A future magma inflation event under the rhyolitic Taupo volcano, New Zealand: Numerical models...

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Journal of Volcanology and Geother

A future magma inflation event under the rhyolitic Taupo volcano,New Zealand: Numerical models based on constraints from

geochemical, geological, and geophysical data

S.M. Ellis a,⁎, C.J.N. Wilson b, S. Bannister a, H.M. Bibby a,W. Heise a, L. Wallace a, N. Patterson a

a GNS Science, PO Box 30-368, Lower Hutt 6315, New Zealandb Geology Department, University of Auckland, Private Bag 92019, Auckland 1020, New Zealand

Received 25 July 2006; accepted 2 June 2007Available online 4 July 2007

Abstract

Catastrophic, caldera-forming silicic eruptions and intervening smaller intra-caldera events represent a major volcanic hazard inmany parts of the world. Central to monitoring and forecasting future eruptive activity at caldera volcanoes are (1) an accurateassessment of the present state of the volcanic system, and (2) a detailed understanding of the inter-relationships between thevolcanic system and regional tectonics and crustal structure. Using Taupo volcano in the central North Island of New Zealand as acase example, we combine geochemical and geological information from the past behaviour of magma bodies with knowledge ofthe present geophysical state of the crust, in order to model a hypothetical inflation event in the subsurface magmatic system.Numerical models of the crust incorporating inelastic rheology, an extensional regional stress field, weak caldera fill, andembedded weak caldera-bounding faults show that these factors can substantially influence and localise the processes and signalsaccompanying the hypothetical pre-eruptive ascent and accumulation of magma. For Taupo volcano, the models demonstrate thatsurface displacements associated with inflation of magma bodies up to the order of 10 km3 in volume may be almost entirelyhidden beneath Lake Taupo. These results highlight the difficulties in prediction of inflation events beneath calderas. There is afeedback between inflation and extensional tectonics, so that surface uplift on short timescales can be followed by subsidence onlonger timescales. The model predictions provide a quantitative, targeted framework for monitoring Taupo volcano and foridentifying any anomalous behaviour that may represent the onset of a future eruption. The results may also prove useful forinterpretation of surface deformation on other caldera locations around the world.© 2007 Elsevier B.V. All rights reserved.

Keywords: Taupo; caldera; numerical model; inflation

1. Introduction

Caldera volcanoes, particularly those associated withrhyolitic magmatism, present the greatest potential for

⁎ Corresponding author. Tel.: +64 4 570 4730; fax: +64 4 570 4600.E-mail address: [email protected] (S.M. Ellis).

0377-0273/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jvolgeores.2007.06.004

destructive explosive volcanism on Earth (e.g., Masonet al., 2004). Gaining a physical understanding of silicicmagmatic systems is an important first step in forecastingfuture activity at such volcanoes andmitigating against thedamaging effects of explosive eruptions. Two approachesgo into such forecasting at present. The first isconsideration of past activity from the historical or

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2 S.M. Ellis et al. / Journal of Volcanology and Geothermal Research 168 (2007) 1–27

geological records so as to discern any patterns of sizeversus repose period or recognise any consistent eruptionsizes or styles that might be a guide to the future (e.g.

Wilson, 1993; Pyle, 1998). The second is monitoring ofthe volcanoes by seismic, geodetic and geochemicalmeans (e.g.,Newman et al., 2001; Battaglia et al., 2003a,b;

3S.M. Ellis et al. / Journal of Volcanology and Geothermal Research 168 (2007) 1–27

Poland et al., 2006) in order to discern the presence ofmagma and evidence for magma movement that wouldmost probably herald the onset of an eruption. However,there is a gap between these two approaches that is noteasily bridged in the case of caldera volcanoes. This gaparises because, although it is straightforward to construct aplausible hypothetical build-up to an eruption once it hasalready occurred (e.g., Sherburn and Nairn, 2004), thereare as yet no soundly based criteria for taking a given set ofgeophysical observations of unrest at a caldera volcanoand using them to reliably forecast or predict thelikelihood, size or timing of a future event. Theuncertainties arise because many caldera volcanoesworldwide show evidence of periodic unrest, reflectingaccumulation or movement of magma and/or aqueousfluids at depth, that do not lead to eruptions: e.g., LongValley, (Langbein, 2003; Hill et al., 2003; Hill, 2006),Campi Flegrei (Berrino et al., 1984; Battaglia et al., 2006;De Natale et al., 2006). Here we use the example of Taupovolcano inNewZealand, to assess its present-day state andto forward-model magma accumulation beneath thevolcano, with the aim of decipheringwhether past eruptiveevents might have been presaged by uniquely identifiablegeophysical signals.

Taupo volcano is one of two highly active calderavolcanoes in the rhyolite-dominated central TaupoVolcanic Zone (TVZ) in New Zealand (Wilson et al.,1995; Fig. 1). Silicic volcanism in central TVZ began atca. 1.6Ma, and numerous caldera-forming eruptions haveoccurred in association with 8 calderas or calderacomplexes over that time, with a cumulative dischargeof over 10,000 km3 of silicic magma (Houghton et al.,1995; Wilson et al., 1995). Activity attributed to Taupovolcano postdates 320 ka, with the largest (530 km3

(magma)), caldera-forming Oruanui eruption at 26.5 ka,and the latest eruption occurring ca. 1800 years ago(Wilson, 1993, 2001). Perceptions and inferences aboutfuture activity are based on the post-26.5 ka eruptiverecord, which contains evidence for 28 eruptions, rangingin volume overmore than 3 orders of magnitude, and withrepose periods ranging between one or two decades andN5000 years (Wilson, 1993). There is no systematicrelationship between the lengths of the repose periodsbefore or after any given eruption and its respectivevolume, such that neither the size of nor the time until thenext event can be forecast except probabilistically.

Fig. 1. (a) Tectonic setting of Taupo Volcanic Zone (TVZ) (inset) and locationrecurrence intervals b2000 years from GNS active fault database, and extensfrom GPS (arrows, ellipses mark 68% confidence level) (Wallace et al., 200example of the distribution of recent shallow seismicity 0–10 km deep (circletransects north of Lake Taupo. MT = magnetotelluric stations from line 3Transect shots (Henrys et al., 2003); CNIPSE = Central North Island Passiv

Taupo has undergone 3 events of ‘unrest’ (cf. Newhalland Dzurisin, 1988) in the past century, in 1922, 1964/65and 1982/83 (Webb et al., 1986; Grindley and Hull,1986; Otway, 1986) with detectable surface deformationand faulting in the first and last of these. Deformationpatterns are largely monitored by using Lake Taupo as agiant spirit level (Otway et al., 2002), and have revealeddecadal patterns of uplift and downwarping, particularlyacross the northern shoreline of the lake. However,paleoshorelines established during high lake standsassociated with formation or refilling of the lake aftercaldera-forming events at 26.5 ka and 1.8 ka, respec-tively (Manville and Wilson, 2003) reveal smaller netdisplacements of the 26.5 ka shoreline than would beexpected from extrapolation of modern displacementrates. The conclusion reached by Manville and Wilson(2003) was that the faulted crust along the northernmargin of Lake Taupo was being buoyed up againstlong-term subsidence associated with rifting, perhaps bymagma injection at depth.

If the ‘unrest’ events at Taupo represent intrusion ofmagma, then similar patterns of uplift and seismicityshould be expected to occur as the prelude to a futureeruption. In some cases, such eventsmay reflect short-termfluid pressure changes and therefore be “false alarms”(cf. Battaglia et al., 2006). The long-term deformationpatterns at Taupo, however, imply some large-scale sourceof buoyancy below the northern part of the lake shore thatcan only realistically be supplied by magmatic intrusion.Recent improvements to geophysical monitoring in theTaupo region are aimed at providing some level ofwarningfor caldera and seismic unrest, via the publicly-fundedGeoNet project (www.geonet.org.nz). To be effective,such monitoring must be accompanied by an understand-ing of what is likely to happen during a magma inflationevent, aswell as the ability to discriminate between such anevent and background rifting processes. Here we assemblegeochemical, geological and geophysical evidence for thepast and present structure of the Taupo Volcanic Zone andcaldera. These data are used to constrain models of hypo-thetical future magma generation or movement, in order toanticipate the associated geophysical signature. Broadconstraints on the rates and depths of magma accumula-tion, as well as the physical properties of themagma, comefrom previous studies of Taupo volcano, summarisedbelow. These data, when combined with knowledge of the

of Taupo and Okataina calderas (dashed lines), major active faults withion rates in mm yr−1 of Axial Ranges block relative to Australian Plate4). (b) Close-up of Taupo area (dotted outline in part (a)) showing ans) from GNS earthquake catalogue, and location of recent geophysicaldescribed in Heise et al., 2007; NIGHT = North Island GeopHysicale Seismic Experiment stations (Reyners and Stuart, 2002).

http://www.geonet.org.nz


present-day system derived from geological and geophys-ical measurements, are used to model the patterns ofsurface deformation and stress that would accompanyaccumulation and/or ascent of magma. The models can beused as a starting framework to feed into accurate, focusedmonitoring of Taupo volcano, and point the way to futurework that must be done in order to fully understand thecomplex interactions between hydrothermal fluids,magma, and regional tectonics.

2. Geological and geophysical setting of Taupo volcano

2.1. Regional tectonic setting

Taupo volcano is located in the thinned, activelyrifting continental crust of the Taupo Volcanic Zone(Cole, 1990; Fig. 1). As a result of major eruptions at26.5 and 1.8 ka, a complex caldera was generated andfilled with ca. 3–4 km of low-density pyroclastic debris(Davy and Caldwell, 1998). To the north and south ofthe caldera lie extensional faults of the Taupo Fault Belt(Grindley, 1960), with the continuation of these faultsinto Lake Taupo overprinted or obscured by the calderacollapse structures (Davy and Caldwell, 1998). Offsetsin the trend of the rift axis to the north and south of LakeTaupo led Rowland and Sibson (2001) to suggest thatTaupo caldera represents a soft-linkage accommodationzone between offset rift segments.

Accurate estimates of neotectonic slip rates alongfaults immediately north of the lake are difficult due toaccumulation of large thicknesses of eruptive deposits.However, Manville and Wilson (2003) used post-eruption paleoshoreline highstands to infer that verticaldisplacement along the normal faults immediately northof Lake Taupo is episodic and temporally related tomajor volcanic eruptions and/or inflation events. Incomparison, recent studies of fault slip further northroughly halfway between Taupo and Okataina (Villamorand Berryman, 2001; Nicol et al., 2006) show a fairlyconstant rate of fault slip of ca. 7.5 mm yr−1 over the lastfew thousand years, although the locus of fault activityshifts in an apparently random fashion betweenindividual segments of the fault belt.

Until recently, only reconnaissance information wasavailable on the deep crustal structure of the TVZ (e.g.Stern and Davey, 1987; Bibby et al., 1998), but thissituation has been remedied by more detailed transectsclose to and around Taupo as part of the NIGHT andCNIPSE projects undertaken in 2001 (Reyners andStuart, 2002; Henrys et al., 2003; Reyners et al., 2006)and the MORC experiment carried out in 2005 (Sternet al., 2005). Studies using electrical and seismic (active

and passive) techniques are now providing images thatextend into the deep crust and mantle, encompassing thedepths at which magmatic systems are expected to occur(e.g., Ogawa et al., 1999; Bryan et al., 1999; Sherburnet al., 2003). Seismic investigations of the crustalstructure of the TVZ along the NIGHT transect justnorth of Lake Taupo (Fig. 1b; Harrison and White, 2004;Stratford and Stern, 2004; Stern et al., 2005; Stratfordand Stern, 2006; Harrison and White, 2006) show: (1)low P-wave velocities of 1.5–3.0 km/s in the top fewkilometres, interpreted as ‘sediment’ fill due to down-faulting from rifting and caldera collapse; (2) interme-diate velocities (5.0 to 6.5 km/s) down to ca. 15–16 km,interpreted as quartzo-feldspathic crust; and (3) either:higher velocities of 6.9–7.3 km/s down to ca. 30 km,interpreted as heavily intruded/underplated lower crust(Harrison and White, 2004; 2006); or: an increase invelocities to 6.8 km/s at 15 km depth followed by agradual increase to 7.4 km/s at 20 km depth, with a strongreflection at 15 km interpreted as new crust formed byunderplating and no clear boundary between crust andupper mantle lithosphere (Stratford and Stern, 2006).

Throughout the TVZ, heat-flow is very high, with totalgeothermal heat output of 4200±500 MW, equivalent toan average heat-flow of ca. 700 mW m−2. These highvalues are consistent with emplacement of magma in thedeep crust belowmuch of central TVZ (Bibby et al., 1995)at an average rate of ca. 1–2 m3 s−1 (30–60 km3 ka−1),roughly 3 to 6 times the average eruptive output. Althoughmodern surface volcanism is focused primarily at Taupoand Okataina, the areas with highest heat flux (andcorrespondingly low shallow resistivity) are concentratedwithin two linear zones of geothermal fluid circulation,parallel to the length of the TVZ (Bibby et al., 1995).

Large-scale investigations of the electrical structurewithin TVZ have been undertaken using magnetotellu-ric techniques (Ogawa et al., 1999; Heise et al., 2007).Results from a profile to the north of Taupo along thecentral TVZ (Ogawa et al., 1999) showed near-surfaceconductivity anomalies corresponding to thicksequences of conductive volcaniclastics, and regionsof increased crustal conductivity at depths of ∼11–13 km which were interpreted as representing bodies ofpartial melt. The presence of mid-crustal anomalies hasbeen confirmed by a more extensive study (Heise et al.,2007), although the anomalies are interpreted to resideat slightly greater depths, more consistent with newerdata from seismic studies.

Extension, with accompanying normal faulting, isactive within the ∼20-km wide Taupo Fault Belt alongthe axis of the TVZ, with overall extension rates in theTaupo region of between 6 and 10 mm/yr (Villamor and


Berryman, 2001; Darby et al., 2000; Wallace et al.,2004). Information about surface deformation in theTVZ comes from GPS surveys and other geodeticmeasurements since 1990, including lake-level monitor-ing (Darby et al., 2000; Otway et al., 2002;Wallace et al.,2004). The GPS surveys indicate a total short-termextension rate of∼8–10mm/yr across the TVZ (∼40 kmwide) in the Taupo region (Darby et al., 2000; Wallaceet al., 2004; Fig. 1a). This figure is slightly higher than thetotal fault extension rate estimated from paleoseismolo-gical studies between the Taupo and Okataina calderas(Villamor and Berryman, 2001; Nicol et al., 2006).

Seismicity in the TVZ is primarily concentrated withinthe Taupo Fault Belt and is characterised by swarm-likeactivity with predominantly normal focal mechanisms(Bryan et al., 1999; Hurst et al., 2002; Fig. 1b). Therhyolitic calderas do not appear to influence the locationsof the seismicity. The depths of seismogenesis are closelylinked to temperatures in the crust, as brittle behaviour canonly occur in quartz-rich rocks at temperatures less than∼350 °C which, in the TVZ, means depths shallower thanabout 7 km. It has been suggested that the convectivegeothermal regime also extends to this depth (Bibby et al.,1995;Bryan et al., 1999). The present-day energy transportrequires temperature to rise rapidly below seismogenicdepths, consistent with the presence of partial melt atdepths as shallow as ∼7 km (Bibby et al., 1995).

2.2. Controls from the eruptive record at Taupo volcano

The characteristics of past magmatic systems atTaupo provide constraints on the modern magmaticsystem, in particular limits on the shapes, depths andgrowth rates of past magmatic bodies. A fundamentalconclusion at Taupo is that its evolution involves acomplex superposition in space and time of subtlydifferent magma systems, rather than the gradualevolution of a single unitary magma body (e.g., Suttonet al., 1995, 2000; Charlier and Zellmer, 2000; Charlieret al., 2005; Liu et al., 2006; Wilson et al., 2006). Inclassical models for Taupo-sized caldera-forming sys-tems, the climactic eruption is seen as being theculmination of an evolution spanning hundreds ofthousands of years, with crystal-poor melt accumulatingabove a zone of crystal-rich melt and mush (e.g. Smith,1979; Jellinek and DePaolo, 2003; Hildreth, 2004). Incontrast, the 530 km3 magma body for the 26.5 kaOruanui event appears to have been built up over at most∼40 kyr, with no evidence of its rejuvenation into theyounger activity (Sutton et al., 2000; Charlier et al.,2005; Wilson et al., 2006). Information from pastactivity at Taupo is used here to constrain the following

parameters for modelling of the magma bodies, whichare summarised in Table 1.

Geographic positions. Post-Oruanui vent sites occur
predominantly down the eastern side of modernLake Taupo in a NNE–SSW corridor (Fig. 2),oriented approximately perpendicular to theregional extension direction and crossing theeastern half of the Oruanui structural caldera(Sutton et al., 2000; Wilson, 1993, 2001). Weassume for our modelling that any futuremagmabody is situated below the greatest concentrationof young vents.
Depths. This covers both the depth to the top of themagma body and its vertical extent, and isassessed from volatile contents in trapped meltinclusions (e.g. Dunbar et al., 1989; Dunbarand Kyle, 1993; Liu et al., 2006). Lowest andhighest calculated pressures from Oruanuiinclusions that were inferred to have beengas-saturated on entrapment are ∼100 MPaand ∼200 MPa, respectively, corresponding todepths of 3.5 to 7 km. The Oruanui body is thusinferred to have been ∼3.5 km thick. Inyounger eruptions, incomplete data (lackingCO2) mean that it is uncertain whether gas-saturation was achieved, and water contents of∼4.5 wt.% (Dunbar et al., 1989; Dunbar andKyle, 1993) thus indicate a minimum entrap-ment pressure of ca. 150 MPa (equivalent to 5–6 km depth). From these data and considera-tions of the depth to the base of the seismiczone (e.g., Sherburn et al., 2003) we adopt amodel depth to the top surface for a large(Oruanui-dimensioned) body of 4 km, and adepth of 6 km for bodies with dimensionssimilar or less than Taupo body.

Shapes. Magma body shapes follow from estimates oferuptive volume and chamber depth. For theTaupo, Waimihia and Oruanui eruptions, divi-sion of the erupted volumes by the verticalextent of the magma tapped – estimated fromglass inclusion volatile data (Taupo, Oruanui—references above) and fluid dynamical model-ling (Waimihia— Blake et al., 1992) – indicatethat magma chambers at Taupo are discoidal inshape, significantly wider than they are tall.

2.3. Overpressure

An additional critical constraint for modelling involvesthe estimate of overpressure prior to eruption, as this has a

Table 1Properties of some past magma bodies in the Taupo caldera, derivedfrom geochemical analyses, and representative values used later in thispaper

Event Oruanui Waimihia Taupo

Age BP 26.5 ka 3.5 ka 1.8 kaVolume (km3) 530 7.5 35Depth (km) ∼4–8 ca. 6 minimum

(if gas saturated)ca. 6 minimum(if gas saturated)

Thickness (km) 3.5 0.25 UncertainTemperature(°C)

760 830 850

Average density(kg m−3)

2300 2200 2200

Estimatedviscosity(Pa s)

2×105 6×104 6×104

Estimatedover-pressure(MPa)

10–15 10–15 10–15

Estimatedgenerationtime

40 kyr (max),17 kyr (min)

∼3000 yr (max) 600 yr (max)

Estimatedresidencetime in crust

40 kyr 4300–7800 yr 410 yr (min)

All estimates are for rhyolite part of magma bodies. Oruanui data fromWilson et al. (2006), Charlier et al. (2005) and Liu et al. (2006);Waimihia data from Blake et al. (1992), Dunbar et al. (1989), andSutton et al. (2000); Taupo data from Wilson and Walker (1985);Dunbar et al. (1989); Dunbar and Kyle (1993); Sutton et al. (2000).Approximate viscosities estimated from temperature and water contentof rhyolite, according to formula in Hess and Dingwell (1996) andZhang et al. (2003) (see also Scaillet et al., 1998).


direct influence on the magnitude of inflation in theoverlying crust. Overpressure can result from a combina-tion of three related factors: (1) the lower density of thehot, buoyant magma body compared to surroundingcountry rock; (2) vesiculation within the magma whichreduces density further; and (3) rapid accumulation ofmagma within the chamber due to an influx from depth.Owing to uncertainties in estimating factors (2) and (3), itis difficult to estimate overpressure for a magma body, butan upper bound prior to eruption is the tensile strength ofoverlying rock, which for intact greywacke is around 10–15 MPa (e.g., Sklar and Dietrich, 2001; Rowland andSibson, 2004).

3. Present state of Taupo volcano

Studies of eruption products at Taupo suggest aspectrum of residence times, from ∼40 kyr for the530 km3 Oruanui body, through periods of b102–103 years for many of the post-Oruanui eruptions, topossibly a decade or less for post-Oruanui dacites (Sutton

et al., 2000; Charlier et al., 2005). A critical question forthe assessment of hazard from Taupo volcano is thuswhether a magma body currently exists within the mid-crust, since the presence of a partial melt is expected tosignificantly influence the inflation response of the crust.To answer this question with modern geophysicalmeasurements is not easy, for the following reasons:

(1) The presence of Lake Taupo hampers detailedinstrumentation within the caldera;

(2) The presence of weak, low-velocity volcaniclasticdeposits near the surface degrades the quality ofsignal for both passive and active seismologicalstudies;

(3) The crust may be on the verge of melting or containsmall pockets of partial melt, without displaying thecharacteristic slower seismic velocities and/orelectrical anomalies associated with bodies ofinterconnected melt (e.g., Heise et al., 2007).

For these reasons, as well as the inherent uncertain-ties in parameter values derived from inversion ofgeophysical data, the current results are rather ambig-uous, as described below.

3.1. Shallow resistivity and heat-flow measurements

Apparent-resistivity measurements within Lake Tauposhow anomalies outlining the Oruanui structural caldera,with a prominent low-resistivity area that surrounds theHoromatangi Reefs (Caldwell and Bibby, 1992; White-ford et al., 1994; Stagpoole andBibby, 1998; Fig. 2b). Theresistivity pattern can be accounted for by a combinationof lower resistivity fill within the caldera (i.e., an intrinsicproperty of the rock matrix) superimposed on an activehydrothermal system near the eastern side of the caldera.Similarly, heat-flow measurements on the floor of LakeTaupo show regions of elevated heat-flow on its easternside associatedwith a hydrothermal system (Caldwell andBibby, 1992; Whiteford et al., 1994; Whiteford, 1996;Fig. 2a). This anomalous region of high fluid flow andheat-flow may result from a combination of severalfactors, the proportions of which we cannot assessaccurately on the basis of the data, but possibly including:(1) Cooling of a remnant magma body (now solidified)from the latest eruption. The Horomatangi Reefs certainlycoincide with the positions of the younger (post-Oruanui)vents. However, there is no evidence for a more vigoroushydrothermal circulation in this region in the past 1.8 kyr,as would then be expected; (2) Upwelling of aqueousfluids as part of a convective cell, focused by ventingwhich provides easy pathways (enhanced vertical

Fig. 2. (a) Present heat-flow within Lake Taupo, simplified fromWhiteford et al. (1994) and Whiteford (1996). Square indicates virtual source for Oruanui eruption and ellipse approximate location ofmost post-Oruanui vents (Wilson et al., 1993). (b) Apparent resistivity contour map of Lake Taupo (Stagpoole and Bibby, 1998, after Caldwell and Bibby, 1992). Array spacing 500m. (c) Residualgravity anomaly contour map of Lake Taupo (Stagpoole and Bibby, 1999; after Davy and Caldwell, 1998).

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permeability; e.g., Rowland and Sibson, 2004). Thispossibility is supported by observations of lower heat-flow that have been interpreted as cold recharge zoneswith downward fluid flow below the lake floor (White-ford, 1996); (3) Small amounts of existing partial melt atdepth, too small to show up using other geophysicalmeasurements (e.g., MT; see below); (4) A steady influxof molten material from below which cools at a rate thatprecludes accumulation of large melt bodies, but whichdrives a geothermal system above it.

3.2. Magnetotelluric (MT) anomalies

The results from Ogawa et al. (1999) in the centralTVZ have been supplemented by recent data from aseries of magnetotelluric profiles north of Lake Taupo(Heise et al., 2007). In Fig. 3a we show the preliminaryresistivity model based on data from the southernmostprofile (MT line 3, Fig. 1). Near-surface conductivezones can be interpreted as volcaniclastic deposits,while zones of low conductivity on either side of thelake at depths of 5–20 km indicate basement rocks(greywacke metasediments). A low-resistivity anomalyat 15–25 km depth east of Taupo may indicate a meltzone in the lower crust. Unlike along the profile furthernorth (Ogawa et al., 1999), MT line 3 does not showevidence of a highly conductive body at the depths (∼4–8 km) estimated from petrological studies of meltaccumulation. Even allowing for the offset from the MTsurvey line of a magma body beneath the lake, thisobservation rules out the presence of a major pool ofshallow interconnected melt corresponding to magmabodies of Oruanui (530 km3) or Taupo (35 km3) sizeunder the northern part of Lake Taupo. However,magma bodies smaller than these may be present and yetnot be resolved by the MT data (Heise et al., 2007), inwhich case temporal changes in the MT signal mayprovide the only clue that magma is accumulatingbeneath the lake.

3.3. Seismic velocities and receiver functions

The P-wave seismic velocity structure just north ofLake Taupo has been modelled to mid-crustal depthsusing P-wave travel times recorded in the NIGHTseismic transect (Fig. 1). Fig. 3b shows P-wave velocitystructure along the transect calculated with the tomo-graphic inversion technique of Hole (1992), using a totalof 288 refracted arrivals from 8 shots. The data showlow P-wave velocities down to about 3–5 km depthbetween shot 6 to the west and the Kaingaroa Fault scarpto the east, coinciding with the large negative gravity

anomaly (Davy and Caldwell, 1998; Fig. 2c), inter-preted as low-strength volcaniclastic deposits. Between5 and 10 km depth the P-wave velocity is lower beneathLake Taupo and the TVZ compared to the basementregions on either side of the TVZ. There is no evidencefrom this refraction data either of low-velocity zonesrepresentative of partial melt, or of high-velocity zonesrepresenting solidified intrusives (cf. Sherburn et al.,2003, who image high-Vp zones that they interpret assolidified intrusives further to the north).

Receiver functions, which are derived from thebroadband seismic wavefield produced by distant earth-quakes, can be used to image the crustal S-wave velocitystructure. Receiver functionmodelling using CNIPSE datahas been mostly restricted to a 2D profile north of LakeTaupo due to the distribution of receiver stations andsources (Bannister et al., 2007). The data quality is poorowing to the thick cover of volcaniclastic deposits andreverberation effects associated with these deposits.However, examination of those receiver functions suggeststhat there are no large anomalous mid-crustal magmabodies to the north of Lake Taupo under the central faultbelt; we do not have sufficient information to say anythingabout magma bodies to the south, because the 3D effectsthat allow partial coverage under the lake for MTmeasurements do not apply for this analysis. In contrastwith these results, further north, near Rotorua andOkatainacalderas, receiver functions image an area with low S-wave velocities at depths between ca. 6 and 16 km, whichBannister et al. (2004) interpret as a zone of partial melt.

3.4. Seismicity and geodetic deformation

Major earthquake swarms in the Taupo region wererecorded in 1922, 1964–65, and 1983. On at least two ofthese occasions (1922 and 1983) the swarms wereassociated with normal faulting, subsidence and tiltingof fault blocks to the north of the lake (Grindley and Hull,1986; Otway et al., 2002). During the 1922 earthquakeswarm, subsidence of 3–4 m (measured by changing lakelevels) was accompanied by displacements of up to 3 mon bounding faults during the early part of the swarm(Otway, 1986; however, in some places this displacementmay have been due to landslips — K.R. Berryman, pers.comm., 2005). The 1983 swarm was preceded by∼6 months of uplift of N3.5 cm, while the swarm itselfwas accompanied by subsidence (Otway et al., 2002).Kaiapo Fault on the eastern side of the Taupo Fault Belt,just north of Lake Taupo, experienced ∼5 cm of verticaldisplacement a week after the swarm began, with groundrupture over a distance of 1.2 km (Otway, 1986; Grindleyand Hull, 1986).

Fig. 3. Geophysical profiles north of Lake Taupo; locations shown in Fig. 1b. (a) Magnetotelluric (MT) resistivity along profile 3, simplified fromHeise et al., 2007. Projection of Lake Taupo onto cross-section marked above section. Areas with low resistivity are consistent with high fluidcontent/weak rock (shallow anomalies) or partial melt (deep anomalies). Inset shows location of profile 3 (black line) and lines further north (grey) notdiscussed here. (b) P-wave velocities (km/s) derived from NIGHT experiment explosive shot first-break data using the finite difference tomographicinversion technique of Hole (1992). Shot locations and projection of Taupo location marked above cross-section. No vertical exaggeration. Note thefairly sharp gradient at 9–10 km depth. Shallow Vp anomalies match MT shallow anomalies quite well.


Webb et al. (1986) argued that the 1983 swarm wasnot due to magmatic intrusion, because of the lack ofcharacteristic low-frequency volcanic earthquake trem-or. Bannister et al. (2006) analysed more recentearthquake clusters in the central TVZ and, based onaftershock sequences and focal mechanisms, suggestedthat fluid pressure changes are a more likely explanationfor these events (T. Hurst, pers. comm. 2006). However,

lack of volcanic tremor is not a sufficient basis on whichto rule out a magmatic cause for swarms (e.g., Latter,1981; Aki, 1984; Smith and Webb, 1986). Magmainflation as a primary trigger of the 1922, 1965, and1983 events cannot be definitively ruled out at thisstage, especially if accompanied by changes in fluidpressure owing to fluids exsolving from a magma body(e.g., Battaglia et al., 2006). Magma inflation can also

Table 2Summary of crustal properties in the Taupo region derived fromgeological and geophysical data

Average surfaceheat-flow (W m−2)

700 Average crustaldensity (kg m−3)

2700

Seismogenicdepth (km)

6–7 Average crustalshear modulus (GPa)

30

Crustalthickness (km)

Transitionalbetween 15and 30

Average crustalPoisson's ratio

0.25

Caldera filldensity, 0–4 km(kg m−3)

2200 Caldera fill shearmodulus,0–4 km (GPa)

5


trigger shallow earthquakes that appear to have normaltectonic signatures, by perturbing the regional stressfield (e.g., Troise et al., 1997, 2003; Feuillet et al.,2006), and from increasing fluid pressure which reducesfrictional yield strength.

3.5. Summary of geophysical information

At present the geophysical investigations near LakeTaupo have failed to reveal a melt body of significant size(i.e., tens to hundreds of km3) located within mid-crustaldepths (4–8 km) (see also Sutton et al., 2000). As noted atthe beginning of this section, most of the geophysicalprofiles run north of Lake Taupo and do not give goodcoverage beneath the lake itself. While the patterns inheat-flow, historical seismicity, and ground deformationmay all be explained without appealing to the presence ofsignificant magma at shallow crustal depths, furtherinvestigation of small unrest events near Taupo is requiredto determine whether these events are magma-related. Acombination of ground deformation monitoring (includ-ing GPS; InSAR, e.g., Fialko and Simons, 2001; and lakelevelling) and precise gravity measurements may helpdetermine to which degree magma and/or fluid pressurechanges act as the triggers for uplift and earthquakeactivity during a future unrest event (e.g., Battaglia et al.,2006); but as stated above, the presence of the lake willmake a unique inversion difficult.

4. Numerical experiments

The numerical experiments are designed to investi-gate the influence of a magma inflation episode onsurface deformation and other geophysical signals. Themodel experiments are kept as simple as possible, whilealso taking into account the local structure and likelyproperties of the magma body, as described above. Wedescribe a general progression from simpler to morecomplex models in order to isolate some of the first-order controls on inflation styles and signatures.

The finite element engineering package Abaqus(Abaqus users manual, 2004) is used to model staticeffects of inflation. Abaqus has been extensivelybenchmarked for elastic, plastic, and ductile rheologiesand allows great flexibility when designing appropriateunstructured meshes. Care must be taken that the finite-element mesh is fine enough to capture the response tomagma inflation, and to keep the boundaries of themodelled region far enough away so that they do notinfluence results. For elastic crustal properties, we useaverage values derived from geological and geophysicalmeasurements (Table 2).

4.1. Comparison between semi-analytical solution andfinite-element approximation for a spherical pressuresource

We first consider the simplest inflation scenario –inflation of a spherical magma chamber in a uniformelastic half-space – with average crustal properties takenfromTable 2. The inflatingmagma body is represented bya uniform pressure acting outward normal to the magmabody surface, and gravitational effects are not modelled.In order to match the volume and depth to the top of theOruanui magma chamber estimated from geochemicaldata (Table 1), it must be centred at 9 km depth with aradius of 5 km. Fig. 4 shows the setup for 3D andaxisymmetric finite-element representations of this body.The axisymmetric model allows finer mesh resolution forspherically symmetric bodies, as there are fewer degreesof freedom compared to the equivalent 3D model; meshresolution is too fine to depict on the figure, as the averagedistance between nodes is 50 m. Fig. 4(b) illustrates theprediction of the two finite-element models compared tothe semi-analytical expression of McTigue (1987) forinflation of a finite sphere in an elastic half-space. Thehigh-resolution axisymmetric model matches the semi-analytical solution well everywhere except directly abovethe magma body. This discrepancy occurs because theMcTigue (1987) approximation is only accurate to O(ε7)where ε=R/D (R is radius of the magma chamber andD isdepth to the centre of the magma chamber). For theOruanui body, O(ε7) ∼0.16, so that a fairly large error ispredicted for the McTigue (1987) solution. We areconfident (after testing with a wide range of meshresolutions) that the finite-element axisymmetric solutionshown in Fig. 4 is more accurate than the semi-analyticalsolution of McTigue (1987). This is confirmed by testswith inflation of smaller-radius bodies, where the twosolutions converge.

Fig. 4. (a) Schematic illustration of the geometry used in the simplest numerical experiments, to investigate surface deformation resulting from inflation ofa spherical magma chamber. Axisymmetric coordinates r (radial) and z (depth); source has pressure of 10 MPa applied; surrounding region is ahomogeneous elastic half-space. Mesh spacing (not shown) averages 50 m. (b) Vertical and radial surface displacements due to inflation of an Oruanui-sized spherical magma chamber situated between 14–4 km depth. Solid line: axisymmetric finite-element model; dashed line: 3D finite-element model;circles: semi-analytical solution of McTigue (1987). Inflation pressure is 10MPa, elastic shear modulus in the crust is 30 GPa, and Poisson's ratio is 0.25.(c) Vertical and radial surface displacements due to inflation of a Taupo 1.8 ka-size spherical magma chamber situated between 6 and 8 km depth. Legendand elastic/pressure parameter values same as (b).



The 3D finite-element solution slightly underestimatessurface displacement compared to the axisymmetricmodel(i.e. the 3D model is too stiff). This is due to the lowerresolution mesh that must be used in this case. However,the error is b5% so we believe the 3D solution is stilluseful. This becomesmore important for caseswe considerlater, which are not spherically symmetric, and for whichthe 3D model is the only valid solution.

The reader may be surprised at how little surfacedeformation is predicted considering the large size of theinflating magma body. For an infinitesimal inflatingsphere, the analytical solution of Mogi (1958) forvertical surface displacement can be written as:

uz ¼ 34PG

e3

ð1þ q2Þ3=2where ε is the ratio of sphere radius to depth as describedabove, P is magma chamber overpressure, G is shearmodulus, ρ is the ratio of radial distance to depth, and aPoisson's ratio of 0.25 has been assumed. The adaptationfor a finite spheroid (as plotted in Fig. 4) is a slightmodification to this expression, but the basic dependenciesremain the same: surface displacement (radial and vertical)scales linearly with P and inversely with elastic strength(G). In themodels summarised by Fig. 4, we have assumedP=10 MPa (Section 2.2.) and we have taken an averagecrustal shear modulus of 30 GPa, derived from seismicvelocity measurements (Section 2.1.). If these estimates areincorrect, so will be the estimate of surface displacementdue to inflation of a sphere. For example, if overpressurewas 100 MPa, or shear modulus was 3 GPa, surfacedisplacements would be 10× higher than those shown inFig. 4. However, as discussed in Section 2, overpressurecannot be too high or the overburden would fail in tensilestress. Laboratory tests on shear moduli of consolidatedsedimentary and/or igneous rocks are∼20–40GPa, similarto the values used here. But the assumption that an averageshear modulus for the crust can be applied to a homo-geneous elastic half-space is an over-simplification. Inviscoelastic models of inflation at the Long Valley caldera,Newman et al. (2006) used a lower shearmodulus of 5GPato represent weak volcanic rocks. Similarly, we show laterthat weak near-surface layers with lower shear moduli canincrease the predicted surface displacement considerably.

4.2. Effect of magma chamber geometry

The geochemical constraints summarised in Section2.2 and Table 1 give the approximate pre-eruptivethicknesses and volumes of moderate to large magmabodies beneath Taupo. Aspect ratios (thickness:diameter)inferred for the Oruanui andWaimihia bodies are ca. 0.1–

0.3, suggesting a sill-like or discoidal shape for themagma body, rather than a spheroid. The finite-elementmodels can be used to investigate the effect of a discoidalpressure source compared to the equivalent-volumespheroid. Fig. 5 illustrates how the discoidal shapeamplifies surface displacement by a factor of about 6–7,because the centre of the pressure source is brought closerto the surface compared to the equivalent spheroid. Thelocation of maximum radial displacement also shiftsfurther away from the centre of the pressure sourcecompared to the equivalent spheroidal pressure source.The difference in the two solutions demonstrates howimportant the shape of the magma body is in interpretinginflation-induced surface displacement (cf. Dieterich andDecker, 1975; Folch and Gottsmann, 2006).

4.3. Effect of magma chamber buoyancy as a cause ofuplift

The tests applied above represent themagma body by ahollow cavity which has a uniform pressure throughout.This is the standard way to model inflation of a magmachamber, where overpressure is assumed to result from thethree factors discussed in Section 2.3 (viz., density changesdue to additional melting of rock; gas vesiculation; and aninflux of fresh magma from below). In such cases it isassumed that themagma chamber already exists so that theinflation is caused by an incremental change in chamberproperties. An alternative is that an entire magma chambermay develop rapidly due to remelting of hot rock, primedby underplating of hot magma (e.g. Annen and Sparks,2002).We can explore the signal due to sudden generationof a magma chamber by imposing a density drop ratherthan a pressure change within the chamber. The effect onthe axisymmetric finite-element model, using materialproperties for the magma body (density, elastic strength)from Table 2, is illustrated in Fig. 6. For a ∼35 km3 body,the resulting surface displacement is similar in maximummagnitude to the imposition of a uniform overpressure of10 MPa. It may therefore be quite difficult to determinewhether surface displacement is caused by the newgeneration of a magma chamber, or by inflation of analready-existing body, although careful repeat measure-ments of gravity in combination with geophysicalsounding may help distinguish between the two cases.

4.4. General prediction of surface displacementmagnitude with size of magma body for shallow crustalinflation

The results from simple inflation models like thoseshown in Fig. 5 can be summarised in a comparison of

Fig. 5. (a) Schematic representation of a discoidal magma chamber with the same volume (530 km3) and depth to top (4 km) as the Oruanui magmabody. Discoid major radius X=5.7 km; small radius x=1.75 km; discoid thickness 3.5 km. A uniform pressure of 10 MPa is applied normal to thechamber surface. Elastic properties of the crust as for Fig. 4 (b). Resulting surface displacements for the discoidal body, using an axisymmetric finite-element approximation. Dashed lines show surface displacements for the equivalent volume spheroid (Fig. 4b). (c) Differential stress field around theOruanui-sized discoid after inflation. (d) Surface displacements for Taupo-sized body, compared to equivalent volume sphere (dashed lines). Discoidradii X=2.3 km; x=0.71 km; discoid thickness 1.4 km, other properties the same as for Fig. 5(b). (e) Differential stress field around the Taupo-sizeddiscoid after inflation. In (c) and (e), lines indicate direction of maximum principal compressive stress around the magma chamber.


maximum surface uplift and surface tilt versus the sizeof the magma body, assuming that the top of the body isat 4 km and that the body is discoidal with an aspect

ratio (thickness:diameter) of 0.3 (Fig. 7). Given theparameter values assumed from Tables 1 and 2, Fig. 7shows that the surface displacement associated with

Fig. 6. (a) Surface displacements for a Taupo-sized discoid magma body assuming the magma body has shear modulus G=30 GPa and Poisson'sratio 0.25. Rather than a pressure being applied to mimic inflation, this model uses the density contrast between crust (density 2700 kg m−3) and a hot,inflating magma body (density 2200 kg m−3) with vertical gravitational acceleration 9.81 ms−2. (b) Differential stress field around the Taupo-sizedbuoyant discoid. Lines indicate direction of maximum principal compressive stress around the magma chamber.


even quite large bodies is relatively modest. In fact, for auniform crustal strength of 30 GPa and overpressure of10 MPa, it would be difficult to pick up the surfacedisplacement signal from any inflating body with avolume less than that estimated for the Waimihia event(∼7.5 km3) using campaign GPS data, although thesignal could be resolved using continuous GPS orInSAR data. (To discriminate a vertical signal from dailyposition scatter for continuous GPS, we assume thesignal must be N1 cm; for campaign GPS we assume itmust be N10 cm). Unfortunately at Taupo the chancesare further reduced than this, because most measure-ments must come from around the lake edges, ∼10 kmaway from the probable centre of inflation. Fig. 7 showshow when we are only able to measure uplift 10 kmfrom the inflation source, inflation of even quite largemagma bodies may go undetected. However, as wediscuss later in this section, the effect of inflation may beamplified by near-surface low-strength layers (such ascaldera fill) and by additional fluid pressure effects.

4.5. Deeper inflation events

Wilson et al. (2006) suggested that the Oruanuirhyolite body was primed by small volumes of maficmagma rising from greater depths. The MT profilereveals anomalies at between 20 and 25 km that areconsistent with the presence of partial melt and that mayrepresent a deep mafic reservoir (Fig. 3a). Would we seeany uplift signal from inflation of deeper bodies? In

Fig. 8 we plot the minimum volume of a discoidalinflation source for which N1 cm of maximum surfaceuplift is predicted, as a function of depth to the top of theinflating body, assuming the same aspect ratio andoverpressure as before. As expected, the necessaryvolume for which uplift could be measured immediatelyabove the body increases rapidly with depth. At 5 kmdepth, the volume is ∼1 km3, but this increases to∼10 km3 at 15 km. The necessary volume is evengreater when considering inflation sources beneathTaupo, because of the presence of the lake. If we canonly measure the uplift signal 10 km or more distantfrom the point directly above the chamber, as shown bythe dashed line in Fig. 8, the volume of a body inflatingwith 10 MPa pressure into a strong elastic crust must begreater than 30 km3. The volume is actually higher forbodies at shallower depths. This counter-intuitive resultarises because the closer the body is to the surface, themore focused the uplift is directly above it. The dashedcurve on Fig. 8 illustrates the handicap that results fromonly being able to take measurements around the lakeedge. However, local crustal structure and inelasticeffects may enhance the uplift signal, as illustrated in thefollowing sub-sections.

4.6. Effect of local crustal structures on inflation

Previous studies using analogue models with infla-tion and deflation of sand have demonstrated howcrustal structure from previous phases of caldera

Fig. 7. Maximum surface uplift at the point directly above an inflatingmagma chamber (solid line) and surface uplift 10 km distant from thispoint (dashed line) representing the limitations imposed by the presenceof Lake Taupo. A 10 MPa overpressure in uniform elastic crust (pro-perties as for Fig. 4) is imposed. Surface uplift is plotted as a function ofmagma chamber size as determined by: (a) radius X of discoid; and (b)volume of discoid. (c) Surface tilt is plotted as a function of the radius Xof the discoid. Discoid has aspect ratio of Oruanui body and top in allcases is at 4 km depth. Following the approach of Fernandez et al.(1999), we place detection thresholds on the plots representingminimumresolvable quantities. For uplift, the grey box depicts minimumresolvable uplifts for campaign GPS data (upper box limit, 10 cm) andcontinuous GPS/InSAR (lower box limit, 1 cm). For tilt, the grey boxdepicts minimum resolvable tilt of 1 μrad using standard clinometricobservations (Fernandez et al., 1999) and 0.01 μrad using extremelysensitive borehole tiltmeter measurements (Sato and Hamaguchi, 2006).

Fig. 8. Minimum resolvable volume (assuming that maximum uplift of1 cm or greater, located directly above inflation source, is resolvable) vs.depth to top of an inflating discoid body. Magma pressure and elasticproperties as for Fig. 4. Dashed line shows equivalent relationshipbetween minimum volume and depth for uplift located 10 km away fromcentre of inflating body. The approximate volume and depth to the Taupo1.8 ka and Waimihia magma bodies (from Table 1) are also shown.Orunanui magma body plots off the scale of the figure.


resurgence and subsidence (creating networks of radialand concentric ring faults) may be reactivated during asubsequent inflation episode (e.g., Troll et al., 2002).Similarly, models in which inflation of a magma body is

preceded by extensional rifting show a change in thepattern of uplift as a result of reactivation of the rifting-related normal faults (Acocella et al., 2003). Theseanalogue models use a frictional material in which faultsdevelop and interact over time. In contrast, the modelsshown here are simpler in that they do not evolve overtime periods long enough to develop fault networks. Nev-ertheless, it is possible to make some simple inferencesabout effects from previous deformation, by imposingweaknesses within the models simulating weak layeringand/or existing fault structures, as we show below.

4.6.1. Weak caldera infillWeak elastic layers near the surface will affect

predictions from inflation and dislocation sources (e.g.,Jovanovich et al., 1974; Gudmundsson and Brenner,2004). There is a large, roughly elliptical region of weakvolcanic rubble within the Taupo caldera ca. 3–4 kmdeep, which is a superposition of the collapse structurefrom the Oruanui eruption and more recent events(Davy and Caldwell, 1998; Fig. 2).

To test the effect of weak volcaniclastic fill within theOruanui caldera boundary, we imposed a weak ellipticalregion in a 3D finite element model, using an inflatingdiscoid of Taupo (35 km3) dimensions. Crustal para-meter values are the same as in earlier models, while theweak caldera fill is represented by a lower elasticstrength and density (Table 2). The resulting surface


displacement (Fig. 9b) shows an increase by a factor ofca. 1.5× compared to the model of inflation withinuniformly strong elastic crust. The weak fill also reduces

Fig. 9. Effect of a weak caldera above a discoidal inflating source. (a)Geometry used in the 3D finite element model. Inflation source hasdimensions of Taupo body as described in Fig. 5; inflating body is atdepth 6–7.4 km. Caldera is an ellipsoid, 4 km deep and 16×10 kmwith vertical sides. Caldera has elastic shear modulus G=5 GPa, andPoisson's ratio 0.25; elastic properties of crust as for Fig. 4(b).Predicted surface uplift for weak caldera fill. Caldera boundaries (ringfaults) are welded to crust. Solid lines and DV_CALD and DY_CALDlabels show vertical and radial displacements, respectively, for modelwith weak caldera fill. Dashed lines and DV, DY labels show predictedvertical displacement for case with uniform crustal strength (i.e. sameresults as Fig. 5d). (c) Predicted surface uplift for weak caldera fill withfree tangential slip allowed along ring faults. DV_RINGF = verticaldisplacement for model with weak caldera fill and ring faults,DY_RINGF = radial displacement for model with weak caldera filland ring faults, other symbols as described above.

the effective wavelength of inflation, with the increaseduplift being most marked within the caldera boundariesand directly above the inflating body.

4.6.2. Weak ring faultsMechanically weak faults typically border calderas

and may exert a major control on the style and amplitudeof surface displacement above an inflating body (e.g.,Troise et al., 1997; De Natale et al., 2001; Troll et al.,2002; Folch and Gottsmann, 2006; De Natale et al.,2006). In Fig. 9c we demonstrate the effect of very weakvertical ring faults on surface displacement for the 3Dmodel with weak caldera fill, i.e. a model otherwiseidentical to that described in Section 4.6. The faults arerepresented by contact surfaces that are free to slip in atangential direction and extend from the surface down tothe base of the weak caldera structure.

During inflation the faults are activated and slip,causing surface uplift and deformation to be focusedwithin the caldera, with the caldera floor popping up like apill in a blister pack (Fig. 9c). The example shown hererepresents the case where the ring faults are much weakerthan surrounding rock. For stronger faults, or for smallinflating bodies where the ring faults are far away from thearea of surface deformation, the effect is less marked.Nevertheless, the discontinuity in vertical displacementshown in Fig. 9c suggests that for caldera settings moreexposed than Taupo, where caldera boundaries are notcovered in water, measuring differential displacementson either side of a ring fault boundary could help deter-mine characteristics of the inflating body. Stress perturba-tions associated with movement along the ring faults mayalso alter the pattern of seismicity (e.g., Troise et al., 1997).

4.6.3. Rift interaction and effect of ductile flowAs discussed in Section 2, Taupo caldera sits within an

actively extending rift, and the crust in the vicinity of


Taupo has been thinned and heated, so that the transitionfrom brittle faulting to thermally-activated ductile rockbehaviour occurs at a depth of ca. 7 km. A hot, low-viscosity magma chamber (Table 1) will interact with theregionally extending stress field. Although on shorttimescales (days–weeks) the response of the systemmay be approximated by inflation within an elastic

medium, over longer timescales (months–years) inelasticrheologies will dominate the system (e.g., Chéry et al.,1991). Fig. 10 shows a numerical experiment designed toinvestigate some of these effects. The model is two-dimensional and the material properties of the magmabody are simplified as described in the figure caption, sothat results can only be interpreted qualitatively, and the

Fig. 10. (a) Setup of 2D numerical model testing interactions between rifting and magmatism. Model domain is a cross-section through 30 km-thickcrust with extensional boundary conditions on right-hand side; boundary condition on base is free slip horizontally. Initial constant geothermalgradient is 25 °C km− 1. Model crust has a combination of elastic, frictional (pressure-sensitive) Coulomb behaviour, and thermally-activated ductilecreep (Ellis et al., 2006). Elastic shear modulus G=30 GPa, Poisson's ratio ν=0.25. Coulomb internal angle of friction ϕ=30° and cohesionC=1 MPa. Ductile creep parameters A, Q, and n are determined from extrapolation of laboratory creep experiments on wet synthetic quartzite(Paterson and Luan, 1990). A=6.5×10−8 MPa−n s−1; Q=135 kJ mol−1; n=3.1. The model is run in two stages (1) setup phase: no magma is present;uniform crustal properties with extension at 1 cm yr−1 for 100 kyr builds up extensional differential stress regime; (2) sudden intrusion of magmabody with approximate cross-sectional dimensions of Taupo magmatic system. Magma has temperature of 800 °C, linear viscosity of 105 Pa s, anddensity of 2200 kg m−3. (b) Differential stress field at the end of stage (1)—frictional yield in the upper crust causing a stress maximum there, whilethermally-activated creep in the lower crust reduces maximum sustainable extensional stress. (c) Elastic strain 100 days after intrusion of magma. (d)Viscous (creep) strain 100 days after intrusion of magma. (e) Frictional plastic strain 100 days after intrusion of magma. (f) Differential stress100 days after intrusion of magma. (g) Vertical surface displacement showing contributions from different rheological components. Elastic responseshows net uplift due to buoyant magma. Elastic+viscous response shows some uplift but with subsidence superimposed due to stretching of low-viscosity magma in extensional stress field. Elastic+viscous+frictional response includes effect due to relief of stresses by distributed faulting.


model cannot be directly applied to the Taupo system.It is also assumed that the magma chamber forms frommelting of existing crust rather than by significant addi-tion of magma from a deeper source, so that volume isconserved, while the magma body experiences a suddenchange in density owing to thermal and gas vesiculationeffects. Despite these simplifications, the model providessome insight into how tectonics and magmatism mayinteract during inflation of a magma chamber.

Prior to formation of the magma (represented by asudden drop in viscosity and accompanying increase inbuoyancy), an extensional stress field is developed bystretching the model crust at a rate of 1 cm yr−1 (Fig. 10b).The imposition of a high-temperature, low viscositymagma body gives rise to both elastic and inelastic strain(Fig. 10c–e). The inelastic strain is an order of magnitudehigher than the elastic strain, showing the importance ofthese effects to the overall evolution of the system (see


also Chéry et al., 1991). Of particular interest is the waythat the low-strength magma body focuses and enhancesextensional deformation, and causes elevated stretchingwithin and above it, both by ductile creep within themagma body (Fig. 10d) and by frictional yielding abovethe magma body (Fig. 10e). The elevated creep within themagma body relieves differential stress there (Fig. 10f),creating a stress “hole” that may continue to perturb thecrust long after the magma body has solidified. At thesame time the differential stress immediately above andbelow the body is enhanced (Fig. 10f) causing an increasein frictional deformation (Fig. 10e). Because thisdeformation is primarily relieving tectonic (extensional)stress, any seismicity associated with it would have anormal tectonic signature (see Section 5).

The regional stress field and inelastic rheology have asignificant effect on predicted vertical surface displace-ments above the magmatic body, as shown in Fig. 10g.When the body forms in a purely elastic homogeneouscrust, the inflation signal manifests itself as upliftcentred immediately above the body, similar to resultsshown in the previous models. With addition of weakviscous behaviour in the lower crust and magma body,the vertical displacements show subsidence over aperiod of 100 days, caused by the stretching of the low-viscosity magma body in the regional stress field (e.g.,Fig. 10d). With frictional yielding also included, thesubsidence is even more pronounced. The subsidencecaused by creep and frictional behaviour occurs overa shorter wavelength than the broad regional upliftassociated with elastic response to the magma body.

The 2D assumption used here (i.e. that the magmabody extends along-strike over a large distance) accent-uates subsidence compared to a 3D discoidal shapedmagma body. An additional simplification is that themodel includes no unstable frictional behaviour; inreality we expect that rather than the frictional com-ponent occurring steadily over a period of 100 days asshown here, it is likely to occur more episodically,separated in time from the instantaneous elastic responseto inflation. This may provide an additional clue as to therate at which the magma chamber is being formed; if itforms suddenly, we might observe rapid uplift at thesurface followed by gradual subsidence over weeks–years with accompanying seismic activity; a slowerformation rate may instead show subsidence occurringearly on, with no large-scale initial uplift phase.

5. Discussion

The model experiments have many simplifyingassumptions and the results should be interpreted with

caution. In particular, we have not fully explored theinteractions between magmatism and fluids in theshallow crust. Our representation of crustal structuresand regional tectonics stress fields are kept deliberatelysimple compared to the more complex fault patternsseen, for example, in analogue experiments of calderainflation (e.g., Acocella et al., 2001; 2003) and in nature.Our assumptions about crustal rheology probably over-estimates elastic strength and underestimates the effectsof inelastic rheologies. We have not considered in anydetail the impact of magma inflation on seismogenesis,although this is likely to be one of the main indicators ofanomalous activity (e.g., Sherburn and Nairn, 2004;Steacey et al., 2005; Feuillet et al., 2006). Nevertheless,several trends are apparent in the models that appearrobust, and which we discuss below.

5.1. Simple inflation scenarios for Taupo volcano

Results shown in Fig. 10 illustrate that it may notalways be possible to separate elastic and inelastic effectsduring inflation of a shallow magma chamber. However,if we assume that the initial response is elastic, and thatfrictional and viscous stress adjustment occurs followingthis initial response, we can use the simple elastic inflationmodels to predict the magnitude of ground displacementthat would be expected during the initial inflationary stagefor a given magma body shape and dimension.

In Fig. 11 we summarise some of the experimentalresults concerning shallow inflation of a discoidal magmachamber with dimensions comparable to those demon-strable from previous eruptions (Taupo, Oruanui). Thecontours of vertical displacement plotted on this figureillustrate how small the surface displacement effect maybe, with only centimetres of uplift predicted for inflationof quite a large magma body such as that which fed the35 km3 Taupo 1.8 ka eruption. Fig. 8 shows that detectinga ground motion signal from even deeper inflation wouldbe even more unlikely, unless for a significantly largerbody.

The inflation signal may be amplified somewhat bynear-surface weak elastic layers (Fig. 11c) and/or byactivation of weak ring faults (Fig. 11d). Nevertheless,results suggest that it may be hard to gain much warningof magma chamber inflation, based purely on measure-ments of ground displacement around Lake Taupo. This isparticularly so because most measurements (GPS,InSAR) must necessarily occur several kilometres awayfrom the likely centre of an inflating body within the lake.Measurements located on the Horomatangi Reefs such asthe lake levelling site HI (Otway et al., 2002) mayimprove chances of detecting significant movement.

Fig. 11. Predicted vertical surface displacements around the Taupo region caused by inflation of a discoid magma chamber with (a) Taupo; (b)Oruanui dimensions. Material properties and inflation as described for Fig. 5. (c) like (a) but with weak caldera fill in region indicated by ellipse;caldera properties and dimensions as described in Fig. 9. (d) like (a) but with weak caldera fill and weak slipping ring faults around region indicatedby ellipse; properties and dimensions as described in Fig. 9. All cases assume chamber centre situated at virtual Oruanui vent source as described byWilson et al. (2006). Note that greyscale contours have irregular spacing, with minimum measurable uplift (1 cm) shown by lightest grey shade andtickmarks.


Stress adjustment and displacement along weak ringfaults, (if accompanied by volcano-tectonic seismicity)could also provide clues as to the nature and size of aninflating body at depth. We recommend construction of adetailed bathymetry of Lake Taupo, particularly focusedon the ring-fault boundaries of the Oruanui caldera, thatcan be used as a baseline for future comparisons. Mea-

surement of the change in displacement with distance(strain and tilt) may also be useful (e.g., Fig. 7c). Maxi-mum tilt occurs at distances of ca. 2–5 km from the pointabove a Mogi-like inflating source when the top of thesource is at 4 km. However, for shallow bodies, tiltamounts fall off quite quickly with increasing distance,and is less likely to be resolved at distances of 10 km or


more, unless extremely accurate borehole tiltmeters areused (e.g., Sato and Hamaguchi, 2006). For a discoidalinflation source, maximum tilt occurs somewhat beyondthe diameter of the body. Whatever the shape of the body,as for uplift, the presence of the lake will significantlyhinder detection of shallow inflation bodies by tiltmeasurements unless the diameter of the inflating bodyis very large.

Lake levelling studies have been used to estimate pastregional ground movement at Taupo, for example toanalyse uplift and subsidence related to the swarm eventof the 1980s (Otway, 1986; Otway et al., 2002). The lakelevel data are presented in terms of differential changes inlevel relative to the outlet of the lake (at Taupo township).The location of most of the lake level sites at the edge ofLake Taupo is problematic for detecting the primaryground deformation signature associated with inflation,because our models predict that the differential upliftbetween different locations around the lake edge is likelyto be an order of magnitude smaller than the upliftsignature itself (e.g., Fig. 11). However, the levelling sitelocated on the Horomatangi Reefs is a good position todetect inflation of largemagma bodies centredwithin or atthe sides of the caldera structure. Lake level data have alsobeen used successfully to detect uplift and tectonic groundsubsidence near the Taupo rift (Otway et al., 2002), and inthe future may provide vital evidence for localisedinelastic deformation triggered by ongoing inflation(e.g., Fig. 10).

5.2. Effect of fluids

Vigorous but episodic hydrothermal circulation offluid occurs at many caldera locations as a result of thehigh heat-flow associated with coolingmagmatic systemsoverlain by permeable caldera fill. At Taupo volcano,active hydrothermal venting presently occurs beneath thelake (de Ronde et al., 2002), and fluid pressure changesassociated with hydrothermal activity are a possibleexplanation for periods of seismic unrest within the TaupoVolcanic Zone (e.g., Bannister et al., 2006). Analysis ofquartz microstructures and fluid inclusions in a similarcaldera setting at the Long Valley exploratory well inCalifornia suggests episodic fluid flow embrittlement andoutgassing triggered by seismic events, rather thandirectly by outgassing from a deep magma chamber(Fischer et al., 2003; cf. Hildreth, 2004). Small changes inthe vigour of hydrothermal systems overlying active orsolidified magma bodies at shallow depths can cause theground surface to rise or drop slowly. Fluid pressureeffects (where by “fluids” we mean water or gas ratherthan molten rock) can often be confused with inflation or

deflation of a magma chamber. For example, there isongoing debate as to whether the ground unrest measuredat Campi Flegrei in Italy in the 1970s and 1980s wascaused primarily by magma inflation/deflation (e.g.,Troise et al., 1997) or by fluid migration (e.g., Battagliaet al., 2006). A further source of confusion is that some ofthe fluid pressure changes may relate to exsolution offluids from a gas-saturated crystallizing magma body (DeNatale et al., 2006). Uncoupling fluid from magmaticeffects is therefore difficult. Joint analysis of gravity data,seismicity, and surface deformation may be one way todistinguish fluid pressure changes from magma inflationunrest at calderas by determining both depth and densitychanges (e.g., Battaglia et al., 2006; Battaglia and Vasco,2006). However, such approaches are not feasible overLake Taupo.

5.3. Stress changes and seismicity

Inflation of a magma chamber within the shallow crustmay be accompanied by (1) volcano-tectonic high-frequency earthquakes, with sources dominated by brittlefailure (shear), and/or (2) long-period, low-frequencyevents with sources dominated by fluid-dynamic pro-cesses (e.g., Hill et al., 2003). Long-period eventstypically have extended coda and appear to be generatedby resonance of fluid-filled cracks, where the fluids can beaqueous at shallow depths, or magma at greater depths.An increase in these types of earthquakes indicatesmigration of magma along dikes, and/or aqueous fluid orgas along fractured pathways, and when present cansometimes indicate an imminent eruption. However, it isnot certain that this type of event will occur duringformation of a magma chamber at depth (e.g., Aki, 1984)unless significant migration of magma or gas and fluids isinvolved. In comparison, volcano-tectonic earthquakeswith normal faulting focalmechanisms are common in theactively extending Taupo Volcanic Zone area (e.g., Smithand Webb, 1986; Bryan et al., 1999; Hurst et al., 2002).The occurrence of this type of earthquake is expected toincrease as a magma chamber grows owing to the per-turbation in regional stresses (e.g., Fig. 10; Troise et al.,1997, 2003). Volcano-tectonic earthquake activity willalso increase if fluid pressure and hydrothermal migrationof fluids/gases above the magma body is enhanced,causing fluid pressure-mediated brittle failure in theoverlying crust (e.g.,Waite and Smith, 2002; Husen et al.,2004). Fluid pressure-mediated volcano-tectonic earth-quakes could explain the observed heterogeneous orien-tations of focal mechanisms and swarm-type behaviourwith characteristically high b-values in the TaupoVolcanic Zone (Smith and Webb, 1986; Bryan et al.,


1999; Hurst et al., 2002; Bannister et al., 2006). In thefuture, more accurate determination of swarm eventlocations and focalmechanisms, the spatial distribution ofchanges in frequency–magnitude relationships, and theuse of events to enhance tomographic inversions, mayallow us to definitively analyse the causes of the swarmevents and to determine possible interactions betweenmagma, fluids/gases, and the regional extensional stressfield.

5.4. Precursor to eruption—effect of diking at shallowlevels

We have used the models above to investigate effectsdue to inflation of a shallow magma chamber, and havedemonstrated that the ground deformation will belimited, depending on the strength of the crustsurrounding the chamber, its shape, and dimensions.These models are useful for considering effects duringthe early stages of a build-up to a possible rhyoliteeruption at Taupo. If the magmatic system does becomeunstable, in the days preceding an eruption there islikely to be further migration of magma along a series ofdikes leading towards the surface. For example, atRabaul caldera in Papua New Guinea, explosiveeruptions around the caldera rim in 1994 were precededby diking that caused several metres of uplift, as well asaccompanying shallow seismicity (Mori and McKee,1987; Saunders, 2001). At Taupo, there is evidence fordiking, at least during the 1.8 ka eruption. First, vents forthe early explosive phases were aligned along a ∼10 kmNNE–SSW line (Smith and Houghton, 1995); eruptionof largely degassed magma from the northeasterly of thevents shows that this diking must have occurred someshort time before the eruption commenced (Houghtonet al., 2003). Second, a locally faulted sequence of the1.8 ka eruption deposits up to but not including the(eroded) climactic ignimbrite has been found (Leonardet al., 2004), implying that dike propagation occurredfor a farther 10 km to the NNE during the eruption.

5.5. Interaction between inflation and regional tectonics

Fig. 10 shows evidence for an intriguing relationshipbetween magmatic inflation and regional extensiontectonics. In particular, the model results suggest thatinitial uplift associated with inflation of a magma bodyis an elastic response, which is modified to subsidenceonce inelastic effects due to thermally-activated ductilecreep and frictional plasticity are given sufficient time toreact. The effects have different length-scales at thesurface, with the inelastic response occurring directly

over the top of the hot, low-viscosity magma body(Fig. 10d,e). The effect is to reduce the regional stressfield in the vicinity of the magma body and to causesubsidence there, while surrounding areas may maintaina net uplift. The area of reduced stress (Fig. 10f) maypersist for thousands of years while the magma bodyslowly cools and strengthens, and regional extensiongradually restores the ambient stress field. The 1.8 kaeruption occurred a sufficiently short time ago that asignificant stress perturbation likely remains near LakeTaupo, which may be affecting the style of grounddeformation and seismicity there. Although we have notmodelled inelastic deformation for the Taupo system indetail, a possible consequence of the balance betweenelastic and inelastic effects, especially if significantmaterial is added to the magmatic system from below, isthat rift subsidence may be suppressed near the caldera(e.g., Manville and Wilson, 2003). Interestingly, thepattern of elastic uplift and inelastic subsidence sug-gested by the model shown in Fig. 10 is similar to thatobserved around the time of the 1983 Taupo swarm,although the cause of the swarm is still disputed, as wasdiscussed in Section 3.4.

5.6. The “space problem” for magma intrusion

Geochemical constraints on sizes and depth range ofpast magma bodies beneath Taupo (Section 2.3; Table 1)indicate that these bodies were sill-like rather thanvertical dikes. Is this consistent with an extensional tec-tonic setting where minimum compressive stress direc-tion is horizontal? How is vertical space for magmacreated in this case?

This “space problem” has been discussed bynumerous studies (e.g., Hogan et al., 1998; Petfordet al., 2000). There are several ways in which sills mayform in a horizontally extending tectonic setting:

(1) Compaction of existing rock via melt extraction.There is evidence that past TVZ magma bodieswere at least partially derived from re-melting ofexisting crust (Charlier et al., 2005; Price et al.,2005). Episodic addition of small batches ofmagma from below triggers melting in-situ, sothat volumes of melt being “added” at any onetime are quite small.

(2) Perturbation in regional tectonic stresses aroundthe intruding body (e.g., Hogan et al., 1998). Theaddition of the magma pressure perturbs principalstress orientations and can cause minimum com-pressive stress to switch to vertical orientations.The inherently 3D stress field and interactions


with local structure around the caldera (e.g.,Rowland and Sibson, 2001) can also createzones where minimum compressive stress is nolonger horizontal.

(3) It is often observed that magma accumulates nearthe brittle–ductile transition, which appears to actas a rheological barrier to upward migration ofmagma, since fracture is necessary to force apathway through the brittle crust. The sill-likeform of magma bodies is then due to lateral mi-gration along an impermeable boundary withinductile crust, where differential stresses are mini-mised and can be relieved by creeping (Vigner-esse, 1995; Aizawa et al., 2006).

5.7. Inversion of surface deformation and other geophy-sical observables to determine magma body properties

If a small surface displacement were observed aroundthe shores of Lake Taupo sometime in the future, howwould we go about determining the cause of thisdisplacement, and if ultimately caused by magmaticinflation, can we determine the size, shape and depth ofthe magma body in order to assess hazard? Unfortu-nately inversions of the ground displacement resultingfrom inflation of magma or other pressure sources suchas aqueous fluids are always non-unique (e.g., Battagliaand Vasco, 2006). In Section 4 we have used forwardmodelling, using plausible guesses for the shape anddepth of a magma body, based on inferences fromprevious eruptions. We have shown how the effect ofcrustal structure and regional tectonics can completelychange the observed deformation field at the surface.Changes due to fluid effects, although not modelled indetail here, can cause surface deformation patterns verysimilar to those caused by magmatic inflation events(e.g., Hurwitz et al., 2007).

Our best hope for determining the cause of a period ofunrest and/or surface displacement, is to jointly invertgeophysical observations from geodesy, gravity (e.g.,Fernandez et al., 2001; Battaglia et al., 2006; De Nataleet al., 2006), and seismicity. Changes in the state of thehydrothermal system (chemistry, temperature) and gasemissions could provide important clues if they weremonitored in the future. In addition, we could search forchanges in the state of the shallow crust using repeatelectromagnetic soundings and observations of seismicvelocity structure. The key is in determining the depth ofan inflating body. The shallower the body, the morelikely that surface displacement is caused by changes inthe hydrothermal system rather than by magma inflation,although it is probable that the two processes are linked

(e.g., Husen et al., 2004; De Natale et al., 2006). Largevolume changes of fluid are also required in order toproduce a measurable ground deformation. However,even small changes to the fluid circulation system maytrigger seismicity above an inflating magma chamber.An additional challenge when inverting geophysicalsignals for cause of inflation or subsidence beneathTaupo, is the presence of the lake, which may make aunique inversion for depth and source impossible.

Even if it is determined that the cause of a particularunrest episode is the hydrothermal circulation ratherthan inflation of a magma chamber, we would still needto understand the cause of episodic fluid circulation.Ultimately it must relate to magma at depth and the highheat-flow and energy present beneath Lake Taupo.While changes in the geothermal system could causerapid and short-lived changes in seismicity, gravity andground deformation (e.g., Gottsman et al., 2005;Hurwitz et al., 2007), the long-term buoyancy of thecrust to the north of Lake Taupo demands a longer-term,consistent source of buoyancy which is most easily metby melt injection (Manville and Wilson, 2003) and thelong-term build-up of low density silicic intrusions maybe one result of this.

6. Conclusions

In this paper we have summarised available geo-physical, geochemical and geological evidenceconcerning the past and present state of Taupo volcano,in order to assess the likely signal due to a hypotheticalmagma inflation event in the future. A summary ofavailable evidence suggests that:

(1) Previous magma chambers at Taupo leading to largecaldera eruptions, had sill-like geometries, andresided at shallow depths of∼6–4 km with volumesthat ranged from very small (b0.1 km3) to extremelylarge (∼530 km3).

(2) Neither magnetotelluric sounding, nor seismicvelocity analyses show any evidence of shallowcrustal melt beneath Taupo at the present time.However, the physical barrier caused by the lakemakes geophysical measurements ambiguous, sothe presence of small amounts of partial meltcannot be ruled out. Continuous monitoring fortemporal changes in geophysical signals, lakelevelling, and bottom instrumentation (OBS, waterbottom MT) may offer the best hope of detectingsuch bodies.

(3) Numerical model experiments using a sill-likeshape for an inflating magma chamber, and


physical properties for crust and magma derivedfrom geochemical and geophysical observation,show that even a large inflating body at shallowdepths beneath Lake Taupo produces a relativelysmall ground deformation signal. This signal canhowever be enhanced by the presence of weakelastic layers (e.g., due to volcanic fill within thecaldera) and if displacement is triggered on weakcaldera ring faults.

(4) Interactions between a regional extensional stressfield and magma inflation when the crust ismodelled including inelastic rheologies, demon-strates that the long-term effects of magma inflationcan cause extensional faulting and subsidence inoverlying crust. This illustrates the importance ofconsidering regional stress fields when interpretingunrest events at calderas.

Acknowledgements

We would like to thank Tony Hurst, Brad Scott,Bryan Davy, Pilar Villamor, Kelvin Berryman, AndyNicol, Grant Caldwell, Julie Rowland, Euan Smith, andJohn Townend for useful discussions. We also thankMaurizio Battaglia and an anonymous reviewer for theirconstructive reviews. The bulk of the funding for thispaper came from Marsden contract GNS202 to ColinWilson and Hugh Bibby, with some additional fundingfrom PGSF funding to GNS Science under contractCO5X0402.

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