however structures within the calderas ofTepev Mons can not be re- solved, most likely due to the presence of a fine grained surflcial deposit [Campbell and Rogers, 1994], We used the finite element program TECTON [Melosh and Raefsky, 1981] to develop a linear elastic model of ihe stresses and displace- ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,849 Table 2. Pai-amctcrs Used in Finite Element Modeling of Parameter Value Density 3000 kg m"' Young's Modulus (within chamber) lu" Pa Young's Modulus (outside chamber) 10"Pa Poisson's ratio 0.33 ments associated with the edifice and underlying crust and mantle. In order lo improve the aecuracy of the finite element repre- sentation of the volcano, we extracted a representative topographic profile for Tepcv fvlons from the Magellan global- average (5,4-km resolution) data set. The model grid was then constructed to conform to this profile shape along the upper surface. Given that Tepev Mons has significant changes in slope along its flanks, tiiis tueihod permitted a more realistic assessment of the role of local topography on the final stress field. The profile we used for the Tepev Moris volcano was taken from the approximate center of the larger eastern caldera (29.6>I, 45.6"E) and extended to the northwest. From the start of this profile, the zone of concentric graben formation begins at approximately 40 km and extends to approximately 115 km. Any additional graben at greater distances may have been obscured by later lava flows. The magma reservoir was modeled as a simple chamber in which inflation occurs as a distribution of outward directed radial forces at specified nodes, with the force magnitude equal to I X lO'' k-g ms'' (1000 MPa). Varying the force magnitude affected the magnitude, but not the distribution, of surface stresses. The model allows analysis of var>'ing magma chamber depth, size, and shape, as well as the density, Poisson's ratio, and Young's modulus of the magma and country roek, The pa- rameters most typically used are listed in Table 2. Figure 9 illustrates an example of the axisymmetric finite element grid used in this analysis containing 8238 nodes and 8181 elements, with a grid size of 100 km by 300 km. This case models a spherical magma chamber which has 107 ele- ments, lies at a center depth, D, of 30 km, and has dimensions ofRx= Ry ~ 16 km. The left boundary is a symmetry axis aiong which horizontal displacements vanish. At the bottom boundary of the grid, at depths much larger than the level of the chamber, vertical displacements vanish, while at large ra- dial distances (right boundary) both horizontal and vertical displacements vanish. Figure 10 illustrates the surface stresses resulting from this analysis. The resulting variations in the stress field were examined and the mode! results were compared with our observations from Magellan images. Specifically, the innermost location of predicted eoneentrie graben formation is defined by the point at which Orr crosses from negative (compression) to positive (extension) in the finite clement results, following metliods used in previous studies [Comer et al., 1979; Zuber and M?u^ims-Mark, 1992]. We also considered a case with no magma chamber to analyze stresses due solely to the volcano, and found relatively small load-induced surface stresses in the vicinity of the summit that were easily overwhelmed by the ef- fects of even a smalt magmachamber. However, this analysis does not account for edifice stresses from other sources such as lithospheric flexure, which would tend to add horizontal com- pression in the upper lithosph?re and may inhibit the transmission of extensional stresses to the surface [McGovem and Solomon, 1993]. Thus the depth of burial for any given magmachamber must be shallower to produce the observed graben than for a scenario without flexural stresses. Likewise, the observable distribution of fractures may have been altered due to burial by superposing flows [McGovarn and Solomon, 1997]. Specifically, the burial of the innermost fractures near the summit region would increase the horizontal radius of the Grr crossover, and bias the prediction of the magma chamber ra- dius tu larger values. Burial of innermost graben would also bias the depth prediction to larger values, since graben forma- tion moves outward with increasing depth to the chamber. Neglecting these additional potentia! factors thus biases our predictions toward larger chamber depths, so our analysis places an upper bound on the depth of burial. 4.4 Results In order to constrain the likely magmachamber geometry, we varied alternately the depth, size, and shape of the model reservoir. Numerous chamber geometries were examined (approximately 90 total variations), from a spheroid with vary- 0 -20 1-40 N -60 -?0 -100 50 100 200 250 150 R (km) Figure 9. An axisymmetric finite clement grid used in the analysis of Tepev Mons, containing 8238 nodes and 8181 elements, with a grid .size of 100 km by 300 km. The magma chamber in this example lies at a center depth (D) of 30 km, and has dimensions of Rx = 16 km (horizontal radius), and Ry= !6 km (vertical radius). 300 16,850 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 2x10? en ^2xl0" -4x10? J_L_L I I I I I I I I I I I I I I I I I 20 40 60 R (km) I I I 80 100 120 Figure l?. Elastic surface stresses resulting fromthe inflation of a spherical magrna chamber beneath Tepev Mens, illustrated in Figure 9. ing radii to ellipsoids with varying horizontal and vertical axes. Table 3 illustrates results from several of these models. As the vertical dimension (Ry)aflhe chamber increases rela- tive to the horizontal dimension (R^) (a vertically elongate ellipsoid), or the depth to the chamber becomes shallower, the stresses become more concentrated towards the center of the load and the zone of extension (graben formation) moves in- ward. It is obvious from Table 3 that neither spherical chambers nor ellipsoidal magma bodies comparable in size to the summit caldera can produce the required stress field within a range of reasonable depths. The 40-km crossover point can be accommodated most eas- ily by a tabular magma chamber 44-52 km in radius, approximately 8 km in maximum thickness, over a range of depths from 18 to 36 km. The tradeoffs between shape and depth are illustrated in Table 3. The thickness of the chamber has less of an impact on the location of the crossover point than the width and depth of burial. The small changes in crossover point with changing thickness reflect the varying Table 3. Variations in Or, Crossover Point (From Compressional to Extensional Regims) With Changes in D (Depth to Center of Chamber), Rx (Horizontal Radius), and Ry (Vertical Radius) Da ? km Rx, km Ry, km Crossover a?. km Shallow: Spherical Chambers: -15 -30 -50 Fllipsoidal Ciianibers: -20 -50 -40 -50 Tabular Chambers: -18 '18 -18 -18 Iniermediate: -28 -28 Deep: -36 -36 Sensitivity to Thickness: -22 -22 -22 -22 16 16 16 16 16 16 10 20 10 20 20 30 20 30 45 4 52 4 60 4 66 4 56 4 48 4 48 4 44 4 62 2 62 4 62 6 62 8 16 22 26 16 19 27 31 35 40 46 49 45 40 42 40 46 48 47 45 ROGERS AND ZUBER; TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,851 150 R (km) 300 Figure 11. Axisymmetr?c finite element grid for a solution of Tepev Mons edifice stresses with a magma cham- ber at an intermediate depth. The magma chamber, representing a sill-like intrusion, lies at a eenter depth (D) of 28 km, and has dimensions of Rx = 48, and Ry = 4. distance to the surface from the upper boundary of the chamber. The width of the reservoir is inversely correlated with the depth, such that more narrow "sills" may produce the required stress field as the centcrlinc depth increases. Note, however, that the surface stress magnitude declines with increased chamber depth, so a shallow chamber may be niore likely to create observable fractures. Our results indicate that the circumferential graben occur- ring on the flanks of Tepev Mons could be the result of edifice Stresses caused by a sheet-like or tabular magma reservoir. Figures 11 and 12 illustrate the results of this solution for an intermediate chamber depth (28 km) with a horizontal radius of 48 km and a vertical radius of 4 km. This sill-like intrusion may possibly have fed smaller magma chambers at shallower depths. However, without better resolution of the structure within the calderas, further analysis is not possible. Our analysis of Tepev Mons shows that the observed spatial dis- tribution of graben may be attributed to stresses caused by magma "chamber intlation, and therefore no inference of lithospheric thickness can be made from these graben loca- tions. However, our earlier analytical model of Tepev Mons flexure based on the possible location of a topographic moat may provide constraints on the thickness of the elastic litho- sph?re. -10 -2x10 40 60 80 R (km) 120 Figure 12. Elastic suri'ace stresses resulting from the inflation of a horizontally e?ongate (sill-like) magma chamber beneath Tepev Mons, illustrated in Figure il. The bar represents the region of fracturing observed in the Magellan images. 5. Discussion and Conclusions In this study, the nature of the stress state and lithospheric structure of Bell Regio have been e?iamined. The style and dis- tribution of tectonic features associated with the volcanic loads in Bell Regio were analyzed in an attempt to understand the regional stresses which produced these features. A com- plex history of stress regimes is illustrated through the vari- ous structural features associated with several different geologic terrains. The oldest units in the region, SW-NE trending tessera blocks, provide constraints on the early re- gional stress Irajectories. These regional stresses do not appear to have affected the emplacement of the large volcanic edifices, Tepev Mons and Nyx Mons. To quantify the stress regime in Bell Regio we have ap- plied analytical models for the formation of similar structures on Earth and other planetary surfaces. We have identifled structural patterns that we believe to be a consequence of lithospheric flexure due to volcanic loading and other features that may be associated with intlation of a magma reservoir be- neath Tepev Mons. Concentric fractures surrounding Nyx Mons were mapped and their distributions examined. By mod- eling Nyx Mons as a surface load on an elastic plate, we used the concentric graben to provide a constraint on the effective elastic thickness at the time the volcano was emplaced. Our analysis indicates that, for an assumed Young's modulus for the plate of 10 Pa and a load diameter of approximately 350 km, a lithospheric thickness of 50 km best describes the condi- tions at Nyx Mons at the time the concentric graben were formed. This predicted elastic thickness is in good agreement with Magellan gravity analyses. Smrekar [1994] indicates that the effective elastic thickness at short wavelengths is 30 ? 5 km, and 50 ? 5 at long wavelengths, where the 30 km value reflects a thinned elastic plate at the time the volcanoes were emplaced and the 50 km value represents presenl day elastic thicknesses. It should be noted that Smrekar was ana- lyzing the overall highland swell, whereas this analysis models the individual volcanic loads in the region. A concentric zone of weakness, represented by graben and coalesced chains of pit craters, surrounding Tepev Mons was also examined. These features, previously identifled as possi- bly due to lithospheric flexure [Solomon ei ai, ?992], occur on the steep flanks of the volcano. Our analysis indicates that they most likely formed as a result of extensional stresses as- sociated with inflation and doming during magma chamber 16,852 ROGERS AND ZUBER; TECTONIC EVOLUTION OF BELL REGIO, VENUS inflation. Reservoir-induced stresses were analyzed using a fi- nite element model, and our results indicate that inflation of a large sheet-like magma reservoir, represented by a horizontal ellipsoid in our model, most likely generated the zone of ex- tension and fractures observed in Magellan images. The tectonic deformation within the venusian edifices ex- amined above can be compared and contrasted with two volcanic regions on Earth: Hawaii and the Galapagos Is- lands. These two volcanic areas differ markedly in their patterns of surface deformation, Kilauea volcano, located at the southeastern end of the Hawaiian island chain, exhibits two iarge rift zones extending cast and southwest from the summit. Rifl zones, linear pattenns of extension on the scale of the individual edifices, form perpendicular to the direction of least compressive stress. The south flank of Kilauea is driven seaward over the downwardly flexed oceanic crust due to gravitational stresses inherent in its shape and by intrusions of high density magma along the rift zones, Stress accumulates due to repeated intrusions along the cast rift zone, producing a net horizontal force within Kilauea's south flank. Opposed by only water on its seaward side, seismic and aseismic slip occurs at the interface between the volcanic pile and sedi- mented old ocean crust {a zone of weakness). The northern flank of Kilauea is buttressed by Mauna Loa, which prevents northward displacement ofthe edifice during dike intrusions [Thurber. 1988; Dieterich, 1988; Ryan, 1988]. In contrast to the Hawaiian volcanoes, the western Gala- pagos shield volcanoes lack prominent rift zones. The Galapagos islands are dominated by six large basaltic shield volcanoes believed to have formed over a hot spot now undei' Femandina and Isabela islands. Galapagos shield volcanoes have steep slopes (15?-35?), broad flat summits and deep cal- deras which contribute to a distinct morphology relative to other shield volcanoes (e.g., Hawaii). The morphology of these shields results from surface processes such as gravita- tional relaxation, the emplacement of lava flow fields, and response to magma chamber stresses \Cullen et al.. 19871. Cuiten et at. [1987J suggested that the stress regime of the Ga- lapagos shields hinders lateral drainage of magma and allows large volumes of melt to solidify as intrusions. Most ofthe eruptions on the Galapagos volcanoes are from linear or ar- cuate fissures (circumferential fissures, around summit calderas, radial fissures lower on flanks) which Chadwicli and Howard [1991] interpret to reflect patterns of underlying dikes from a subsurface magma chamber. The circumferential and radial dik- ing has been attributed to episodes of broad volcano inflation and subsidence [Chadwicli and Howard, 1991; Simkin, 1972] where dikes are emplaced perpendicular to the least compres- sive stresses. Tcpcv Mons appears morphologically similar to the Gala- pagos volcanoes (steep flanks, broad summits, large calderas, ? and lack of rift zone deformation). Based on these discussions, the Galapagos islands may be the better terrestrial analog to Tepev Mons than typical Hawaiian volcanoes. As discussed above, there are no large regions of thru-going extension or rifling at Bell Regio, nor is there any indication ofthe more lo- calized rifting that is evident on Kilauea. Recent work by McGovern [1996] indicates that the lack of these structures, important to the development of volcanoes on Earth and Mars, might result from an absence of a distinct layer of clay sedi- ment, preventing the formation of the basai detachment beneath volcanoes such as those of the Galapagos chain. The major edifices within Bell Regio may have been domi- nated by two distinct volcanic regimes. Lithospheric flexure appears to have occurred at both Tepev Mons (evident from the topographic moat) and Nyx Mons (resulting in the concentric graben). However, Tepev Mons appears to have experienced additional deformation due to the stresses associated with magma chamber inflation. Whereas the Tepev Mons load is relatively concentrated in a central region with a zone of frac- turing surrounding the edifice and flows which are relatively limited in extent, Nyx Mons is much broader, with relatively expansive flows and large radial chains of pit craters possibly indicating a more distributed magmatic system. In the analysis by McGovern and Solomon [1995], a thick lithosph?re is proposed as a precursor to the growth of a large shield vol- cano on Venus. A thin lithosph?re would lead to plains- forming vol can ism, or smaller shields. In our scenario, Nyx Mona, which is strutigraphieully older, could represent the transitional state between broad, effusive plains volcanism to more shield-forming eruptions represented by Tepev Mons. In addition, horizontal compressive stresses would in- crease as the edifice grows, inhibiting the easy rise to the surface and release of magma {McGovern and Solomon, 1995]. Therefore, for volcanism to occur in a construct as large as Te- pev Mons, a pressurized magma reservoir, which we have postulated is responsible for this volcano's concentric frac- tures, would be needed. This pattern of increasing shield height and steeper flank slopes with decreasing apparent age is also supported by the presence of two very steep volcanoes on the SE flank of Tcpcv Mons. The flows from these steep edifices post-date those of Tepev and Nyx Montes, and are the likely source ofthe rough lava flow which traces the flexural moal north of Tepev Mons (Figure 1) [Campbell and Rogers, 1994]. 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