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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. Ell, PAGES 18,295-18,307, NOVEMBER 25, 1992

Caldera Subsidence and Chamber Depth of the Olympus Mons Volcano,

M. T. ZUBER1

Geodynamics Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland

P. J. MOUGINIS-MARK

Planetary GeosciencesDivision, School of Ocean and Science and Technology, University of at Manoa, Honolulu

Observations of the distribution of tectonic features and their relationship to local surface topography indicate that the floor of the oldest and largest crater of the summit caldera of Mars' Olympus Mens volcano may have undergone subsidence in response to depressurizatien of a subsurface . In this study, we construct an axisymmetric finite element model to calculate elastic stressesin a volcanic edifice to investigatethe relationshipbetween surface tectonism, caldera subsidence, and the physical characteristics of Olympus Mens' magmatic reservoir. Con- straints on the model are provided by the stressfield within the crater indicated by the distribution of radial ridges and circumferential graben that we hypothesize formed due to a postcollapse and pestresurfacing phase of subsidenceof the caldera floor. Model results show that the surface stress state is not strongly sensitiveto the aspect ratio or pressure distribution of the magma chamber, or to the contrast in stiffnessbetween the magma chamber and surroundings,but is strongly dependent on the width and depth of the chamber. For a range of plausible model parameters, we find the maximum depth to the top of the magma chamber to have been -<16 km, which indicates that the chamber, at the time of crater floor subsidence, was positioned within the Olympus Mens edifice, at a level much shallower than the estimated source depth of Martian (--•140-200 km). The allowable range of solutionsindicates that the vertical position of the magma chamber may have been controlled by the neutral buoyancy level of ascending magma. Our results suggest a gross similarity between the configurations of the magmatic plumbing systems of Olympus Mens and several well-studied terrestrial volcanoes such as the Hawaiian shields.

INTRODUCTION [Wilson and Head, 1988; Thomas et al., 1990]. In the vicinity of the summits of Martian volcanoes that exhibit a clear Studies of the eruptive characteristics of terrestrial basal- record of tectonism, however, models of the stress field may tic volcanoes indicate that magma is generally transported represent an alternative and arguably more direct means of from a deep, upper source region to the surface via a understandingthe nature of magma accumulation and trans- shallow holding chamber [Eaton and Murata, 1960]. The port at shallow subsurface levels. configuration and depth of this chamber have implications The summit caldera of the Olympus Mons volcano, shown for the nature of magmatic transport as well as for the in Figure 1, displays one of the clearest examples of tectonic processes which initiate and sustain eruptions. In closely processesassociated with shield . Within monitored shields such as Hawaii's Kilauea volcano, the the -90 x 60 km structure are six nested craters that geometry and depth of the magma chamber have been indicate that the summit has undergone multiple collapse constrained from seismic and gravity data [Crosson and episodes [Mouginis-Mark, 1981]. Observations of the Endo, 1981; Karpin and Thurber, 1987; Klein et at., 1987; caldera include high-resolution Viking images and local Thurber, 1987;Ryan, 1988], as well as from geodetic leveling topography derived from stereophotogrammetry [Wu et at., and triangulation measurements [Dieterich and Decker, 1984] and photoclinometry [Mouginis-Mark and Robinson, 1975; Ryan et at., 1983; Delaney et at., 1990; Yang et at., 1992]. Comparison of these data sets shows that the central 1992]. portion of the largest and oldest crater (hereafter, crater 1), Shield volcanism is a common process on Mars, and the contains radial and circumferential ridges and represents a major shields have been the focus of numerous morpholog- topographic low. In contrast, the outer part of the crater is ical studies [cf. Cart, 1973; Greeley and Spudis, 1981; characterized by circumferential graben which are found on Mouginis-Mark et al., 1992]. Unfortunately, due to the a topographically elevated region along the perimeter of the absence of seismic data, high spatial resolution gravity crater floor. The total change in relief from the central ridges measurements, and measured ground displacements, analy- to peripheral graben is -•1300 m [Mouginis-Mark and Rob- ses of magma chamber positions within Martian shieldshave inson, 1992]. Tectonic features within the interior of the been limited to gravitational scaling of terrestrial volcanoes caldera as a whole are most abundant in areas with the greatest surface slopes [Watters and , 1990]. Pho- 1Also at Departmentof Earthand Planetary Sciences, The Johns togeologicevidence for -like re surfacingof the caldera Hopkins University, Baltimore, Maryland. floor [Greeley and Spudis, 1981], in combination with the Copyright 1992 by the American Geophysical Union. observed topography, has been interpreted to indicate that a Paper number 92JE01770. large lake within the crater has subsided in its central 0148-0227/92/92JE-01770505.00 region due to pressure reduction in the underlying magma

18,295 18,296 ZUBER AND MOUGINIS-MARK: OLYMPUS MONS CALDERA SUBSIDENCEAND MAGMA CHAMBER DEPTH

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Fig. 1. Image of the Olympus Mons caldera showing six nested craters. The largest and oldest crater (referred to as crater 1 in text) has a radius of--•32 km. The tectonic features used in this study as constraints on magma chamber depthare located within the box. The resolution of theimage is approximately156 m pixel-• . Northis at thetop of the image. Illumination is from the right. (Viking Orbiter image 890A68.) chamber [Mouginis-Mark, 1981; Mouginis-Mark and Robin- possible relationship between tectonic features within the son, 1992]. Olympus Mons caldera and the nature of the magma cham- On the basis of geologic mapping and numerical modeling ber. To accomplish this, we begin by reviewing the geologic of the stress regime of the Olympus Mons caldera complex, and structural context of the caldera, then describe a simple we suggestthat certain tectonic features within crater 1 may model of magma chamber depressurization and surface preserve a record of the proposed subsidenceevent. If this is subsidencethat can explain the distribution and timing of a the case, then the stress field inferred from the features may specific assemblageof tectonic features within crater 1. We contain information about the magma chamber at the time of apply the model, with constraints provided by the observed subsidence. The objective of this study is to explore the spatial distribution of the tectonic features, to investigate the ZUBERAND MOUGINIS-MARK:OLYMPUS MONS CALDERASUBSIDENCE AND MAGMA CHAMBERDEPTH 18,297

;""• RADIALWRINKLE RIDGE

-•- CIRCUMFERENTIAL RIDGE

• CIRCUMFERENTIAL GRABEN 5 km

N

Fig. 2a. Sketch map of tectonic features within the area of crater 1 outlined in Figure 1. The center of the crater is in the direction of the top of the image. This area was mapped from Viking Orbiter images 473S27-29 and 474S25-30.

extent to which the size, shape, depth, and pressurization the radial wrinkle ridges and are often superimposedupon state of the magmatic reservoir can be determined. We find the radial ridges. Unlike superficially similar features on the that a wide range of magma chamber aspect ratios and volcano Alba Patera, which were interpreted by Catterrnole pressure distributions can produce surface stressesconsis- [1986] to be spatter ridges, we see no evidence of compara- tent with the observed pattern of tectonism and conclude ble individual constructional cones or small flows within the that neither the relative dimensions of the magma chamber Olympus Mons caldera. We interpret the Olympus Mons nor the details of its pressurization can be confidently circumferential ridges, which are distributed from the center constrained from the tectonics alone. We also find that the of the crater out to approximatelyhalf its radius (r -• 0.53Rc distribution of surface stress is a sensitive indicator of the width and depth of the magma chamber. From our model results and observations,we find the depth to the top of the magma chamber at the time of subsidence to have been within the volcanic edifice, possibly at the level of neutral buoyancy, as is the case for several well-studied terrestrial volcanic shields.

CALDERA TECTONICS

Structural Context

Figure 2a shows a structural sketch map of crater 1. The area was mapped from high-resolution Viking Orbiter im- ages, such as Figure 2b, which have a maximum spatial resolutionof 15-20m pixel-• [Mouginis-Markand Robin- son, 1992]. The map shows three types of tectonic features. The first consists of prominent wrinkle ridges oriented radially from the center of the crater. These features are morphologically similar to wrinkle ridges that occur on spatially extensive plains units elsewhere on Mars and on the lunar maria [Greeley and Spudis, 1981; Plescia and Golombek, 1986; Watters, 1988]. The features have topo- graphic amplitudesof---300 m, average widths of---2 km, and lengths of 5-15 km. The orientation of these features indi- cates that they formed as a consequenceof circumferentially directed horizontal compression within the caldera. The second set of features consistsof narrow, concentric ridges Fig. 2b. High-resolution(16.5 m pixel-•) imageof the part of that are characterized by minor topographic expression Figure 2a noted by the box. Illumination is from the left. (Viking (---20-40 m). These ridges are morphologically different from Orbiter image 473S30.) 18,298 ZUBER AND MOUGINIS-MARK' OLYMPUS MONS CALDERA SUBSIDENCEAND MAGMA CHAMBER DEPTH

[Zuber and Mouginis-Mark, 1990]), to have formed as a 2OO I I I consequence of radially directed compression. The third 100 -- O'zz type of feature consistsof prominent circumferential depres- 0 sions that have previously been interpreted as graben [Mouginis-Mark, 1981; Watters and Chadwick, 1990]. These -100 -- O'rr features have lengths of more than 25 km, widths of-420- -200 -- 450 m, and depths of-180-200 m and are located in the -300 -- outer part of the crater (r >- 0.53R c [Zuber and Mouginis- Mark, 1990]). The transition from a state of compression in -400 -- the inner part of the crater, as indicated by the radial and -500 concentric ridges, to extension in the outer part of the crater, -600 as indicated by the circumferential graben, is sharp, occur- ring in some areas over distancescomparable to the widths -700 of individual features. -800 I I I I I I I I The assemblage of tectonic features discussedabove can 0 0.2 0.4 0.6 0.8 1.0 onlybe mapped at highspatial resolution (<50 m pixel-i) on r/Rc the eastern side of the crater. However, lower-resolution Fig. 3. Elastic surface stressesarising due to an instantaneous images(>100 m pixel-1) of the westernand northwestern pressure drop in an elliptical subsurface source vs. distance from segmentsof the crater floor display the same general trends. crater center (r/Rc, where Rc is crater radius). The sourcehas a Specifically, concentric graben are observed around the width a = Rc, height c = 0.5a, depth beneath the surface d = perimeter of the crater floor, and there are hints of the 0.25Rc, and maximum force vector within the source Fmc = 1 x 109 narrow circumferential ridges closer to the crater center. kg m s-2. The Young'smodulus contrast between the sourceand surroundings(Emc/Es) = 0.01. Negative stressesare compressional Watters and Chadwick [1990] cite the topography and dis- and positive stressesare extensional. tribution of tectonic features within the caldera as evidence for asymmetric subsidence,with greater downward displace- ment in the southern half of the caldera floor. However, this Stresses Due to Subsidence interpretation is based on observations of all of the craters that compose the caldera, rather than of crater 1 alone. If the tectonic features within crater 1 formed as a conse- There is no evidence for a significantdeviation from axisym- quence of surface subsidence related to magma chamber metry in crater 1 from the observed distribution of tectonic deflation, then the distribution of the features should be features. consistent with the pattern of deformation implied from The relative sequenceof formation of the tectonic features stresses arising from this process. Figure 3 shows the and their relationship to the formation of crater 1 can be theoretical distribution of elastic surface stresses associated derived from superposition relationships. Because all of the with an instantaneouspressure drop within an ellipsoidally structures of interest are located within smooth materials on shaped source situated within a simple axisymmetric volca- the floor of the summit caldera, they must postdate both the nic edifice. (Details of how the stresseswere calculated are collapse event responsible for the formation of crater 1 and discussedlater.) The source is intended to approximate a an episode of subsequent(probably volcanic) resurfacing of subsurface magma chamber. The distribution of surface the crater floor. The radial wrinkle ridges predate both the deformation associated with a given stress field can be circumferential ridges and graben in all but possibly one deduced if the signs and relative magnitudes of principal instance shown by the arrow in Figure 2a. In this case, two stresses are known [Anderson, 1951]. At the surface where radial ridges terminate against different parts of the same the tectonic features are observed, shear stresses vanish, circumferential ridge. Here the timing of formation is ambig- and the principal stressesare identical to the normal stresses uous, since the radial ridge may either predate or postdate plotted in Figure 3. Near the crater center (r/R c _<0.5), the the concentric ridge. The circumferential ridges and graben maximum compressive stress is the circumferential or hoop do not exhibit any superpositionrelationships and therefore stress(c r000, where the subscript0 indicatesstress at the may have formed either concurrently or at different times. surface (z - 0)). Interpretation in the context of the However, both must have formed subsequentto many of the Anderson [1951] criteria for faulting and a critical value of resolvable radial ridges. stressnecessary to overcome the frictional resistanceof slip We suggest that the spatial and temporal distribution of surfaces [Byerlee, 1978] predicts the formation of radial this assemblage of tectonic features can be explained by ridges in this region. In the outer part of the crater, where subsidence of the floor of crater 1. Subsidence is a common Crrrøis theleast compressive and or00 øthe mostcompressive event in the evolution of calderas [cf. Williams, 1941; Smith principal stresses, circumferential graben are predicted by and Bailey, 1968] and is often associatedwith depressuriza- interpretation of Anderson's [1951] criteria. The possibility tion of the underlying magma chamber. On Olympus Mons, that observed concentric graben are alternatively controlled depressurization could be attributable to flank eruptions by a tensile failure criterion for rock, in which the least [Mouginis-Mark, 1981] or simply to withdrawal of magma to compressiveprincipal stress (in thiscase cry0) exceeds some lower levels in the volcano. In the case of crater 1, the limit at the inner and outer limits of faulting, has also been amount of subsidencewas probably a maximum in the center explored [Comer et al., 1979;Solomon and Head, 1980;Comer of the crater, since the (presumably) originally horizontal et al., 1985; Hall et al., 1986], as has the assumptionthat central region of the floor is now 600-1000 m lower than the surficial graben form where the maximum principal stress perimeter of the crater floor [Mouginis-Mark and Robinson, differencecr1 - cr3 (equivalentto Cr•r0 - or000in ourmodel) 1992]. exceeds a critical value [Gephart, 1987]. These criteria ZUBER AND MOUGINIS-MARK: OLYMPUS MONS CALDERA SUBSIDENCEAND MAGMA CHAMBER DEPTH 18,299 predict surface stressesconsistent with the observed transi- r,u r=Rc tion of inner radial ridges to outer concentric graben. Thus, on the basis of the surface stress field associated with deflation, we suggestthat radial ridges near the center of the crater and circumferential graben at larger radii may be indicative of subsidence of the crater floor associated with deflation of a subsurface magma chamber. Faulting, which presumably accompanies wrinkle ridge formation [Plescia and Golombek, 1986; Watters, 1988; Golombek et al., 1991], will be characterized by a decrease w=O in the magnitude of the stress in the vicinity of the faults, Fig. 4. Axisymmetric finite element grid used in the analysis. with radial ridges preferentially releasing the circumferen- The grid contains 1827 nodes connecting 1878 quadrilateral ele- tially directed component of the stress. mechanics ments. The left boundary is a symmetry axis on which the horizontal displacement (u) vanishes. On the bottom boundary the vertical models incorporating realistic material properties would displacement (w) vanishes, and on the right-hand boundary, both ultimately be required to ascertain the magnitude and distri- horizontal and vertical displacements vanish. The crater perimeter bution of the stress drop. However, dislocation models of is located at r = R c. The grid is sufficiently large so that the mode III cracks [Pollard and Segall, 1987] show that areas boundary conditions do not influence the stress field in the vicinity of the summit. within approximately three crack lengths both parallel and perpendicular to the crack would be influenced by the crack stressfield. This distance is larger than the spacingsof radial ential ridges with the proposed subsidence event, while ridges in crater 1. A reduction of stress along the radial supported by superposition relationships, is not a require- reverse fault presumably associated with the ridge would ment of our model. thus be accompanied by a reduction in the hoop stressof the surroundings. A significant stress drop associated with the formation of the radial ridges would modify the pattern of MECHANICAL MODEL stressshown in Figure3. For sufficientdecreases in rr000,rrrr0 Method of Solution would become the maximum compressive stressin the inner part of the crater. Thus, circumferential ridges might be To quantify the edifice stress field, we employed a finite expected to form subsequentto radial ridges in the inner part element approach in which the volcano and its surroundings of the crater, as is observed within crater 1. Solomon and were approximated by a grid composed of a specified num- Head [1980], though they did not specifically invoke the ber of structural elements that are connected at nodal points. argument offered here, used the radial component of stress We used the program TECTON [Melosh and Raefsky, 1980] associated with surface loading to explain the formation of to develop a general linear elastic model that includes the concentric wrinkle ridges within some lunar maria. In this effects of gravity and self-compression. For simplicity, we scenario, concentric ridges that postdate the radial ridges in used an axisymmetric model. the interior of the crater may be explained by subsidenceas In a finite element analysis, the nodal displacements, well, though this scenario is admittedly based upon assump- which we represent by a vector U, are the principal un- tions regarding the nature of how rocks will respond to stress knowns and define the number of degrees of freedom in the after initial failure, which is difficult to either observe or problem [cf. Bathe, 1982]. This vector can be related to model. another vector F that contains the components of force We recognize the possibility that the tectonic features we acting at each node and a global stiffness matrix K by identified were produced by a mechanism other than subsid- F = KU (1) ence related to deflation, such as simple cooling of the proposed lava lake that comprises the smooth matedhalsin where K was constructed from the elastic constants, element which the tectonic structures formed. However, we note dimensions, and local force-displacement relationships. that the pattern of observed surface deformation within Equation (1) constitutes a set of simultaneousequations that crater 1 is not consistent with the theoretically predicted was solved for a specified set of boundary conditions using a distribution of thermal stressesinduced in a uniformly cool- Gaussian elimination routine [Desai and Abel, 1972]. A ing circular plate [Boley and Wiener, 1966]. In addition, this quadratic interpolator was used in the computation of the pattern of features is not observed in recently cooled lava nodal displacements. lakes in Hawaii [Wright and Okamura, 1977; Peck, 1978]. Neither is it likely that convective shear stressesat the base Boundary Conditions of a cooling lava lake would produce stresses that can be consistent with the observed pattern of deformation. Figure 4 illustrates the boundary conditions on one of the If the tectonic features in crater 1 are indeed a conse- grids used in the analysis. The grid represents the Olympus quence of floor subsidenceassociated with magma chamber Mons volcano, with a radius of 300 km and height of 30 km deflation, then their spatial distribution provides a constraint and the underlying down to a depth of 150 km on the geometry and depth of the deflational source, i.e., the beneath the base of the volcano. The following conditions subsurfacemagmatic reservoir, at the time of the subsidence were imposed: vanishing horizontal displacements(u) at the event. We adopt this working hypothesis and develop mod- center of symmetry of the volcano (left boundary), vanishing els of magma chamber deflation constrainedby the transition vertical displacements (w) at depths much greater than the from compressional radial ridges to extensional concentric crater radius (bottom boundary), and vanishing horizontal graben within the caldera. The association of the circumfer- and vertical displacements at radial distances far from the 18,300 ZUBER AND MOUGINIS-MARK: OLYMPUSMONS CALDERASUBSIDENCE AND MAGMA CHAMBERDEPTH

Magma Chamber Geometry Constraints on the shapes of terrestrial magma chambers are based on observations of exposed plutonic complexes and models based on observed tectonics, structure, and eruptive characteristics [Chevallier and Verwoerd, 1988]. Structures range from simple ovoidal plutons of the Ker- guelen Archipeligo [Giret and Lameyre, 1983] to a complex network of interconnected dikes and conduits for the Kilauea volcano [Ryan, 1988]. Due to the absence of sub- surface information for Olympus Mons, the magma chamber was modeled as a simple ellipsoidally shaped source (Figure 5a). Inward directed point forces on nodes within an ellip- tical cross section were imposed to represent an instanta- neouspressure drop. The cross section was characterized by a horizontal half axis of length a, vertical half axis of length c, and depth d to the top of the chamber at the center of the Fig. 5a. Geometry of the magma chamber. Parameters of inter- crater. Models with both constant and variable vector mag- est include the horizontal (a) and vertical (c) axial half lengths, and the depth beneath the center of the crater to the top of the chamber nitudes were considered. In most of the numerical experi- (d). ments it was assumed that each force vector within the magma chamber was directed normal to the boundary of the chamber, as illustrated in Figure 5b. However, force distri- butions in which vectors were directed radially toward the center of the chamber, and those in which all forces were crater rim (right boundary). Numerical analyses were per- directed downward (parallel to the z direction) were also formed to assure that the calculated stress fields in the analyzed. Because of the enhanced temperatures in active vicinity of the caldera were not sensitive to any of the far terrestrial magma chambers indicated from the attenuation field conditions. The boundary condition on the magmatic of seismic waves, it was assumed that elements within the reservoir, which is discussed in more detail in the next model magma chamber were characterized by a lower value section, was taken to be a force per length simulating a of Young's modulus than elements composingthe surround- uniform change of pressure on the walls. ing volcano. The magma chamber geometry was chosen so

Fig. 5b. Distribution of point forces on nodes within the magma chamber. In this example, forces are directed normal to the boundary of the chamber. ZUBER AND MOUGINIS-MARK: OLYMPUS MONS CALDERA SUBSIDENCEAND MAGMA CHAMBER DEPTH 18,301

TABLE 1. Typical Model Parameters correlates with the inner limit of circumferential graben. We then compared the stress patterns to the observed radial Symbol Parameter Value Units positions of concentric graben in crater 1 of Olympus Mons. Emc Young'smodulus of magma 1 x 109 Pa The approach of using the radial component of stress to chamber explain the positions of circumferential graben has previ- Es Young'smodulus of surroundings1 x 10TM Pa ously been employed in analyses which estimated the effec- v Poisson's ratio 0.25 p density 2700 kg m-3 tive elastic thickness of the lithosphere in the vicinity of -2 g acceleration of gravity 3.71 m s lunar maria and Martian volcanoes [Comer et al., 1979; Fmc magmachamber force vector 1 x 109 kgm s-2 Solomon and Head, 1980; Comer et al., 1985; Hall et al., 1986].

that its size, shape, depth, orientation, stiffness,density, and RESULTS pressure distribution could be varied without modifying the grid, which allowed numerical experiments to be performed Baseline Solution over a broad parameter space by simply varying input values. In addition, it was possible to construct solutions for We first consider the case of a magma chamber with an even simpler magma chamber geometries than shown in aspect ratio of c/a - 0.5 and Young's modulus contrast Figure 5 (e.g., point and line sources). These solutionswere between the magmachamber and surroundingsof Emc/Es -- directly compared to existing analytical [cf. Mogi, 1958] and 0.01. The chamber width was assumed to equal the width of finite element [Dieterich and Decker, 1975; Decker, 1987] the crater (a - Rc- 32 km), as is generally observed for solutions to test the accuracy of the finite element code and terrestrial volcanoes [e.g., Ryan, 1988]. Figure 6 plots the the reproducibility of numerical solutions from different distributionof theradial surface stress, trr•0, as a functionof codes. Table 1 lists typical material properties used in the radius, r/R c, from the center of the crater (where r/R c - 1 is analysis, though all parameters were varied to characterize the crater perimeter) for a range of d. At shallow depths the model sensitivity. (e.g., d - 0.125Rc), trrr0 is compressionaland large in To constrain the characteristics of the magma chamber, magnitude close to the center of the crater. With increasing we calculated surface stresses as a function of radius in the distancefrom the center,the magnitudeof trrrø decreases, crater that would be expected due to deflation of a magma and at about halfway to the crater perimeter it becomes chamber for a range of specified model parameters. We extensional. At progressively increasing depths, the dy- calculated the entire stresstensor but in order to most simply namic range of surface stress magnitudes decreases, and the compare various model configurations, we plot only the transition from compression to extension shifts to greater radial component of stress. Our examination of the three distances from the crater center. At shallow depths, a normalstress components indicates that the crossover of trr•0 specified change in the depth of the magma chamber corre- from compression to extension is indicative of the radial sponds to a much smaller shift in the compression to position of the onset of surface extension that presumably extension crossover point than at greater depths. Conse-

lOO 1 I I I I

1.5Rc

Rc

-lOO 0.5Rc

tl:l -2oo

o • -3oo

-400

-500-600 • d = 0.125Rc

-7oo I I I I I I I I 0 0.2 0.4 0.6 0.8 r/Rc Fig. 6. Radialsurface stress (Crrr 0)due to magmachamber deflation as a functionof distancefrom the crater center (r/Rc, whereR c is the crater radiusof 32 km). Stresspatterns are shownfor a rangeof depthsto the top of the chamber (d). Assumesa chamber with width a = Rc, height c = 0.5a, maximum magma chamber force vector magnitude Fmc= 1 x 109 kgm s-2, andYoung's modulus contrast between chamber and surroundings Emc/E s = 0.01.For these parameters, the theoretical distribution of stressesthat best fits the observed pattern of tectonic features (transition from radial ridges to circumferentialgraben at r --• 0.53Rc) occurs for d = 0.25Rc = 8 km. 18,302 ZUBER AND MOUGINIS-MARK.' OLYMPUS MONS CALDERASUBSIDENCE AND MAGMA CHAMBERDEPTH

lipsoidally shaped chamber, in which the half axes of the magma chamber were assumedto be tilted with respect to 0.125 the r and z coordinateaxes. While this shapeis idealizedand -lOO 0.25 not physically justifiable, it was easily implemented and 0.5 -200 served to illustrate the effect of varying magma chamber shapeon the best-fit depth. For this solution,a positive tilt -300_ 0.7 angle 0 corresponds to a counterclockwise rotation of the chamber axes and a negative angle 0 correspondsto a -400 _ 1.0 clockwiserotation. Figure 8 showsthat positive and nega- tive tilts causethe transitionfrom compressionto extension -500 to shift slightly farther from and closer to the center, respectively.However, for the rangeof tilt anglesexamined -600 the changein the crossoverdistance is insignificant.Unless the magmachamber was highly inclined with respectto the -700 - ;o 0.2 0.4 .06 0.8 1.0 horizontal, chamber orientationis not an important factor in r/Rc constrainingthe best fit depth. Fig. 7. Plotof rrrr0versus r/Rc for a rangeof magmachamber aspectratios (c/a) assuminga = Rc, d = 0.5Rc,Fmc = 1 x 109 kg Stiffness Contrast m s-2 andEmc/E s = 0.01. The sensitivity of the solution to the contrast in Young's modulus between the magma chamber and surroundings quently, the model is not very sensitiveto the observational (Emc/Es) is shown in Figure 9. Figure 9 demonstratesthat if constraintsfor very shallow depths (--•1 km). Emc < Es, the depth of the magma chamber is essentially The magnitudesof the stressesare most strongly a func- insensitiveto this ratio. For Emc/Es -- 1, the transitionfrom tion of the assumedYoung's moduli (Es and Emc) and force compressionto extension shifts to a greater distance from magnitudeof the deflatingmagma chamber (Fmc). For the the center and would require a shallower magma chamber parametervalues assumed in Figure6 (Es = 1 x 10• Pa, than determined in Figure 6 to explain the observed pattern Emc= 1 x 109Pa, and Fmc = 1 x 109kg m s-2), boththe of tectonism.The case in which Emc/Es > 1, which corre- compressionaland extensionalradial stressmagnitudes at- sponds to a magma chamber that is more stiff than its tain values sufficientto causefailure in intact rock through- surroundings,is characterized by an even greater transition out much of the radial extent of the crater. In crater 1 of distance.However, this situationis not physically realistic. Olympus Mons, the distribution of ridges and graben indi- cate that the transition from radial compressionto extension Magma Chamber Pressure Distribution occurs at a radial distancefrom center (r) of approximately 0.53R c (17 km [Zuber and Mouginis-Mark, 1990]). For the In addition to assuming magma chamber point force parametersassumed in Figure 6, the magma chamberdepth vectors directed normal to the wall of the magma chamber that most closely corresponds to the observations is d = (Figure 5b), we also calculated solutions in which vectors 0.25Rc (8 km), though solutionswith d up to 0.5R c are allowable when model uncertainties are taken into account. We next examine the sensitivity of the model to various 5O parameters and demonstrate that the solution shown in Figure 6 likely representsa maximum depth to the top of the magma chamber.

Magma Chamber Aspect Ratio Q_o:1 -5o Figure 7 showsthat the best-fit depth is not very sensitive ,_o to the aspect ratio of the chamber for c/a < 1, which '- -100 correspondsto an oblate ellipsoid (semimajor axis in the x direction). For c/a > 1, correspondingto a prolate ellipsoid (semimajor axis in the z direction), the transition from radial -150 0•.0 ø compressionto extension shifts to greater distances. There- fore, if the magma chamber is prolate, it must have been -200 either shallower or narrower than determinedin Figure 6 at the time of crater floor subsidenceto explain the observed -250 transition from radial compressionto extension. Since it is 0 0.2 0.4 0.6 0.8 1 unlikely that the chamber is significantly narrower than the r/Rc collapsecrater [cf. Marsh, 1984], a shallower magmacham- ber would be implied. Fig. 8. Plotof rrrr0versus r/Rc for a rangeof magmachamber orientations(0) assuminga = R c, d = 0.125R c, c/a = 0.5, F c = 1 x 109 kgm s-2 Emc/Es = 0.01 andFmc = 1 x 109 kgm Magma Chamber Orientation s-n•.The orientation 0='0 ø corresponds •oa magma chamber with axes orientated along the x and z coordinate axes. Positive 0 In order to investigate the stress field associated with a correspondsto a counterclockwiserotation of the magma chamber tilted magma chamber, we examined a model with a nonel- axes and negative 0 correspondsto a clockwise rotation of the axes. ZUBER AND MOUGINIS-MARK' OLYMPUSMONS CALDERASUBSIDENCE AND MAGMA CHAMBERDEPTH 18,303

200 lOO I I I I 0.1125I I I I 100

0

-100 -lOO a/Rc = 2.0 -200

-300 o -200

-400 - -300 -500

OOl -600 -400 o.ool -700 -8oo /I I I I I I I I I / -500 I I I I I I I I 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 r/Rc r/Rc

Fig. 9. Plotof •rrr0versus r/Rc for a rangeof Young'smodulus Fig. 11. Plotof •rrr0versus r/R c for a rangeof magmachamber contrastsbetween the magma chamber and surroundings(Emc/Es) widths (a) assumingc = d = 0.25Rc and Emc/Es = 0.01. Note that assuminga = R c, d = 0.125Rc, and c/a = 0.5. In this solution,E s a wide magma chamber undergoes the transition from compression is held fixed. Notice that the transition from compression (•rrr (negative) to extension (positive) at greater distancesfrom the crater negative) to extension (•rrr positive) is not sensitive to this ratio center than a narrow magma chamber. Therefore a chamber that is except for the unrealistic case of Emc/Es • 1. wider than the crater (a/Rc • 1) must be shallowerthan a chamber that is lessthan or equalto the crater width (a/Rc -• 1) to explain the transition from compressional to extensional deformation at r • were oriented radially from center and in which all vectors 0.53Rc in crater 1 of the Olympus Mons caldera. were directed downward along the z axis. The crossover points of the radial stress for these cases were found to be virtually indistinguishablefrom the case in which the vectors the distributions of magnitudes of the point forces modified were oriented normal to the chamber wall. We also consid- the magnitudes of the surface stresses and some details of ered the potential importance of the magnitude of magma the shape of the radial stress distribution, but in no cases did chamber pressurization. This was done by varying all force thesechanges significantly alter the transitionof %r0from vector lengths by the same amount. Figure 10 shows that this compression to extension. We thus conclude that the best fit affects the magnitude of the radial stress. However, the depth range is not strongly sensitive to the details of the distance from center of the transition of radial compression imposed pressure distribution as long as the chamber is to extension, and the depth of the magma chamber implied depressurizing. by the transition, remain unchanged. We also investigated a If the magma chamber were instead overpressured, i.e., variety of distributions of point force magnitudes. In addi- inflating instead of deflating, then the signs of the stressesin tion to the case of uniform magnitudesat all nodes within the Figure 3 would be reversed. The center of the crater would chamber shown (Figure 5 b), we also calculated solutionsfor be in extension rather than compression and the crater models in which magnitudeswere dependent on the distance periphery would be in compression. Such a state of stress is from the center of the chamber. For some cases, changing not consistent with the observed distribution of tectonic features within the Olympus Mons caldera, indicating that the magma chamber could not have been significantly over- lOO pressured at the time the tectonic features formed.

Magma Chamber Width Figure 11 demonstrates that the depth of the magma -lOO chamber is highly sensitive to chamber width. Again, the magma chamber is unlikely to have been markedly narrower

-200 than the crater [Marsh, 1984]. If it was wider, then the transition from compression to extension would have oc- curred at a greater radius from the crater center than for the scenarioin Figure 6 where the magma chamber radius equals the crater radius. For a wider magma chamber, a shallower maximum depth than determined for the parameters as- -4oox1,,• Fmc=1 X 109 kgms'2 sumed in Figure 6 is implied. -5oo •1 I I I I I I I I 0 0.2 0.4 0.6 0.8 DISCUSSION r/Rc Fig. 10. Plotof %r0versus r/Rc for a rangeof magmachamber Influence of Far-Field Stresses force vector magnitudes(Fmc) assuminga = R c, d = 0.125Rc, c/a In all of the solutions discussed above we assumed a = 0.5, and Emc/Es = 0.01. The plot showsthat the transitionfrom compression(Crrr0 negative) to extension(•rrr0 positive) is insensitive continuity of stresses across the crater edge. We did not to this parameter. explicitly include in the model a steeply-dipping bounding 18,304 ZUBER AND MOUGINIS-MARK: OLYMPUS MONS CALDERA SUBSIDENCEAND MAGMA CHAMBER DEPTH fault, which is commonly observed in terrestrial calderas 1 of the Olympus Mons caldera complex formed as a [Williams and McBirney, 1968; Smith and Bailey, 1968]. It is consequenceof subsidencerelated to magma chamber with- not clear to what extent stress would be transmitted across drawal, then at the time of subsidencethe magma chamber such a structure, so we consider the limiting case of a must have been located within the volcanic edifice. perfectly frictionless fault which effectively isolates the Analyses of magma chamber depth for a number of crater floor from the surroundingvolcanic edifice. Analytical terrestrial intraplate volcanic islands indicate a shallow solutions for loading of circular plates [Timoshenko and reservoir between 2 and 4 km beneath the summit [Chevalier Woinowsky-Krieger, 1959] show that the radial stress for a and Verwoerd, 1988]. In addition, magma chamber depths plate that is welded to its surroundingswill be modified from for Iceland's Krafla [Tryggvason, 1986], and Hawaii's that for a freely floating plate if a remote stressis transmitted Mauna Loa [Zucca et al., 1982] and Kilauea [Ryan et al., across the boundary. However, for remote stresses to be 1983; Decker, 1987; Klein et al., 1987; Thurber, 1987; Ryan, important, they must be similar in magnitude to those for 1988; Delaney et al., 1990; Yang et al., 1992] volcanoes are magma chamber depressurization and accumulate on com- approximately 2-5 km. In a volcano, magma ascendingfrom parable timescales. partial melt zones at depth decreases in density due to One possible source of remote stress is flexure of the decompressionand, at shallow depths, volatile exsolution. underlying lithosphere due to the load of the volcanic edifice. The density of volcanic country rock increases with depth At times shortly (compared to the Maxwell time of the due to compaction associated with the weight of the over- asthenosphere)after an episode of significantshield building, burden. The depth of terrestrial magma chambers has been the near-summit stress field would not be significantly al- interpretedto represent a state of neutral buoyancy at which tered by flexure [McGovern and Solomon, 1990]. However, the density of ascending magma equals the density of the at later times, the most compressive stress axis near the surroundings[Rubin and Pollard, 1987;Ryan, 1987; Walker, summit becomes nearly horizontal [McGovern and So- 1988]. Since the distribution of compaction with depth lomon, 1990], which would cause the radial stress calculated depends on the lithostatic pressure, the depth to a given in our models to become more compressional.Superposition compaction state will scale inversely with gravity [Wilson of stressesdue to depressurization and flexure would shift and Head, 1990]. With appropriate scalingfor the difference the transition from compression to extension farther from in gravity between Mars and Earth, the 2-5 km range of the center of the crater, which would require a shallower terrestrial depthswould correspondto an approximaterange magma chamber than indicated by Figure 6 to explain the of 5-13 km for Martian magma chambers. This gravity- observed transition from compression to extension. How- scaled depth range is in good agreement with our calculated ever, the time scale for the accumulation of flexural stresses depth range of d -< 16 km, which suggeststhat if the is likely to have been much greater than that for magma densities of melt and country rock on Mars are generally chamber depressurization. For flexure to have contributed similar to those on Earth, then the depth of the Olympus to modifying the stressfield examined in this study, depres- Mons magma chamber may have been controlled by neutral surization would have had to occur at a presently indeter- buoyancy as well. The allowable range of magma chamber minate time after flexural stresseshad begun accumulating. depths is much shallower than the estimated depth of Mar- tian primary melts of 140-200 km [Carr, 1973; Blasius and Cutts, 1976; Thurber and Toksoz, 1978; Bertka and Hollo- Implications of Model Results way, 1987]. This result, in combination with photogeologic Solutions for ellipsoidal chambers with a variety of force evidence for multiple eruptions and summit collapse epi- distributionsas well as those invoking simple line sourcesdo sodes [Greeley and Spudis, 1981; Mouginis-Mark, 1981; not yield significantlydifferent stresscrossover points. This Mouginis-Mark et al., 1992], suggests that magma which result, in combination with the insensitivity of the model to formed in a partial melt zone at depth was transported to a a wide range of chamber aspect ratios (Figure 7), unfortu- shallow subsurface reservoir where it fed intermittent erup- nately indicates that the state of stressimplied by the surface tions. If this scenario is viable, then the structure and tectonics does not provide useful constraintson the relative magmatic transport process of Olympus Mons may be fun- geometry, volume, or degree of depressurization of the damentally similar to those of terrestrial volcanoes such as magma chamber. Determination of these quantities would the Hawaiian shields. require detailed models of eruption mechanics[e.g., Spera, 1984; Wilson and Head, 1988] and geodetic measurements of Terrestrial Subsidence Studies surface displacements[e.g., Dvorak et al., 1983], neither of which are available for Martian volcanoes. One of the best-known examples of tectonic features For the range of models that we have examined, parame- associated with deflational subsidence of a subsurface mag- ter uncertaintiestend to shift the calculateddepth of the top matic reservoir on Earth are the "ring dikes" that have been of the magma chamber to shallower levels than indicated by mapped within the Cullin intrusive complex in Skye, Scot- our baseline model (Figure 6). This trend holds for plausible land [Anderson, 1936]. Ring dikes consist of narrow, out- ranges of values of density and Poisson's ratio. We therefore ward sloping, concentric intrusions that surroundindividual considera value of 0.5Rc (16 km) to be an upper limit of the plutonic complexes. These structures were hypothesized to depth of the magma chamber. Because of the nature of the have formed along zones of maximum shear stress associ- observational constraints and the model behavior, it is not ated with deflation of a subsurfacemagmatic reservoir. The possibleto reliably define a lower limit, so we conservatively peripheral graben within crater 1 of Olympus Mons are assumethat all depths -<16 km are allowable. The summit of characterized by a sense, orientation, and spatial position Olympus Mons rises 27 km above its surroundings [Wu et that could plausibly correspond to a surficial manifestation al., 1986]. Thus if concentric ridges and graben within crater of the ring dikes described by Anderson. However, the ZUBER AND MOUGINIS=MARK:OLYMPUS MONS CALDERASUBSIDENCE AND MAGMA CHAMBERDEPTH 18,305 ground surface on which the ring dikes are exposed at Skye ical properties, and manner of depressurization of the is erosional and thus does not correspondto the surface that magma chamber may have contributed. existed at the time of the deflation event. Anderson [1936] expressed uncertainty concerning whether the ring fractures SUMMARY in the Skye region extended to the ground surface at the time of formation. In contrast, the floor of crater 1 at the summit If certain ridges and graben, shown in Figure 2, formed as of Olympus Mons shows little evidence of erosion, from a consequence of subsidence of the floor of the Olympus which we infer that features currently at the surface formed Mons caldera in response to deflation of the underlying in its vicinity. Consequently, it is not clear whether or not magma chamber, then the stress field implied by these the features within crater 1 formed in a manner analogousto features can be used as a constraint on models to investigate those at Skye. the gross characteristics of the chamber. Application of a Most other terrestrial deflational subsidence studies focus linearly elastic, axisymmetric finite element model to deter- on surface displacements rather than surface stresses[e.g., mine elastic stresses in the vicinity of a volcanic summit Mogi, 1958], as the former observation is more diagnosticof demonstrates that a broad range of magma chamber aspect a particular subsurface source geometry. Unfortunately, ratios and pressure distributions can produce surface stress ground displacementdata is not available for volcanic struc- fields consistent with the observed pattern of tectonic fea- tures on Mars. tures. Therefore the relative geometry, volume, and details of the pressurization of the magma chamber cannot be confidently constrained on the basis of stressesalone. How- Summit Tectonics of Other Major Martian Shields ever, the surface stress field is sensitive to the width and The summit area of the volcano Alba Patera is perhapsthe depth of the chamber; the width of the chamber trades off second most interesting locus of volcanic edifice tectonism with its depth such that a wider chamber implies a shallower on Mars. Despite the low elevation of this structure com- depth. The constraint that the chamber cannot have been pared to other major shields, the appearance of the caldera significantly narrower than the crater, and observations of complex is essentially shield-like [Wood, 1984]. Multiple the distribution of tectonic features within the crater, con- collapse events were associated with the formation of two strain the depth to the top of the Olympus Mons magma discrete calderas [Mouginis-Mark et al., 1988]. Large wrin- chamber at the time of subsidence to have been _<16 km. kle ridges are found both on the caldera floor and radial to This depth range suggeststhat if the densities of melt and the summit region. Circumferential graben also bound the country rock associated with terrestrial and Martian shield approximate border of the summit as defined by the two volcanoes, respectively, are similar, then the chamber calderas. Without good topographicinformation, however, it formed at the level where ascendingmagma and surrounding is not possible to infer the locations and/or magnitudes of rocks were gravitationally stable. A magma chamber at this subsidenceevents for the volcano. Such a study should be depth would have been located within the Olympus Mons possible with topographic information to be obtained in the edifice, at a level much shallower than the probable source upcoming Mars Observer Mission [Zuber et al., 1992]. depth of Martian primary magmas. Thus the general model Pavonis Mons also displays radial ridges within its caldera for the internal magmatic plumbing system of many terres- and circumferential graben outside the rim [Crumpier and trial volcanoes [Eaton and Murata, 1960], i.e., a deep source Aubele, 1978]. The positions and orientations of some of the of partial melt which ascends to a shallow magma chamber ridges and graben of these shields can be consistent with a that fuels episodic eruptions, may describe Olympus Mons stage of postcollapse subsidencecomparable to that which as well. we postulate for Olympus Mons. The summit caldera of Ascraeus Mons consists of eight separate craters. The floor Acknowledgments. We thank Lionel Wilson and Bruce Marsh of the largest and youngestcrater contains very small ridges for helpful discussions, Mark Robinson for the photoclinometric of probable tectonic origin, while the edificejust outsidethe measurementsof caldera topography, and George Wyatt for writing crater rim exhibits mare-type wrinkle ridges and circumfer- the graphicsdisplay software. We also thank Jay Melosh for making ential graben [Mouginis-Mark, 1981]. The summit caldera of available the TECTON finite element code and for answering numerousquestions concerning its use. MTZ acknowledgessupport Arsia Mons is infilled with flows of probable volcanic origin from the NASA Planetary Geology and Geophysics Program and and no tectonic features are visible on the floor, though The Johns Hopkins University Space Grant Consortium. P.M.-M. circumferential graben occur outside the rim [Crumpier and was supported by grant NAGW-437 from the NASA Planetary Aubele, 1978]. 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