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Icarus 165 (2003) 242–252www.elsevier.com/locate/icaru

Phreato-magmatic dike–cryosphere interactions as the origin of smridges north of Olympus Mons, Mars

Lionel Wilsona,b and Peter J. Mouginis-Markb,∗

a Environmental Science Department, Institute of Environmental & Natural Sciences, Lancaster University, Lancaster LA1 4YQ, UKb Hawaii Institute of Geophysics and Planetology, University of Hawaii at Manoa, Honolulu, HI 96822, USA

Received 30 June 2002; revised 22 April 2003

Abstract

Using images from the Mars Orbiter Camera, we have identified several linear ridges located 10–60 km north of the volcanoMons, Mars, at the edge of the Olympus Mons aureole materials. These ridges appear to be made of unconsolidated material by vmany dust avalanche scars seen on their upper slopes. Based upon their morphology (several ridges have crater-like central deprsuperposition relationships, the ridges appear to have formed very recently and post-date the formation of the youngest lava floover the northern escarpment of Olympus Mons. Several possible origins for the ridges, including an eolian, periglacial, or deorigin have been considered, but we favor a ridge origin by a series of small explosive eruptions initiated by the intrusion of aa volatile-rich substrate. To explore this process, we develop a numerical model for dike intrusion into a volatile-rich substrate thplausible dike widths between 2.4–3.5 m. The total volume of a single ridge system is∼ 65× 106 m3, and we calculate that it may havtaken only a few minutes to form. Viable solutions only exist when the thicknesses of the ice-rich layer is less than∼ 1000–2000 m. Thisstrongly suggests that the ice-rich region is limited in its vertical extent to a value of this order. 2003 Elsevier Inc. All rights reserved.

Keywords:Mars, surface; Volcanism; Geological processes

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1. Introduction

Since its discovery by Mariner 9, the aureole of OlympMons volcano has been recognized as an enigmatic feon Mars (Masursky, 1973; Carr, 1973; Harris, 1977). Fran analysis of the ridge, graben and fracture patterns oaureole material Lopes et al. (1982) and Francis and Wa(1983) proposed an origin by gravity sliding of the ouflanks of the Olympus Mons edifice. Using high resolut(6.85 m pixel−1) Mars Orbiter Camera (MOC) images, whave conducted an initial survey of the aureole and hidentified several very young linear ridges at a locationnorth of the Olympus Mons escarpment at 24◦ N, 133◦ W(Fig. 1). These ridges appear to be made of unconsolidmaterial and, based on their morphology, we infer that twere produced by recent explosive volcanism. This exsive activity must have been recent, because the ridges

* Corresponding author.E-mail address:pmm@higp.hawaii.edu (P.J. Mouginis-Mark).

0019-1035/$ – see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/S0019-1035(03)00197-0

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formed on top of young lava flows from Olympus Mons (uAom2, Scott et al., 1981).

In this analysis, we first describe the distribution and mphology of the ridges. We then develop a numerical mofor their formation that involves the intrusion of a shallodike into ground containing volatiles. Our preferred moinvolves small-scale phreato-magmatic eruptions thateach have lasted only a few tens of minutes. By virtuetheir young age, these ridges have implications not onlyour understanding of explosive volcanism on Mars, but afor the distribution of subsurface volatiles relatively recenin martian history. They also suggest a new mode of fortion for at least some of the segments of the aureole.

2. Observations

Topographic data from the Mars Orbiter Laser Altime(MOLA) indicate that the base of the Olympus Mons escament is at an elevation of about−1300 m. A series of lobatlava flows can be found just north of the Olympus Monscarpment (Fig. 2), and these flows dip towards the north

Dike-cryosphere interactions on Mars 243

hef Mars.

Fig. 1. Location of the main study area discussed here. The field of view is 22.7◦–25.5◦ N, 130.2◦–136.5◦ W. Inset shows the location of larger image on tnorthern flank of Olympus Mons volcano. Main image shows the location of Fig. 2. Base image is the US Geological Survey Digital Image Model o

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experience an elevation change of∼ 800 m over a distancof 60 km. These flows are morphologically similar to maexamples seen in the Tharsis (Moore et al., 1978) andsium Planitia (Mouginis-Mark and Yoshioka, 1998) regioof Mars. Within 10 km of the base of the scarp there isfirst of several linear ridges aligned ESE–NNW (Fig. 3). Tmost striking attribute of this ridge is that it is constructon top of the lava flows, and so is very young. Three diffent flow boundaries can be traced from the south side oridge and connected with flows north of the ridge (Fig.None of the lava flows appear to have been diverted byridge as they flowed northward, and thus our interpretais that the ridge did not exist at the time that the flows wemplaced.

The ridge is∼ 4.15 km long and has a maximum widof ∼ 1 km (Fig. 3). There are several low-albedo scarsthe sides of the ridge, which are interpreted to be recentslides (Malin and Edgett, 2001). These slides imply thatridge is most likely made of unconsolidated material.have estimated the ridge volume by approximating its shas three adjacent segments, each having a triangularsection, with lengths 1.35, 0.95, and 1.85 km, respectivThe average basal width of each section is obtained direfrom the image (440, 670, and 900 m, respectively). Tsides of these ridges facing away from the Sun all appto be just going into shadow, so that their slopes musclose to the elevation of the Sun, which is 6.83◦. The heightsof the ridge segments are therefore approximately equhalf the width multiplied by the tangent of 6.8◦, i.e., 26, 40,and 54 m, respectively. The volumes of the individual ridsegments are thus 7.8, 12.8, and 44.9× 106 m3 and the totalvolume of the ridge system is∼ 65× 106 m3.

Additional examples of linear ridges can also be fouat distances up to 60 km from the base of the OlymMons escarpment (Fig. 4). Unfortunately, we cannot demine whether all of these ridges formed on top of the ba

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material as no lava flow lobes can be identified at the noern end of our study area. While some of these ridges hthe same linear shape (e.g., “b,” “c,” “f” and “h” in Fig. 4there is also a diversity of shapes. Some of these ridgescentral depressions. In particular, example “d” has a cendepression that is∼ 3.4 km wide and it is apparent from thshape of the landslide scars that the floor of the depressisignificantly higher than the surrounding ground. Only ifew rare instances (e.g., Fig. 4d) do we see any stratificaon the upper walls of these ridges, so that in most casesinferred that the entire unit is uniform in character. Wefer that the features “d” and “g” in Fig. 4 may be explosicraters. The ridges have two dominant trends, with rid“c,” “h,” and “i” oriented NE–SW rather than following thESE–WNW alignment of the other examples.

A common characteristic of the ridges is that they all hdust avalanche scars on their sides, implying that theyconsist of friable materials. However, there are no dunethe adjacent lava flows, suggesting that, although the mial is friable, it is difficult to transport more than a few teof meters in the martian winds. This probably implies tthe typical sizes of the clasts forming the surface layerthe ridges are at least several mm in diameter (see Fig.in Greeley and Iversen, 1985).

Topographic features with this young age are intriguiWe have considered several possible mechanisms forformation, but all but one model (small-scale explosive vcanism) appear to be untenable. For instance, becausridges lie close to the Olympus Mons aureole, their oricould be closely tied to the formation of the complex terrthat forms the aureole. But no real consensus appears tist as to the origin of the aureole, although giant landsdeposits (Lopes et al., 1982) most easily explain the apent concentric pattern of lobes. The two dominant treof the ridges considered here could be due to them bthe exposed upper surfaces of an aureole lobe that has

244 L. Wilson, P.J. Mouginis-Mark / Icarus 165 (2003) 242–252

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Fig. 2. Distribution of the lava flows and ridges discussed in the text.is a single MOC image, which runs from the bottom left to top right ofpage (see Fig. 1 for context). Certain features are replicated in both colto facilitate an overview of the whole swath. Each part of the image is pawith a sketch map showing the location of the lava flow boundaries (with barbs showing down-throw) and the superposed ridges (in black)extreme northern segment of the Olympus Mons escarpment is shomid-tone at the bottom of the left hand image. The locations of Figand 4 are indicated. North is towards the top of the image. MOC imSP2-46605, courtesy of NASA/JPL/MSSS.

Fig. 3. Close to the escarpment, the veneer of fine material is sufficithin to allow numerous lava flow fronts to be identified. The general trof these flows is from the bottom to top of image. Within 10 km ofescarpment, a linear ridge has formed on top of the flows. The best exaof such a ridge on these flows is shown here. Note how the edge owestern flow is buried on the eastern side (letters “A”), and how the nortpart of the eastern flow appears from beneath the ridge (letters “B”). Nof the flows shown here appear to have been diverted by the ridge, swe interpret this relationship to mean that the ridge was formed afteflows by explosive volcanism. Dust shoots are shown on the ridge. Nis towards the top of the image. Part of MOC image 46605; see Fig.location.

almost totally buried by lava flows from Olympus MonHowever, our close inspection of the ridges shown in Fifails to reveal any indication that the lava flows embapre-existing ridges. At MOC resolution (∼ 6 m pixel−1), theflow features that can be identified on the lava flows alldicate that the flows were not diverted around the ridge.possible that talus slopes on the ridges may have burieinterface between flow and ridge; nevertheless, if the ridpre-dated the lava flows then we feel that there wouldstrong morphologic evidence for diversion of the later floThis evidence does not exist, and so we conclude tharidges formed after the flows, making a landslide originthe ridges untenable.

Eolian dunes are common features on Mars at the sof MOC images (Malin and Edgett, 2001) and often ovlie relatively young units. However, we find no morpholoevidence to suggest that the ridges are eolian in origin.

Dike-cryosphere interactions on Mars 245

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Fig. 4. Numerous small peaks can be found north of the Olympus Mescarpment. Note that all of these peaks show signs of being superon the underlying basement, but that their volcanic origin cannot befirmed. However, several characteristics are common to these peaks, ining (a) a general linear trend either ESE or ENE, with a central “spinemost of the peaks; (b) the pervasive occurrence of talus dust shootsplying an unconsolidated material; and (c) two examples (d) and (genclosed structures suggestive of craters. North is to the top of eacage, which are all to the same scale. See Fig. 2 for location of each isegment.

ridges lack the typical crescent shape, and there is no ametry between the leeward- and windward-facing slopesaddition, no smaller-sized dunes are observed in the aThe two dominant trends in the ridges studied here woalso require winds from two different directions.

An origin by periglacial processes has also been conered. Eskers are ridge-like structures that form at the bof terrestrial glaciers and several strong candidate exples have been identified on Mars (Kargel and Strom, 19Ridges may also form as moraines deposited by retrea

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ice sheets. We discount the idea that the ridges under shere are formed by periglacial processes because oflarge widths and the fact that they lie within 25◦ of theequator, where recent surface ice seems highly unlikelyalso considered and eliminated other geomorphic proceFor example, this part of the aureole has been proposea paleo-shoreline for a polar ocean (Parker et al., 19so that a depositional origin comparable to tombolos mhave been possible. However, tombolos on Earth, andpossible martian equivalents, are narrow (100 m to 2 khave less relief than the ridges studied here, and joinadjacent high points (Parker et al., 1993). A similar sproblem exists if the origin of the ridges is similar to thof the “thumbprint” terrain seen in Isidis Planitia (Kargelal., 1995; their Fig. 1c). Thumbprint ridges may be depotional features, are typically 0.5–2.5 km wide and 1–40long but only 10–200 m high, making them typically smalthan the Olympus Mons ridges. In view of the above mtioned problems in forming the ridges by other geomorpprocesses, we conclude that ridge formation by local exsive volcanism is the most plausible mechanism for proding these ridges. We now present a conceptual model forprocess.

3. Conceptual model of ridge formation

We propose that the ridges shown in Figs. 3 and 4 wformed by small explosive eruptions initiated by thetrusion of a dike into a volatile-rich substrate. In thisstance, the interaction between a dike and ground ice/wis suggested by the linear nature of the features. Suprocess has been proposed for other areas of Mars (Sqet al., 1987), and several other investigations have splated on the effects of interactions between intruded dor sills and ground ice deposits on Mars (e.g., Allen, 19Scott and Wilson, 1999; McKenzie and Nimmo, 1999; Wson and Mouginis-Mark, 2003).

We infer that the small volume of the linear ridges,described in the previous section, implies small-scale etions, since no signs of flow away from any construct cbe identified. Thus the entire volume of erupted materiacontained within the observed ridges.

We propose the following scenario for ridge formati(see Fig. 5), consistent with the above features. A dike progates to shallow depth in an area containing a sub-horizolayer of ice which fills the pore space in the country roGiven estimates of the vertical extent of the zone in whice will be stable at this latitude and elevation (Mellonal., 1997), we assume that the ice may be present fromthe surface down to a depth of∼ 1 km. This is, of coursemuch deeper than the ice layers detected by the GRSperiment on the Mars Odyssey spacecraft (Boynton et2002), which only measured ice in the regolith to a deof a meter or so, and gave no information of relevancethe eruption model presented here. As the dike reaches

246 L. Wilson, P.J. Mouginis-Mark / Icarus 165 (2003) 242–252

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Fig. 5. Sketch of dike in relation to country rock (a) before surface bthrough; (b) shortly after surface breakthrough; (c) part way througheruption; (d) after activity has ceased.

given depth (Fig. 5a), heat begins to be exchanged atlevel between the magma and the surroundings, leadinchilling of the magma near the dike wall and melting ofadjacent ice. As long as there is significant interconnecbetween pores, the resulting water carries heat convectto more distant ice (Ogawa et al., 2002). At the same tisome of the water in contact with the dike begins to band the resulting phase change to lower density produchigh pressure in the vapor, causing some shattering ocountry rock fabric and improving heat transfer to the iIn principle this pressure increase could be very largetook place at constant volume; however, some of the srequired to accommodate the vapor is obtained by comping bubbles of CO2 gas which will have exsolved from thmagma as it nears the surface. Eventually the dike reacshallow enough depth that the high pressure causes shing to extend as far as the surface and an explosive dischof steam, juvenile magma and shattered country rock be(Fig. 5b). Removal of near-surface material exposes unlying layers, so that an expansion wave spreads downinto the system allowing successive layers to begin tocelerate upward (Fig. 5c). The duration of the whole evis the sum of the time required for the expansion wavepropagate to the bottom of the ice-rich layer and the timequired for material excavated from the maximum depthreach the surface. We shall estimate these timescalesalso discuss the final state of the system after activity e(Fig. 5d).

4. Numerical model of ridge formation

4.1. Magma–host rock interaction

The starting point for our analysis is an estimate ofmaximum pressure reached by the water vapor create

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heat is transferred from the intruding magma to therounding ice-rich rocks. This can be assumed to be not mgreater than the breaking strength of these rocks, wshould lie in the range∼ 0.5 to 20 MPa, depending owhether failure is in tension or compression. We adopt aries of pressures within this range and for each we determthe equilibrium temperature of the water vapor,Te, as fol-lows. Let the masses of magma, ice, and country rock winteract thermally bemm, mi , andmc, respectively. Then after equipartition of all the sensible and latent heat,Te is givenby

mmcm(Tm − Te)=mi[ci(Tf − Tz)+H

]

(1)+ αmccc(Te − Tz)

whereTm is the magma temperature (∼ 1400 K for a maficmagma);Tf is the freezing point of water (∼ 273 K);Tz is themean temperature of the crustal rocks (we adopt 250 K);cm,ci , andcc are the specific heats of magma, ice, and courock,∼ 1000, 2000, and 1000 J kg−1 K−1, respectively; H isthe enthalpy of water between the ice point andTe, avail-able from standard tables (ICT, 1933); andα is the fractionof the incorporated country rock which is in good thermcontact with the magma and therefore experiences sigcant heating on the timescale of the interaction. For epermutation of the values ofmm, mi , andmc we calculateTe and then determine the mass fraction of vapor in thesulting mixture of explosion products, by definition given[mi/(mi +mm +mc)]. If we assume, for example, that icfilled pores occupy one tenth of the volume of the counrock, that the (void-free) rock density isρc = 2900 kg m−3,that the (bubble-free) magma density isρm = 2600 kg m−3,and that the ice density isρi = 917 kg m−3, then the ratioof country rock mass to ice mass ismc/mi ≈ 28.5. Then ifequal volumes of magma and country rock interact, the mfraction of water vapor is 0.017, i.e., 1.7 mass %.

4.2. Expansion of explosion products

Next we determine the amount of internal energy whis released during the decompression of the water vappressureP down to either the ambient martian atmosphepressurePa or the pressurePc at which water vapor condenses or freezes, whichever is encountered first. Strspeaking, the mass fractions of any magmatic gases thatbeen exsolved prior to the explosion or that become exsoduring the decompression process should be added tvalue of n given by (2). There are no direct estimates ofvolatile contents of martian magmas, but if we assumewe are dealing with basaltic to andesitic magmas, as selikely (McSween et al., 1999), then we can plausibly uGerlach’s (1986) study of the basaltic magma reservoiKilauea Volcano, Hawaii, to suggest that 0.27 mass % H2O,0.06 mass % CO2, and 0.07 mass % S might be a reasable magma volatile inventory. Allowing for their molecuweights, these amounts of volatiles would correspond to

Dike-cryosphere interactions on Mars 247

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equivalent of 0.67 mass % H2O, i.e., 0.0067 mass fractionand so we add this proportion of the magma mass toevaporated ice mass to yield a final expression for the mfraction of water vapor in the explosion products,n:

(2)n= [(mi + 0.0067mm)/(mi + 1.0067mm +mc)

].

The internal energy per unit mass,E, available for con-version to the kinetic energy per unit mass of the explosproducts is given by (e.g., Wilson, 1980; Fagents and Wson, 1996)

E = n(Q/m)[γ /(γ − 1)

]Te

[1− (Pc/P )

[(γ−1)/γ ]]

(3)+ {[(1− n)(P − Pc)

]/ρm

}

whereQ is the universal gas constant (8314 J kmol−1 K−1),m is the molecular weight of water (18),γ is the ratio ofthe specific heats at constant pressure and constant voof water vapor (1.30),ρc is the mean density of the mamatic and country rock solids (taken as∼ 2600 kg m−3), andPc is the pressure at which the vapor condenses, thus tenating the gas expansion process. BecausePc is a functionof temperature, it is necessary to follow the vapor expsion numerically from the initial conditions(P,Te) until thecondensation curve is reached at(Pc, Tc). The relationshipbetweenPc (in Pa) andTc (in K) is given to sufficient accuracy by

log10Tc = 2.55688568− 0.0648148709 log10Pc

(4)+ 0.0135262194(log10Pc)2

where the coefficients were obtained by fitting a secondder polynomial to published experimental data (ICT, 193GivenE from Eq. (3), the mean velocity,V , of the explosionproducts is obtained by equating the internal energy relto the kinetic energy of the products:

(5)E = 0.5V 2.

Finally the maximum range,R, to which the fragments catravel is given by

(6)R = [V 2 sin(2θ)

]/g

where we have taken the angle of ejection from the vtical, θ , as 3 degrees on the grounds that most of theplosion process consists of material traveling to the surfrom great depth within the dike system and hence eming at the surface in a rather strongly collimated fashEquation (6) assumes that the fragments experience ngible atmospheric drag, which is not automatically a sassumption for Mars despite the low atmospheric presand density. In an earlier model of transient explosivetivity on Mars, Fagents and Wilson (1996) showed thatabrupt, short-lived, explosions the martian atmospherean important influence on the ranges of even meter-sejecta. However, in the present case we are dealing witexplosive discharge which continues for at least severalof seconds (see below), and so only the first-ejected c

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are subject to atmosphere drag; once a relatively steadycharge has been established, the atmosphere has beentively “pushed out of the way” of the bulk of the subsequmaterial.

4.3. Efficiency of magma–host rock interaction

In order to proceed with the analysis, we need to ada value forα, the fraction of the country rock materialgood thermal contact with the magma and water vapor. Iftimescale for the interaction of magma and host materiτ , heat will penetrate into an equant clast to a depthλ givenby λ = (κτ )1/2 whereκ is the thermal diffusivity, withinabout 30% of 10−6 m2 s−1 for all silicates. If the clast sizeis greater than 2λ, only about one half of the clast is signiicantly heated. The relevant timescale for most of the clis the time from the moment when they first come intotimate contact with the magma or the water vapor to wthey are ejected. Once the explosive process begins, thefor excavation of material will be only a few tens of seconas we shall demonstrate shortly; however, some of the mrial deep in the system will have been in close contact wthe intruding dike for the time required for dike propagatover a vertical distance of∼ 1 km at a speed of perhaps 0m s−1 (Wilson and Head, 1981, 1994), i.e., up to a mamum of∼ 3000 s. Using 1500 s as an average impliesλ is ∼ 40 mm, whereas using, say, 20 s for shallow marial implies λ ∼ 4.5 mm. The median sizes of ejecta fromost phreato-magmatic explosions on Earth (see summin Wohletz, 1983) are concentrated between 0.1 and 3although both very coarse and very fine particles areproduced. The same size range is likely to apply to Msince the magma-volatile interaction process in this kinderuption is not a function of gravity or atmospheric pressuThe above thermal calculation then suggests that virtuallof the clasts produced will be in good thermal equilibriuwith the heat source, implyingα ≈ 1. However, the important factor here is the mass distribution, which differs frthe size distribution in that the mass is proportional tosize cubed, so that a numerically small proportion of laparticles can represent a significant fraction of the total mWe therefore conservatively assume a value ofα = 0.5 forthese events.

The size distribution of ejected clasts also has a beaon the assumption in Eq. (5) that the gas and all of the rfragments travel at the same speed. This is not a goodsumption if most of the ejected clasts are sufficiently coaThe vertical velocity of clasts will be less than the gas spby an amount equal to the terminal fall velocity of the clin the gas and so the gas and small clasts travel fasterthe speedV given by Eq. (5) whereas the coarse clasts tramore slowly (Wilson, 1999). However, given the above srange for ejecta from phreato-magmatic explosions, themajority of clasts will have terminal velocities (calculatedthe appropriate temperatures and pressures using theods of Walker et al., 1971) in the volcanic water vapor l

248 L. Wilson, P.J. Mouginis-Mark / Icarus 165 (2003) 242–252

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4.4. Results

Given the above assumptions and caveats, Table 1 sthe results of this analysis for an illustrative explosion prsure ofP = 3 MPa and Fig. 6 summarizes the maximejecta ranges for several values ofP . The following patternsare seen. First, as the assumed initial pressure increaserange of values ofmm/mi (the ratio of magma mass to icmass) for which explosions are possible decreases; spcally, small values ofmm/mi are progressively eliminatedi.e., a larger proportion of magma is required to causeexplosion. Furthermore, for a given value ofmm/mi , theejection speed, and hence the range, decrease asP increasesThis counter-intuitive effect is due to the shape of the cdensation curve: condensation, and hence the end of gapansion, sets in proportionately earlier at large values oP .Most important, however, is the fact that for all the permu

Table 1For a pre-explosion pressure of 3 MPa and a series of values ofmm/mi ,the ratio of magma mass to ice mass involved in the explosion provalues are given for the temperature of the mixture after thermal interabetween magma in a dike and it surroundings,Te; the ratio of magma masto country rock mass,mm/mc, corresponding tomm/mi ; the implied massfraction of the explosion products which consists of water vapor derfrom the ice and the magma,n; the pressure at which gas expansion frthe initial pressureP stops,Pc; the velocity of the ejecta after acceleratiby the expanding gas,V ; and the range,R, reached by the ejecta whelaunched at 3 degrees from the vertical

mm/mi Te mm/mc n Pc V R

(K) (MPa) (m s−1) (m)

8.0 513 0.281 0.028 2.73 35 359.0 548 0.316 0.028 1.72 85 20

10.0 581 0.351 0.027 1.17 110 3312.5 656 0.439 0.026 0.56 146 5915.0 711 0.527 0.025 0.32 166 7720.0 806 0.703 0.023 0.16 189 9925.0 878 0.878 0.021 0.10 200 111

Fig. 6. Maximum ejecta ranges as a function of the magma to ice massmm/mi , for several values of the initial water vapor pressure,P ; each curveis labeled by the value ofP in MPa.

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Table 2Example of solution for larger ridge

Z (m) Pd (MPa) K (MPa m1/2)

1000 16.2 5001500 12.5 4622000 10.5 4362500 9.0 4063000 7.8 3693500 6.6 3194000 5.5 2564500 4.2 1775000 2.9 815500 1.5 −34

For a thickness,X, of the ice-rich layer intersected by the upper part ofdike equal to 1000 m, values are given as a function of the half-height odike, Z, for the implied excess pressure in the dike magma,Pd, obtainedfrom Eq. (9) and the stress intensity,K , at the upper dike tip implied bEq. (10).

tions of P andmm/mi , ejecta ranges are predicted to be ato several hundreds of meters, entirely consistent withobserved half-widths of the ridges we are modeling, whare in the range 220–450 m (Figs. 3 and 4). The impltion is that the explosive interaction is capable of producridges with the observed widths without having to invoimprobably high pressures or improbably large sub-surice contents.

The values ofP , Pc, andn in Table 2 and Fig. 6 can bused to determine the timescale of the eruption. The sof sound in the mixture of gas and rock fragments as it rto the surface is found, using the methods given by Kie(1977), to be∼ 90 m s−1. The expansion wave decompreing the mixture will travel at roughly half of this spee∼ 45 m s−1 (e.g., Knudsen and Katz, 1954), and so will ta∼ 20 seconds to travel the 1000 m to the base of therich region. The acceleration of the fragments occurs qrapidly to reach a final upward speed within a factor of 270 m s−1. This enables them to reach a maximum rang440 m, and the travel time from 1 km depth at∼ 70 m s−1 is∼ 15 seconds. The additional time required for fragmentreach their final ranges is a further few tens of seconds. Tthe entire event probably requires between 1 and 2 minu

4.5. Implication for dike dimensions

We now examine the implications of the model for tsizes of the dikes required. If we accept the model pretions at face value, the fact that the observed ridges exfor 220–450 m from their axes would imply thatmm/milay between about 7 and 10 for small values ofP and be-tween about 12 and 15 for large values ofP . Using thesame assumption as that made earlier, that ice fills pore soccupying 10% of the volume of the country rock so tmc/mi = 28.5, these values would imply that the mass raof magma to country rock,mm/mc, lay between 0.25 an0.35, or between 0.4 and 0.5, respectively. Consider Fiwhich is an elaboration of Fig. 5d. We assume that theis relatively uniform along most of its horizontal length a

Dike-cryosphere interactions on Mars 249

ons.

ein

these inethe

f theter-

, athal-cksnd ad-f theer

this-tthehanitycturethess

ushe

e

ikelvedingma

ong

ed

alld of, if

d

m-hat

ail-

ve

idthtotal

b-ges,

ies

fterould

uti-airofce)

val-d

Fig. 7. Sketch of the geometry of the dike used in the volume calculati

has a vertical extentX (which we assumed earlier to b∼ 1000 m) within the ice-rich zone. The dike tapers withthe ice-rich zone as indicated, with its tip just reachingsurface. Its width at depthX is W and we assume that itshape is dictated by the elastic stresses imposed by thternal excess pressurePd, the gravitational load due to thmagma in the dike, and the external lithostatic load ofoverlying country rock with uniform densityρc. We inferfrom the general geometry and great horizontal extent oridges that the underlying dike has propagated mainly laally with its center trapped at a depthZ where the magmadensity is equal to the density of the country rocks, i.e.a neutral buoyancy level. This implies that at depths slower thanZ the magma is denser than the country robecause of the presence of country rock pore space adepths greater thanZ it is less dense; for the purpose of moeling this system we assume that the absolute value odensity difference,�ρ, is the same in the upper and lowhalves of the dike: for a magma density of 2600 kg m−3,a shallow country rock bulk density of 2300 kg m−3 and adeep country rock density of 2900 kg m−3 (values typicalof volcanic areas on Earth; Rubin and Pollard, 1987),would imply�ρ = 300 kg m−3. The dike is then symmetrical about its centerline at the depthZ, and its half-heighis numerically equal toZ. Because we are assuming thatdike extends for a much greater distance horizontally tthe extent of the region within which the explosive activhas taken place we can model it as a 2-dimensional struof effectively infinite extent along strike, with the dike widW being only a function of depth. It is convenient to exprthe shape of the dike in terms of the variablez= (Z−X)/Z.W is then given as a function ofz by (Pollard, 1976)

W = 2Z[(1− ν)/µ

][(Pd − P ′)

(1− z2)1/2

(7)− P ′z2 ln∣∣z/(1− (

1− z2)1/2)∣∣],whereν andµ are the Poisson’s ratio and rigidity modulof the country rocks,∼ 0.25 and 3 GPa, respectively, and t

-

t

quantityP ′ is given by

(8)P ′ = (g�ρZ)/π.

The cross-sectional area,A, of the dike between the surfac(wherez = 1) and any general value ofz is then found byintegrating equation (7) to be

A= 2Z2[(1− ν)/µ]

×[Pd

{(π/4)− (z/2)

(1− z2)1/2 − (1/2)sin−1 z

}

− (P ′/3){2− 2z− z

(1− z2)1/2

(9)− z3 ln∣∣z/(1− (

1− z2)1/2)∣∣}].The width of the zone of country rock around the d

(assuming that both have the same bulk density) invoin the explosive excavation process is found by notthat the ratio of the volumes of country rock and magis [(mc/ρc)/(mm/ρm)] = [(mcρm)/(mmρc)] and so the to-tal cross-sectional area (i.e., volume per unit length alstrike) of material involved in the explosion is(A{1 +[(mcρm)/(mmρc)]}). This material bulks on being excavatby some factorβ (which we assume is∼ 1.5), and so thecross sectional area of the available material is (βA{1 +[(mcρm)/(mmρc)]}). Some of the erupted material must fback into the vacated space (i.e., the vent) at the enthe eruption. The maximum amount that could fall backthe vacated region maintained its shape, would be(A{1 +[(mcρm)/(mmρc)]}), which would leave an above-grounamount of((β−1)A{1+[(mcρm)/(mmρc)]}). However, re-moval of the magma allows the nearby country rocks, copressed by the dike injection, to relax elastically so tsome fraction, which we assume to be∼ 0.5, of the dikevolume is not available to accommodate fallback. The avable sub-surface space then corresponds to the area(A{0.5+[(mcρm)/(mmρc)]}) and so the area of the deposit aboground is{A(β−1)[(mcρm)/(mmρc)]+A(β−0.5)} which,with β = 1.5, becomes{A(1+ 0.5[(mcρm)/(mmρc)])}. Thesmallest ridge segment has a height of 26 m and a total wof 440 m; the largest segment has a height of 54 m and awidth of 900 m. Thus their cross-sectional areas are∼ 5720and∼ 24300 m2, respectively. Table 1 shows that the oserved ejecta ranges, equal to the half-widths of the rid220 and 450 m, respectively, requiremc/mm to be 0.32 forthe small ridge and 0.385 for the large ridge; this implthatA≈ 1280 for the small ridge andA≈ 6230 for the largeridge. If we did not assume that the country rocks relax aexcavation of the dike material, these estimated areas wbe increased by 25 to 30%.

With these estimates of the values of A, we canlize Eq. (9) as follows. For any given choice of the pof variablesX andZ we can define the relevant valuez = (Z − X)/Z to insert into Eq. (9) and, since the choiof Z fixes the value ofP ′ via Eq. (8), we can solve Eq. (9for Pd. We can then impose a constraint on plausibleues ofPd andZ by noting that, if the dike is to be trappe

250 L. Wilson, P.J. Mouginis-Mark / Icarus 165 (2003) 242–252

ficro-

sgasthe,

ich7

ete

therfor

lues

esromer

dikeentbin,theustse,

ofsed

lau-forheaterers thaue

t (b)

nsvol-

ism,eran,arsbe

d onli-entavaalsohortientd a

ices. 1her

in the way we envisage, the stress intensityK at its uppertip must lie close to the apparent fracture toughnessK∗ ofthe country rocks which, for mafic dikes penetrating macountry rocks, is likely to lie somewhere between the zepressure laboratory value of∼ 3 MPa1/2 (Rubin, 1993a) andthe value of∼ 100 MPa m1/2 deduced for rift-zone dikeon Kilauea volcano, Hawaii, having small amounts oftrapped in their tips (Pollard, 1987; Parfitt, 1991). Forpresent dike geometryK is given by (Rubin and Pollard1987)

(10)K =Z1/2[Pd − 2P ′].Table 2 shows a typical example for the large ridge, whhasA = 6230 m2. If X is chosen to be 1000 m, then Fig.shows thatZ must of course be 1000 m or greater. IfK is tobe close to the above upper limit estimate of 100 MPa m1/2,then the values in Table 2 imply thatPd must be close to3.2 MPa and thatZ must be close to 4900 m; if instead wassume thatK should be close to the lower limit estimaof 3 MPa m1/2, thenPd must be∼ 2.0 MPa andZ mustbe ∼ 5400 m. This process can then be repeated for ovalues ofX, and finally the entire analysis is carried outthe smaller ridge segment.

Figure 8(a) shows the values of dike driving pressurePdrequired for a wide range of values ofX to causeK to beeither 100 MPa m1/2 or 3 MPa m1/2 for both ridges.Pd isseen to be constrained to lie between∼ 1.9 and∼ 3.4 MPafor the large ridge and between∼ 1.2 and∼ 3.5 MPa forthe small ridge. Figure 8(b) shows the corresponding vaof dike half-heightZ, which must lie between∼ 4.2 and∼ 6.0 km for the large ridge and between∼ 1.1 and∼ 3.8km for the small ridge. The maximum widths of the dikat their neutral-buoyancy center line depths are found fEq. (7) by settingz = 0; if K is chosen to be the smallvalue, both dike widths are less than 0.1 m, whereas ifK ischosen to be∼ 100 MPa m1/2, the widths are∼ 3.5 m forthe large ridge and∼ 2.4 m for the small ridge.

It is very tempting to assume that the larger value ofK,corresponding to the accumulation of gas in the uppertip, is more appropriate than the smaller value: all rectreatments of dike propagation (e.g., Lister, 1990; Ru1993b) make the point that a low pressure, buffered byexsolution of magmatic volatiles (most probably water) mexist in the advancing tip of any dike. If that is the cathen Figs. 8(a) and (b) imply a much narrower rangedike driving pressures, from∼ 2.8–3.5 MPa for both ridge(though the dike half-height is still only poorly constrainat ∼ 1–3 km for the small ridge and∼ 4–6 km for the largeridge). Furthermore, this assumption yields the more psible dike widths, 3.5 and 2.4 m. Finally, we note thatthis value ofK no viable solutions exist in the case of tsmaller ridge for thicknesses of the ice-rich layer grethan ∼ 1000 m and for the larger ridge for ice-rich laythicknesses greater than 2000 m. This strongly suggestthe ice-rich region is limited in its vertical extent to a valof this order.

t

Fig. 8. Graphs of the dike driving pressure (a) and the dike half-heighas a function of the thickness of the ice-rich layer,X.

5. Discussion

Our analysis of the MOC images of the Olympus Moaureole has revealed ridges on the northern flanks of thecano that appear to have formed by explosive volcanprobably the result of dike intrusion into a shallow layof ice-rich regolith. No other geomorphic process (eoliperiglacial, landslide, or shallow marine deposition) appeviable for their mode of formation. The ridges appear tovery fresh, made of unconsolidated material, and formetop of young lava flows from Olympus Mons. The impcation is that the dike intrusions took place in the recgeologic history of Mars, after some of the youngest lflows in the Tharsis region were emplaced. We notethat each explosive eruption would have been of very sduration, probably on the order of 2–3 minutes. Transphreato-magmatic eruptions of this kind would have hanegligible effect on the martian atmosphere.

Although Olympus Mons would be the obvious chofor the source of the dikes, the ridge orientations (Figand 2) imply at least two different igneous centers ot

Dike-cryosphere interactions on Mars 251

eralibletionver,

on-99;ad,unginim-tianpusnlyd toateralsoayasethethe

ur.Forani-ter-ur-rea,f acusthe

areto

thehinons

ust

veionscedif-al.rousnsel

usor-

de-in

ikebutto

s. Inent

ikesewof

plyof

thet fur-on-thism-

ifiedng

t al.,w?

waiily-nd

aretioncstion

. 84,

ear, 81–

2.n by

rsal

177–

ridge

. 82,

as-ent,

Geo-

em-hedn-

20,

haw,n in

than Olympus Mons. Most of the ridges have a genESE–WNW orientation, making Ascraeus Mons a posscandidate source. A few ridges have a NE–SW orientaindicating that Alba Patera might be the source. Howeboth Ascraeus Mons and Alba Patera are> 1700 km fromthe ridges, so that “mega-dikes” of considerable horiztal extent must be postulated (McKenzie and Nimmo, 19Scott and Wilson, 2002; Scott et al., 2002; Wilson and He2002). Thus our interpretation that the dikes are very yomay indicate that intrusive activity has continued withthese volcanic centers until very recently. A reason why silar ridges cannot be identified associated with other marvolcanoes may be that the plains to the north of OlymMons are at an unusually low elevation, and so it is ohere that sufficient cryosphere volatiles have accumulatecause the explosive eruptions. However, we note that wdischarge on the southern side of Olympus Mons hasbeen identified (Mouginis-Mark, 1990), and this too mhave been due to a recent intrusive event. If this is the cadditional work will be required to place constraints ondimensions of the dikes and the physical properties ofsubstrate to help refine when explosive activity may occ

Some aspects of this dike model remain enigmatic.example, we do not see this type of feature in Elysium Pltia, where numerous examples of volcano/ground ice inactions have been identified (Mouginis-Mark, 1985). Fthermore, unlike the graben found in the Athabasca awhere lava flows appear to have been the last phase otivity (Mitchell et al., 2002; Head et al., 2003), the OlympMons region shows no evidence of effusive activity fromdikes. Other aspects of the comparison with Athabascadifferent as well, including the lack of surface collapseform graben along the trend of the dike. Differences indepth to the top of the dike, or the amount of volatiles witthe regolith at the time of dike intrusion, are possible reasfor these differences (Scott and Wilson, 2002).

Our model of explosive volcanism implies that there mhave been ice present at∼ 24◦ N at a shallow depth inthe very recent history of Mars. Mellon et al. (1997) hashown that ground ice is unstable in the equatorial regin the current martian climate, and that if they were onpresent these volatiles would undergo sublimation andfusive loss to the atmosphere. Interestingly, Mellon et(1997) place the depth to the steady-state ice table for porock as∼ 60–70 m for the area north of Olympus Mo(their Fig. 4b), which would be consistent with our modresults.

Only a few examples of the ridges within the OlympMons aureole that have been imaged by MOC show mphologies suggesting explosive volcanism of the kindscribed here. Large numbers of similar features visibleViking Orbiter images have a somewhat “meandering” strconsistent with the characteristics of terrestrial dikes,partial covering by eolian materials makes it impossiblesee the contact between ridge and basement materialspection of Viking images suggests that some ridge segm

,

-

-s

may be 100–150 km long, with maximum lengths> 300 km.Although none of these ridges can be confirmed to be dby analysis of MOC images, if subsequent analysis of nMOC images were to show that even a small proportionthem were indeed produced by dikes then this would imthat intrusive volcanism was far more widespread northOlympus Mons than has previously been proposed.

Several questions remain enigmatic with respect tophysical characteristics of these features and must awaither work. For example, why is the ejected material cstrained so close to the vent? Why do we not seetype of feature in Elysium Planitia, where numerous exaples of volcano/ground ice interactions have been ident(Mouginis-Mark, 1985)? Why do we not see collapse alothe trace of the dike, as occurs at Athabasca (Head e2003)? And why did the eruption fail to produce a lava flo

Acknowledgments

This research was supported by a grant from the HaSpace Grant Consortium, by the NASA Mars Data Anasis Program under grant NAG5-9576 (PJMM, PI), aby PPARC grant PPA/G/S/2000/00521 (LW, PI). Wegrateful for useful discussions on shallow dike propagawith Falk Amelung. This is Hawaii Institute of Geophysiand Planetology contribution 1300, and SOEST publica6222.

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