Volcanotectonic interactions between Mauna Loa and Kilauea: Insights from 2-D discrete element simulations

Journal of Volcanology and Geothermal Research 151 (2006) 109 – 131 www.elsevier.com/locate/jvolgeores

Volcanotectonic interactions between Mauna Loa and Kilauea: Insights from 2-D discrete element simulations Julia K. Morgan * Rice University, Department of Earth Science, 6100 Main Street, Houston, TX 77251, United States Accepted 15 July 2005 Available online 10 January 2006

Abstract Numerical simulations using the discrete element method (DEM) are carried out to examine the dynamics and internal deformation of overlapping volcanoes constructed upon a weak de´collement horizon, as analogs to the Kilauea–Mauna Loa system of volcanoes in Hawaii. Employing a frictional rheology, the DEM simulations capture much of the complex deformation behavior of Mauna Loa and Kilauea volcanoes, here referred to as the primary and secondary edifices, respectively. The models demonstrate incremental displacements of the outer flanks of the volcanoes and concurrent summit subsidence, leading to characteristic low slopes and inward dipping strata. Slip discontinuities that develop within the piles define steeply dipping normal faults along the upper flanks and beneath the edifice summits, that accommodate subsidence and flank spreading. Edifice overlap influences dynamic behavior significantly; even small topographic perturbations restrict the internal deformation and spreading of the confined flanks. The degree of buttressing depends on the relative positions of the two edifices. If the secondary edifice grows high upon the flanks of the primary edifice, outward spreading of the underlying flank is enhanced; if the secondary edifice is built low upon the primary flanks, spreading of the underlying flank is effectively prevented, or possibly reversed. Furthermore, as the second edifice grows, it subsides into the underlying flank, partitioning it into a mobile downslope region entrained by spreading of the second edifice, and a comparatively stable upper flank region. These results suggest that much of the mass of Kilauea volcano may lie deeply buried within the underlying flank of Mauna Loa, while older Mauna Loa rocks may lie far from their source beneath the mobile flank of the younger volcano. D 2005 Elsevier B.V. All rights reserved. Keywords: Mauna Loa; Kilauea; volcanotectonics; volcanic spreading; Hawaii; landslides; subsidence

1. Introduction Kı¯lauea volcano is built upon the southeastern flank of the enormous edifice of Mauna Loa volcano, and together, these two volcanoes comprise ~70% of the area of the Big Island of Hawaidi (Fig. 1). Both volcanoes are subject to gravitational stresses that contribute

* Tel.: +1 713 348 6330; fax: +1 713 348 5214. E-mail address: [email protected]. 0377-0273/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jvolgeores.2005.07.025

to summit, rift zone, and flank deformation, resulting in substantial lateral spreading during their growth (e.g., volcanic spreading, Borgia et al., 2000). This spreading is manifested through seaward displacements of the volcano flanks (e.g., Owen et al., 1995, 2000; Delaney et al., 1998), distal shortening (Denlinger and Okubo, 1995; Morgan et al., 2003), and long-term summit subsidence (e.g., Walker, 1992; Delaney et al., 1993; Miklius et al., 1997; Quane et al., 2000). The threedimensional configurations of these and adjacent volcanoes lead to complicated interactions as the volca-

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Fig. 1. Shaded relief map of the southern portion of the Island of Hawai‘i and offshore regions, showing relative positions of Mauna Loa (ML), Kı¯lauea (Kil), and Lo¯dihi (Loi) volcanoes, as well as Hualalai (Hua) and Mauna Kea (MK). Darker shaded region outlined in black denotes the island. Subaerial Kı¯lauea volcano, built along the flank of Mauna Loa, is indicated by inclined white lines. Dashed lines delineate volcanic rift zones, emanating from encircled calderas. Hachured lines indicate normal fault scarps, with the hachures pointing in the down dip direction. Lines decorated with teeth outline the boundaries of interpreted overthrust packages at the toes of the spreading volcanoes (dashed where less certain; teeth lie on the hanging wall). Arrows denote relative directions of strike-slip fault motion. Important subaerial and submarine features are labeled as follows: HFZ—Hilina fault zone; KFZ—Kaoiki fault zone; KoFZ—Koae fault zone; KaFZ—Kahuku fault zone; KeFZ—Kealakekua fault zone; MSB—midslope bench of Kı¯lauea’s south flank; KWB—Kı¯lauea’s western boundary; SKS—South Kona slump; NKS—North Kona slump; ERZ—East Rift Zones of Kı¯lauea and Mauna Loa; SWRZ—Southwest Rift Zones of Kı¯lauea and Mauna Loa; CSM—Cretaceous seamounts. Heavy dotted line traversing the mapped area marks the position of interpretive cross-section in Fig. 12. Bathymetry gridded at 100 m from Smith et al. (1994).

noes grow and deform. Due to their proximity, Kı¯lauea and Mauna Loa buttress each other, restricting faulting and displacement of their adjoining flanks. Their seaward flanks, however, show evidence for substantial past deformation, in the form of extensive seaward dipping normal faults along their upper flanks, and uplifted midslope benches along the submarine flanks (e.g., Swanson et al., 1976; Lipman et al., 1985, 1988; Moore et al., 1989, 1994). Present-day motions of Kı¯lauea’s south flank are also substantial, and include seaward creep of up to 10 cm/yr in recent years, and possibly even higher in previous decades (e.g., Swanson et al., 1976; Delaney et al., 1993, 1998; Denlinger and Okubo, 1995; Owen et al., 1995, 2000; Delaney and Denlinger, 1999), as well as intermittent damaging flank earthquakes (e.g., Ando, 1979; Furumoto and Kovach, 1979; Crosson and Endo, 1981; Bryan, 1992). Mauna Loa’s flanks are much less active, showing lower displacement rates and fewer large earthquakes (e.g., Wyss, 1988; Wyss and Koyanagi, 1992; Gillard et al., 1992; Miklius et al., 1995, 1997). The contrasting behaviors of the two volcanoes raise the question as to what degree the two edifices influence each other dynamically, both today and in the past.

Numerical simulations can be used to investigate gravitationally induced stresses that influence volcanotectonic deformation. In a previous study using the discrete element method (DEM), the self-similar growth and gravitational deformation of symmetric granular piles were simulated as analogs for natural volcanoes subject to Coulomb rheology (Morgan and McGovern, 2005-a,b). These preliminary simulations successfully reproduced structural and morphologic features recognized at several basaltic volcanoes, including their low surface slopes, deep-seated and surficial detachment faults, and distal overthrusting at the toes of the flanks (Morgan and McGovern, 2005-a). Although magmatic processes are no doubt important, the results demonstrate that gravitational stresses alone can explain much of the observed deformation at natural volcanoes. Furthermore, the mode of edifice deformation proves to be highly dependent upon the strength of the volcanic substrate (Morgan and McGovern, 2005-b). Surface slopes and dips of detachment faults that develop during steady state volcano growth are directly predicted by the basal strength conditions, yielding distinct layer geometries that can be compared with natural analogs

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to make predictions about past and future volcano dynamics. In this study, I extend the DEM modeling approach to investigate dynamic interactions between overlapping edifices subject to volcanic spreading. In this way, we can explore the degree to which overlapping volcanic edifices either enhance or buttress flank deformation and spreading. First-order results demonstrate that the growth of even small topographic features can suppress spreading of the underlying flank, resulting in dramatic changes in volcano behavior and associated deformation. Based on these findings, it appears that even during the earliest stages of growth, Kı¯lauea volcano may have pinned much of Mauna Loa’s south flank. Furthermore, as the younger volcano grew in size, locally induced gravitational settling resulted in summit subsidence and increasing displacement of its seaward flank, consistent with supporting geophysical and geodetic evidence. 2. Geologic background Hawaiian volcanoes represent some of the best examples of volcanic spreading on earth (e.g., Borgia et al., 1990, 2000). Geodetic data reveal ongoing creeping displacements of Kı¯lauea volcano’s southeast flank, seaward of the summit and two radial rift zones (e.g., Swanson et al., 1976; Owen et al., 1995, 2000; Delaney et al., 1998). Flank motion is punctuated by intermittent earthquakes. The most recent large earthquake, the 1975 M 7.2–7.7 Kalapana earthquake, yielded a bestfit focal mechanism consistent with low-angle seawarddirected thrusting beneath Kı¯lauea’s southeast flank (Ando, 1979; Furumoto and Kovach, 1979; Crosson and Endo, 1981, 1982; Nettles and Ekstrom, 2004). Flank displacements are attributed to slip along a weak detachment plane, probably coincident with the top of the oceanic crust. Mauna Loa also exhibits some flank creep, as well as de´collement earthquakes, particularly along its southeast flank (Wyss et al., 1992; Wyss and Koyanagi, 1992; Walter and Amelung, 2004), but at much lower rates and frequencies than Kı¯lauea. The great Kau earthquake of 1868, estimated at M 8.0 and the largest in the islands in historic time, initiated rift zone eruptions at both volcanoes (Stearns and Macdonald, 1946; Macdonald and Abbott, 1970; Clague and Denlinger, 1993), and is thought to have accommodated seaward slip of both Mauna Loa’s and Kı¯lauea’s southeast flanks (e.g., Wyss, 1988). Although there is little geodetic evidence for present-day flank displacements along Mauna Loa’s west flank (e.g., Miklius et al., 1995), occasional small de´collement earthquakes

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this century (Gillard et al., 1992; Wyss and Koyanagi, 1992) point to continuing effects of lateral shear stresses that can drive outward flank displacements. The causes for such flank mobility have been debated for years. The presence of high velocity, high density intrusive materials beneath the summits and rift zones suggests that forceful magmatic intrusions may push the flanks seaward (e.g., Swanson et al., 1976; Hill and Zucca, 1987). Alternatively, gravitational settling of the volcanic edifice may generate sufficient outward directed shear stresses (Delaney et al., 1998; Morgan and McGovern, 2005-a). Both conditions, which may act in tandem (e.g., Dieterich, 1988), require low effective strengths along the base of the edifice. The low strength could reflect weak materials, such as overpressured pelagic clays along a basal de´collement (e.g., Nakamura, 1980; Iverson, 1995), or ductile materials within a deep magma chamber or cumulate body (e.g., Delaney et al., 1990; Borgia, 1994; Clague and Denlinger, 1994). The surface of the Island of Hawaidi is intersected by systems of normal faults, many of which have been active in historic times. These structures reflect the past state of stress within the island, although unfortunately, their depths and orientations are subjects of continuing debate. The seaward-dipping Hilina fault system on Kı¯lauea’s south flank (Fig. 1) has been interpreted to define a set of steeply dipping normal faults that intersect the top of the oceanic plate and contribute to flank sliding (e.g., Lipman et al., 1985; Moore et al., 1989, 1994; Okubo et al., 1997). Alternatively, the faults have shallow dips and listric geometries, bounding a surficial slump that rides on top of the mobile south flank of Kı¯lauea (e.g., Swanson et al., 1976; Cannon et al., 2001; Cervelli et al., 2002; Morgan et al., 2003). Similar outward dipping normal faults exist elsewhere on the island, also with poorly constrained dips; the traces of the Kahuku and Kealakekua fault zones extend inland from the south and west coastlines of Mauna Loa, respectively (Fig. 1), and may once have defined a throughgoing landslide detachment that cut the upper flank of this massive volcano (Lipman et al., 1988; Lipman, 1995). The unusually steep slopes on Mauna Loa’s west flank may reflect the underlying landslide scar produced by catastrophic sector collapse along these faults. The Kaoiki and Koae fault systems bracket, and generally dip toward, the summit of Kı¯lauea volcano (Fig. 1). The Kaoiki faults lie near the junction of Kı¯lauea and Mauna Loa, and trend toward a set of steep seaward dipping scarps along Mauna Loa’s flank to the southwest (Fig. 1). This combined system

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of faults may once have accommodated seaward slumping along Mauna Loa’s flank before becoming buttressed by Kı¯lauea volcano (Lipman et al., 1990). Seismic tomographic models suggest that the fault zone extends nearly to the base of the volcanic edifice and dips steeply seaward beneath Kı¯lauea’s north flank (Okubo et al., 1997). Recent seismicity along the Kaoiki fault zone indicates a large component of strike slip sense of motion, reflecting complex interactions between Mauna Loa and Kı¯lauea’s volcanoes (Bryan and Johnson, 1991; Jackson et al., 1992; Wyss et al., 1992). The Koae fault system extends between the two active rift zones bounding Kı¯lauea’s south flank, and appears to accommodate similar extensional displacements (e.g., Duffield, 1975; Swanson et al., 1976; Fiske and Swanson, 1992). Their inward dips, however, remain enigmatic. New marine surveys in the area have helped to clarify the structures of the submarine flanks of the two volcanoes. Seismic reflection surveys and submersible studies confirm that the frontal benches near the toes of the flanks arise from overthrusting and accretion of volcaniclastic debris as a result of seaward flank movements (Smith et al., 1999; Morgan et al., 2000, 2003; Lipman et al., 2002, 2003; Morgan and Clague, 2003), supporting previous interpretations based primarily on morphology and kinematics (e.g., Moore et al., 1989; Borgia et al., 1990; Denlinger and Okubo, 1995). Flank displacements of 15–24 km estimated for Kı¯lauea’s frontal bench (Morgan et al., 2000; Hills et al., 2002) imply substantial rates and/or a long history of volcanic spreading at this relatively young volcano (Morgan et al., 2003). Recent submersible surveys along Kı¯lauea’s submarine flank have now revealed that volcanic rocks with Mauna Loa affinities lie at shallow depths near the western boundary of Kı¯lauea’s mobile submarine flank, and near the base of the frontal bench (Lipman et al., 2006; Kimura et al., 2006). It also now appears that the younger volcano initially erupted at or near sea level, potentially constraining the pre-existing morphology of Mauna Loa (Coombs et al., 2006). These observations have led to the enticing suggestion that Kı¯lauea is actually a relatively small volcano, overwhelmed volumetrically and geodynamically by the much larger and older Mauna Loa volcano upon which it is built. If so, is it possible that the substantial deformation at the toe of Kı¯lauea’s south flank was induced by topographic stresses generated by Mauna Loa, with Kı¯lauea riding piggyback along its flank (Lipman et al., 2006)? This is a hypothesis that can be tested more completely through modeling.

3. Numerical methods The discrete element method (DEM) is a discontinuous numerical technique analogous to molecular dynamics, but optimized for elastico-frictional particles, e.g., grains of sand (Cundall and Strack, 1979). The numerical approach is attractive for studying shallow crustal materials subject to frictional (Coulomb) behavior, because the DEM assemblage of particles can exhibit localized deformation comparable to brittle faulting. DEM simulations have long been used to investigate geotechnical and related problems, e.g., soil deformation, slope stability and failure (e.g., Mustoe et al., 1987; Chang, 1992; Sitharam and Nimbkar, 1997). Geophysics applications include studies of the micromechanics of granular shear and fault friction (e.g., Antonellini and Pollard, 1995; Morgan and Boettcher, 1999; Morgan, 1999; Aharonov and Sparks, 1999; Mora and Place, 1993, 1998). DEM is also well suited to simulating large-scale geodynamic phenomena, serving as a numerical sandbox in which mechanical as well as kinematic observations can be made. Recent applications include the reactivation of basement faults (Saltzer and Pollard, 1992), compressional fold and thrust complexes and orogenic evolution (Morgan, 1997; Burbridge and Braun, 2002; Strayer et al., 2004; Vietor, 2003), fault-propagation folding (Finch et al., 2003), and graben formation (Seyforth and Henk, 2003). This study extends the geodynamic applications of DEM to granular (sand) piles as analogs to interacting natural volcanoes; the simulations are conducted in two dimensions (2-D). This work follows upon two previous reports on gravitationally driven deformation and associated evolution of symmetric 2-D granular piles (Morgan and McGovern, 2005-a,b). We use a soft-sphere particle dynamics method that includes the effects of elastic particle deformation during contact. Particle motions are induced by gravitational forces, external forces prescribed by stress or strain rate boundary conditions, and by forces resolved at interparticle contacts. Particles obey discontinuous elastico-frictional contact laws (e.g., Cundall and Strack, 1979; Mora and Place, 1998; Aharanov and Sparks, 2004): the elastic stiffness of the particles resists relative particle approach, imparting a force normal to the contact; shear displacement is resisted by interparticle friction coefficient, l p, according to Amonton’s Law (e.g., Johnson, 1985). Interparticle cohesion can also be introduced (e.g., Morgan and McGovern, 2005-a), but is neglected in this study. The net force and moment on a particle are substituted into Newton’s equations of motion to obtain velocities and displacements (Cundall and

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Strack, 1979; Morgan and Boettcher, 1999). The disequilibrium of forces acting on a particle drives its displacement, leading to interactions with other particles. The simulation cycle alternates the calculation of contact forces and particle displacements in response to the net force acting on each particle, until the assemblage is at equilibrium in a minimum energy configuration. Energy of the system is dissipated at each time-step using a viscous damping coefficient (e.g., Cundall and Strack, 1979; Cundall, 1987; Walton, 1995). Interparticle mechanical parameters, such as friction coefficient and cohesion, do not uniquely describe the bulk strength of the assemblage of interest here. The bulk friction coefficients for internal sliding, l int and basal sliding, l bas result from the coordinated deformation behavior of the assemblage of particles, and must be determined empirically in terms of l p. These relationships have been established through a series of internal shear and boundary sliding experiments of 2D assemblages of round particles (e.g., Morgan, 1999), which show that a unique one-to-one parametric relationship between l p and l int can be obtained to values in excess of one if particle rolling is restricted (Morgan, 2004). The maximum value for l bas, however, proves to be limited to ~0.3 due to assemblage dilatancy. Deformation of the assemblage, both basal and internal, will occur when the resolved shear stress, s # reaches or exceeds s #max defined by the Coulomb yield criterion for noncohesive materials: ¼ l# rn ; smax #

ð1Þ

where r n is the normal stress acting upon a potential slip plane, and the subscript ‘#’ is given to refer to either bas or int, as appropriate. More complete descriptions can be found elsewhere (e.g., Cundall and Strack, 1979; Morgan and Boettcher, 1999; Morgan and McGovern, 2005-a). 4. Experimental design 4.1. Experimental set-up Incremental growth of granular piles representative of volcanic edifices is simulated by brainingQ frictional particles upon a planar substrate and allowing them to settle under gravity. Note that this condition is a simplification of the actual growth of Hawaiian volcanoes upon an elastic oceanic lithosphere, which flexes downward as the edifices grow, affecting both basal and internal stress states (e.g., McGovern and Solomon, 1993; Martel, 2000). The simulations are conducted in two dimensions (2-D), approximating the generally lateral growth of the volcanoes perpendicular to their rift

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zone; particles are centered on a central plane, and lack out of plane interactions. The model domain is scaled to 150 km in width, which approximates the dimensions of the Mauna Loa–Kı¯lauea system (Fig. 1). The domain is bounded by a fixed row of basal particles, and two columns of vertical particles that prevent interactions across the lateral periodic boundaries. The x-axis is positive to the right; the y-axis is positive upward. Scaled dimensions of the particles and particle abundance are summarized in Table 1. Two particle sizes are used to build the pile, at 1200 and 900 m in diameter, preventing formation of ordered granular packings. This particle size constrains the minimum thickness of a deforming layer to ~1 km, corresponding to shallow surficial avalanching along the volcano flanks. The vertical walls are composed of particles 1500 m in diameter. The base is constructed of particles 750 m in diameter, creating a relatively smooth basal surface. Particle densities are set to 2030 kg/m3 throughout the domain, slightly low relative to typical densities of basalts; however, this partially accounts for the buoyancy of particles in submarine environments, and the associated reduction in gravitational potential. Particles are randomly generated, 75 at a time, within narrow bands immediately above the granular piles, referred to as the first and second piles (Pile 1 and Pile 2, respectively). Particles are allowed to settle onto the substrate and growing piles, and do so by spreading across the pile surfaces, much like lava flows erupted from the volcanic centers. Towards the ends of the simulations, particle and flank displacements occasionally impinge on the lateral walls, which serve to buttress the flanks causing uplift and shortening, similar to that interpreted along the distal flanks of Hawaiian volcanoes (Denlinger and Okubo, 1995; Morgan et al., 2003). Velocity damping during particle deposition ensures that the particles do not introduce dynamic forces when they reach the pile surface. Once each new batch of particles has settled, and the assemblage has reached equilibrium conditions (~4000 time steps are allowed for each increment), particle positions, contact locations, and force magnitudes are Table 1 Particle dimensions and abundance Particles

Diameter (m)

Abundance

Walls Base Pile 1 (gray outlines) Pile 2* (black outlines)

1500 750 1200 900 1200 900

59 per wall 200 total 15 per increment 30 per increment 10 per increment 20 per increment

*Pile 2 growth initiates after Increment 12.

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Table 2 Numerical simulations and parameters Test

Pile spacing (km)

Basal friction

L26C L17C L18C L19C L20C L24C L27C L22C L21C L23C L25C

– 24.00 26.25 28.50 33.75 41.25 – 28.50 33.75 38.25 46.50

0.20 0.20 0.20 0.20 0.20 0.20 0.10 0.10 0.10 0.10 0.10

recorded for future processing. Particle batches are assigned one of four colors at formation (two colors for each pile), and the colors are cycled every 300 particles (or less for Pile 2) to define the internal stratigraphy, further clarifying particle displacements and deformation history as the piles grow. The addition of particles to the granular piles increases their gravitational potential and lateral shear stresses, which must be reduced by avalanching of particles down the pile slopes or by internal reorganization, e.g., through localized faulting or distributed deformation, and slip along the base of the pile. The frictional parameters that govern this deformation for each experiment are listed in Table 2. As shown by Morgan and McGovern (2005-a,b), the preferred mode of deformation is influenced by mechanical properties of the particle assemblage, in particular, the internal and basal friction coefficients l int and l bas, respectively, through the Coulomb yield criterion, Eq. (1). In this study, we hold l int constant at 0.6, in accordance with Byerlee’s law (Byerlee, 1978), and all particles are non-cohesive. This approximation is justified on the basis of the highly fractured nature of the volcanic rocks, both on and offshore. The previous simulations of symmetric granular piles described by Morgan and McGovern (2005-a) reveal a spectrum of deformation structures, layer stratigraphies, and slope morphologies for a range of l bas values. Based on these simulations, l bas is assigned to the low values of 0.1 and 0.2 for this study, ensuring internal deformation of the pile. 5. Results 5.1. Symmetric edifice growth

which is analogous to the large edifice of Mauna Loa, upon which Kı¯lauea grew. Simulations are conducted for the two different basal friction coefficients to explore the influence on pile geometry and deformation. During symmetric growth, the piles grow self-similarly upon the planar substrate, spreading outward by slip along a portion of the basal de´collement. The simulations with l bas of 0.2 develop an axial high preserved in the colored layers of particles, denoting a stable core of the pile that is not subject to internal shearing (Fig. 2a). This stable core grows in size as the pile builds, incorporating material that underwent shearing during earlier growth stages. Steeply dipping normal faults, denoted as zones of high displacement gradients, form at the boundaries of the stable core and accommodate downslope displacement of the outer flanks, transferring slip onto the de´collement surfaces about half way along their lengths (Fig. 2b). The surfaces of the flank are concave up, with a range of dips between 158 (lower flank) and 248 (upper flank). In simulations with l bas of 0.1, the pile develops with much lower slopes, and the central high is reduced in size. Instead, the lowest layers are extremely thinned in the central region, but thickened and inward dipping in the distal reaches of the flanks (Fig. 3a). A greater length of the de´collement experiences slip, and the relative positions of the internal detachment faults shift inward and intersect each other below the summit of the pile (Fig. 3b). Accordingly, the stable core beneath the summit is much smaller than for the stronger base. In this lower basal strength configuration, the conjugate, normal faults in the core of the pile accommodate summit subsidence, which in turn drives the flanks of the pile outward along the basal de´collement. This is in contrast to the stronger basal strength configuration, in which only the flanks deformed and subsided (Fig. 2b). Again, the final pile configuration shows a distinct concave up morphology, but much lower slopes, ranging from 68 to 178. Layering dips uniformly inward, defining a broad axial syncline. The equivalent continuum stress field within each pile can be calculated by summing the directional components of the interparticle contact forces for all particles within a domain (e.g., Thornton and Barnes, 1986; Morgan and Boettcher, 1999): " # N m   X 1 X a a rij ¼ r f ; ð2Þ V p¼1 a¼1 i j p

The initial stage for all simulations involves symmetric growth of a granular pile of significant size,

where r ij represent the components of the average stress tensor (in indicial notation; i, j = 1,2, or x,y in

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Fig. 2. Representative simulation results for symmetric granular piles built upon substrate with l bas = 0.2, Test L26C, after growth Increment 21. (a) Particle configuration; particle layers indicated by different shades. Strata show axial high, flank synclines, and inward dipping strata along the outer flanks. (b) Displacement discontinuities for previous increment of settling are highlighted by taking the vertical gradient of the horizontal displacement field, obtained using a nearest neighbor searching algorithm (Wessel and Smith, 1995). Darker zones denote regions of high shear strain, indicating surficial avalanching of particles along the upper flanks, and outward dipping, high angle normal faults extending from the summit. (c) Vertical normal stress component, r yy. Contour roughness near the base of the pile reflects discrete grain bridges that support the load. Stress contour interval is 30 MPa. (d) Horizontal normal stress component, r xx . (e) Maximum principal compressive stresses, r I . Note increasing deflection from vertical with distance from the center of the pile, due to increasing topographically induced lateral shear stresses.

2-D Cartesian coordinate), V is the volume of the averaging domain containing N particles, each with m contacts, rai are the components of the particle radius normal to the contact, and f ja is the total contact force

acting in the ith direction (see Morgan and McGovern, 2005-b). The gridded directional components of the stress tensor then can be fit to continuous surfaces for plotting using GMT (Wessel and Smith, 1995).

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Fig. 3. Representative simulation results for symmetric granular piles built upon substrate with l bas = 0.1, Test L27C, after growth Increment 21. (a) Particle configuration; shaded layers show axial syncline, and inward dipping layers. (b) Displacement discontinuities for previous increment of settling. High angle normal faults undercut the summit, and intersect the basal de´collement. (c) Vertical normal stress component, r yy. (d) Horizontal normal stress component, r xx . (e) Maximum principal compressive stresses, r I . Compressive stresses remain subvertical throughout the pile, indicating reduced shear stresses due to the weak de´collement.

The stress field within a granular pile depends on pile geometry and friction parameters, and compares favorably with stress distributions obtained for analogous elastic models (e.g., McGovern and Solomon, 1993; Martel, 2000). Contours of vertical stress, r yy tend to mimic the topography of the surface (Figs. 2c and 3c), primarily reflecting the weight of the overbur-

den at any given point; irregular highs near the base of the pile result from chains of particles that bear high contact forces. Contours of horizontal stress, r xx show a similar pattern, paralleling topography (Figs. 2d and 3d), but only reach values up to 50–60% of r yy. The peaked topography of the granular piles causes the progressive rotation of the maximum compressive

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stress, r I with distance from the axis of the pile; r I is subvertical along the axis, and is increasingly deflected outward with distance from the summit (Figs. 2e and 3e). The greater rotation of r I for l bas = 0.2 than for l bas = 0.1 reflects the higher shear traction stresses along the base, governed by s max bas , as in Eq. (1). As expected, the results of these two simulations of symmetric pile growth match those described by Morgan and McGovern (2005-a). The results of the simple symmetric simulations presented here compare well to several volcanic systems, specifically Kı¯lauea volcano, La Palma in the Canary Islands, and Olympus Mons on Mars (Morgan and McGovern, 2005-a). The surface slopes, deepseated, high angle detachment faults, and outward displacements of nearly the entire flanks demonstrated for the low l bas configuration, most closely match characteristics of Kı¯lauea volcano and Olympus Mons, both of which are thought to have undergone volcanic spreading (Denlinger and Okubo, 1995; Borgia et al., 2000). Higher slopes associated with l bas N 0.2 tend to develop more surficial landsliding, consistent with observations in the Canary Islands, which are thought not to have experienced basal sliding and volcanic spreading (Car-

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recedo, 1999; Day et al., 1999; Mitchell et al., 2002). For this reason, the lower basal strength condition is preferred for the subsequent study of the Mauna Loa– Kı¯lauea volcanic system, but for completeness, simulations are carried out for both l bas = 0.2 and 0.1. 5.2. Interacting edifices Volcano overlap will lead to complicated interactions induced by the gravitational stresses that drive volcanotectonic deformation of each edifice. Additional factors that may influence the deformation behavior of overlapping volcanoes include the onset of edifice growth, the relative growth rates, and the distance between volcanic centers. In the simulations presented here, modeled after the Mauna Loa–Kı¯lauea system, a new granular pile grows upon the right flank of a preexisting symmetric, older and larger pile, following the 12th growth increment of Pile 1. The internal and basal strength conditions are the same for each pile. Only the spacing between pile centers will be varied, to assess how similar granular piles interact and influence each other’s stress fields and evolution. Due to the exposure of deeper layers in the more distal reaches of the

Fig. 4. Particle configurations following 24 increments of pile growth, for overlapping piles constructed upon l bas = 0.2 substrate; lighter outlines denote Pile 1; darker outlines define Pile 2. (a) Test L17C. Spacing between pile centers of 24 km. (b) Test L19C. Pile spacing of 28.5 km. (c) Test L20C. Pile spacing of 33.8 km. (Note, y-axis is centered on Pile 1.)

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spreading piles, Pile 2 begins to grow on progressively older layers with increasing interpile spacing, although the onset of pile growth does not change. In all cases, the piles grow at constant rates. During concurrent growth, the first edifice grows by increments of 45 particles, and the second by increments of 30 particles; particles in each edifice are distinguished from each other by darkness of the particle outlines (e.g., Fig. 4). Mechanical parameters, particle abundances, and edifice spacings are shown in Table 1. 5.2.1. Intermediate basal strength: l bas = 0.2 Fig. 4 shows three final configurations after 24 increments of growth for piles with spacings of 24.0, 28.5, and 33.8 km. By design, layer thicknesses are greater for the primary edifice (light particle outlines) and smaller for the second (dark particle outlines). The left flank of Pile 1 resembles the flanks of the symmetric piles built upon the stronger base (Fig. 2a), indicating that it is little influenced by changes to its right flank; layers dip outward above an axial high, but are tilted inward near the edge of the flank to form a shallow flank syncline. Layer thicknesses are greater on the right flank of Pile 1, where Pile 2 abuts the deeper layers (Fig. 4).

The spacing between the centers of the growing pile influences the final geometry of the complex. For the closest spacing of 24 km (Fig. 4a), the second pile begins to grow high upon the right flank of the primary pile, contributing to the mass that drives outward spreading. Due to its proximity to the summit of Pile 1, Pile 2 produces little distinct topographic relief, but rather merges smoothly with the right slope of Pile 1 (Fig. 4a). The flanks of the combined assemblage, however, are asymmetric, with the right flank spanning a distance of 63.8 km compared to 56.3 km to the left flank. The buttressing effect of Pile 2 on Pile 1 is also evident from the thicker layers within the right flank of Pile 1 relative to the left flank, which have been thinned by internal shearing (Fig. 4a). With the shift of Pile 2 to the right to a spacing of 28.5 km (Fig. 4b), an increasingly obvious topographic mound develops upon the right flank of the primary pile; the total length of the right flank extends to ~68 km. Interestingly, the left flank also increases to a length of 60 km for this configuration, while pile height decreases from 4.3 to 4.1 km. Apparently, as the topographic mound corresponding to Pile 2 becomes more prominent with distance from the summit of Pile 1, it contributes to the

Fig. 5. Representative displacement discontinuities for overlapping piles constructed upon l bas = 0.2 substrate. (a) Test L17C, Increment 22. Pile spacing of 24 km. (b) Test L18C, Increment 21. Pile spacing is 26.3 km. (c) Test L20C, Increment 22. Pile spacing of 33.8 km.

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shear stresses that drive the spreading of the left flank of the larger pile. The buttressing and thickening of layers within the right flank is still evident, but most significant for the deeper layers. A thin layer of Pile 1 strata persists and is entrained beneath Pile 2 as it spreads outward. In the last configuration, the spacing between piles is 33.8 km. Layering in Pile 2 has developed a distinct S-form, similar to that observed in the left flank of Pile 1 (Fig. 4c), reflecting the heterogeneous shearing of strata. Only the deepest layers of Pile 1 are thickened and buttressed. Pile 2 appears to pin the tip of the right flank of Pile 1, preventing further spreading (Fig. 4c). Throughout this suite of simulations, the layering in Pile 2 dips consistently outward, a result of shallow normal faulting within the edifice. The position of Pile 2 relative to the first pile strongly influences the distribution of deformation within the assemblage (Fig. 5). As noted for symmetric pile growth upon a base with l bas = 0.2 (Fig. 2b), the left flank of Pile 1 is characterized by deep-seated, steeply dipping detachment faults that extend from the summit to the base, accommodated by slip along the outer half of the de´collement (Fig. 5a to c). The right flank of Pile

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1 experiences much less internal deformation subsequent to the growth of Pile 2; an asymmetric wedge uncut by normal faults, buttressed by Pile 2, develops along the right flank of Pile 1. The outer flank of Pile 2, however, consistently shows outward-dipping fault geometries, some of which exhibit multiple sub-parallel fault strands (Fig. 5b). Fault position migrates to the right as the pile center shifts (compare Fig. 5a, b, and c). With increasing distance between the two piles, surficial avalanching becomes more common along the upper slopes of Pile 1 (e.g., Fig. 5c). The stress field that develops within the overlapping topographic loads is more complicated than that for the symmetric edifice with the same basal strength conditions (Fig. 2). Again, the contours of r yy generally mimic the topographic surface, at least at shallow depths (Fig. 6a), as do those for r xx (Fig. 6b). A subtle high in r xx also develops near the base at the juncture of the two piles (25 km, Fig. 6b). The effects of Pile 2 on the shear stress distribution of the complex is indicated by the reduced outward deflection of r I beneath Pile 2 (Fig. 6c); the additional topographic load introduces lateral shear stresses that counteract those gener-

Fig. 6. Components of stress field for Test L19C (see Fig. 4b), built upon l bas = 0.2 substrate, following Increment 24. (a) Contours of vertical normal stress, r yy, generally mimic surface topography. (b) Horizontal normal stress component, r xx . Note slight increase near the junction of the two piles (~6 km position). (c) Maximum principal compressive stresses, r I , are generally subvertical, but are deflected near the intersection of the two piles.

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ated by the primary pile, accounting for the reduced spreading of its right flank. 5.2.2. Low basal strength: l bas = 0.1 The picture is slightly different for interacting piles constructed on a lower strength substrate. Fig. 7 compares configurations of four different pile spacings after 24 increments of growth. In all cases, the left flank of Pile 1 has undergone substantial subsidence, leading to thinning of strata beneath the summit and inward tilting of thicker layers the distal flank (Fig. 7). The enhanced spreading of the left flank causes interaction with the left boundary of the domain, but with minimal effect on the rest of the pile. As with the stronger substrate, the growth of Pile 2 buttresses the right flank of the primary pile, but to differing degrees depending on pile spacing. Layers within the right flank of Pile 1 tend to be relatively thick, particularly at depth; the uppermost

layers remain thin, however, due to the tendency for new material for flow down the steeper slopes of the left flank (Fig. 7). In all cases, Pile 2 grows upon pre-existing strata of Pile 1, which becomes entrained within the spreading outer flank of the second pile. Consequently, by the end of the simulation, a substantial thickness of Pile 1 material lies along the right edge of the profiles, and impinges upon the right boundary (Fig. 7). When the piles are relatively closely spaced (Fig. 7a through c), layers in Pile 2 tend to dip outward, due to internal shearing induced by deep-seated normal faulting. Layers generally dip inward along the edge of the right flank, outboard of the shearing portion of the flank. If Pile 2 is constructed further out on the flank of Pile 1, it grows more symmetrically, and as a result, layering is subhorizontal (Fig. 7d). Furthermore, due to its distal position, Pile 2 entrains less strata of the

Fig. 7. Particle configurations following 24 increments of pile growth, for overlapping piles constructed upon l bas = 0.1 substrate. (a) Test L22C. Pile spacing of 28.5 km. (b) Test L21C. Pile spacing of 33.8 km. (c) Test L23C. Pile spacing of 38.3 km. (d) Test L25C. Pile spacing of 46.5 km.

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underlying flank, and less material piles up against the right side boundary of the domain (Fig. 7d). Instead, the topographic high corresponding to Pile 2 pins and prevents the outward spreading of the right flank of Pile 1. Particle configurations for five increments of concurrent growth for Test L22C are shown in Fig. 8, beginning immediately following the initiation of Pile 2. With a pile spacing of 28.5 km, Pile 2 grows initially upon exposures of the deeper strata of Pile 1 (Fig. 8a).

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During subsequent growth increments, Pile 2 subsides into the flank of Pile 1 (Fig. 8b through e), and pushes the underlying strata out of its way. By the end of the simulation, the deeper layers in Pile 1 over the x-range of 35 and 55 km have been substantially thinned and displaced to the right (compare Fig. 8a and e). The greater tendency for gravitational spreading of both edifices built upon the low strength substrate, leads to complicated patterns of deformation. Four increments of deformation for Test L22C are shown

Fig. 8. Particle configurations for sequential increments of pile growth for overlapping piles constructed upon l bas = 0.1 substrate, for Test L22C (see Fig. 7a). Pile spacing of 28.5 km. (a) Increment 14. (b) Increment 16. (c) Increment 18. (d) Increment 20. (e) Increment 22.

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in Fig. 9. Throughout the experiment, the left flank of Pile 1 displays deep-seated detachment faults that extend beneath the summit and accommodate subsidence and outward spreading. The right flank exhibits evolving behavior as Pile 2 grows in size. During the initial stages of growth, Pile 2 perturbs the stress field of the underlying pile enough to localize a listric normal fault that breaks the surface of Pile 1 just upslope of its intersection with Pile 2, at a distance of 15 to 22 km from the center of Pile 1 (Fig. 9a). Over the same increment, Pile 2 is undergoing diffuse subsidence into the underlying flank. A sequence of three increments near the final stages of the simulation shows the variability of deformation through time. During Increment 21 (Fig. 9b), the de´collement beneath Pile 1 is

inactive, as a major detachment beneath Pile 2 soles into the basal decollement, accommodating displacement of entire outer flank. Increment 22 (Fig. 9c) shows the reactivation of the de´collement surface beneath Pile 1, with a pronounced zone of slip beneath the left flank (x =  10 to  45 km), linked to a deep-seated normal fault that undercuts the summit of Pile 1 (x = 5 to  10 km), and a thrust fault along the lower flank (x =  45 to  50 km). Also, despite the buttressing effect of Pile 2, a narrow zone of de´collement slip underlies the right flank of Pile 1 (x = 10 to 15 km), with a small offset detachment fault intersecting the inboard edge of the slip zone (x = 0 to 10 km). Detachment faulting and de´collement slip beneath the right flank of Pile 2 continues (Fig. 9c). By Increment 23, de´collement slip

Fig. 9. Representative displacement discontinuities for Test L22C, built upon l bas = 0.1 substrate, with pile spacing of 28.5 km. (a) Increment 16. Pile 2 begins diffuse subsidence into the underlying flank. Note listric normal fault just upslope of Pile 2. (b) Increment 21. Mass of Pile 2 mass localizes detachment faults beneath its summit, driving outward flank displacement. (c) Increment 22. Both flanks of Pile 1 exhibit detachment faulting; the right flank experiences incipient basal sliding. Pile 2 undergoes outward spreading. (d) Increment 23. Basal slip beneath the right flank of Pile 1 propagates outward to merge with slip beneath Pile 2.

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Fig. 10. Representative displacement discontinuities for widely spaced piles built upon l bas = 0.1 substrate. (a) Test L23C. Pile spacing of 38.3 km—Increment 24. The unbuttressed flanks of both piles undergo detachment and outward flank sliding. The mass of Pile 2 prevents displacement of the right flank of Pile 1. (b) Test L25C. Pile spacing of 46.5 km—Increment 23. Unbuttressed flanks still experience spreading. Shear stresses generated by Pile 2 also cause detachment faulting along its left flank, and back-slip along the basal de´collement.

Fig. 11. Components of stress field for Test L25C built upon l bas = 0.1 substrate, following Increment 24. (a) Vertical stress component, r yy. (b) Horizontal stress component, r xx , shows highs near the junction of the two piles (~7 km position), and near the lateral boundaries. (c) Maximum principal compressive stresses, r I , are generally subvertical, but converge near the intersection of the two piles, ~7 km distance.

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beneath Pile 1 has propagated to the right and merged with the active de´collement beneath Pile 2, accommodating outward sliding of both piles (Fig. 9d). Although the increased topography of the second pile acts counter to the shear stresses generated by Pile 1, it is not great enough to completely lock the flank of the older pile. An increase in spacing between the two piles, however, introduces a greater buttressing effect than shown in Fig. 9. When Pile 2 is positioned 38.25 km away from the summit of Pile 1, it effectively restricts the outward displacement of the right flank of the first pile, almost from the onset of growth of the second pile (Fig. 10a). Finally, when Pile 2 sits at 46.5 km away (Test L25C), it pins the right flank of Pile 1, and in fact drives backslip on the basal de´collement, thereby preventing further spreading of Pile 1 (Fig. 10b). The stress field that develops for this final assemblage (L25C), shows the effects of such pronounced edifice interactions. By the final stages of growth for the two piles spaced 46.5 km apart (Fig. 10b), r yy is still controlled primarily by topography, showing two distinct highs beneath the two piles (Fig. 11a); r xx is still ~50–60% of r yy beneath the topographic peaks, but shows a sharp increase at the junction between the two piles, at 28 km distance (Fig. 11b), where right-directed spreading of Pile 1 impinges upon left-directed spreading of Pile 2. In this region, r xx actually exceeds r yy, causing the shallowing of the principal stress vectors, r I (Fig. 11c). The high horizontal compressive stresses in this location reduce the tendency for normal faulting in either edifice, and promote thrust faulting. Values of r xx are also high adjacent to the domain boundaries where the sliding flanks impinge upon the lateral walls, but these have little effect on the stress field of the larger edifice. 6. Discussion 6.1. General features The simulated growth of granular piles demonstrates the important processes of lateral spreading of the pile flanks due to topographically induced shear stresses. In their previous study, Morgan and McGovern (2005-a) present the spectrum of deformational features that develop during self-similar growth of piles for a wider range of l bas values. Their results demonstrate that edifices constructed with identical internal mechanical properties exhibit distinctly contrasting morphologies, layer stratigraphies, and modes of deformation, as a function of l bas. If slip along the base is restricted by high basal cohesion, the pile maintains angle of repose

slopes due to surficial particle avalanching; layers within the pile dip uniformly outward. With decreasing de´collement strength, slip occurs along increasing lengths of the basal de´collement, activating increasingly deeper and steeper detachment faults. The predominant mode of deformation shifts from surficial avalanching, to shallow slumping, then deep-seated landsliding, and finally, to axial subsidence of the edifice. These changes are accompanied by a gradual decrease in surface slope, increasingly concave-up surface morphology, and formation of inward-dipping layers. The mechanical theory that explains the observed deformational features is presented in detail by Morgan and McGovern (2005-b). In summary, the correlations among slope morphology, mode of deformation, and basal slip result from the balance between gravitational loading forces that drive the mass of the pile downward and outward, and the basal resistance to sliding, as predicted by critical Coulomb wedge (CCW) theory (e.g., Davis et al., 1983; Dahlen, 1984). Unlike common applications of CCW, however, in which the stress state ensures that the domain is at failure throughout, the spatially varying topographic load of granular piles and volcanic edifices restricts the regions that are at failure. The resolved shear stress along the de´collement increases outward with distance from the pile axis, until it reaches a critical value determined by Mohr–Coulomb failure criterion (Eq. (1)), at which point basal sliding will occur. This enables the formation of normal faults that intersect the de´collement, allowing the downward and outward displacement of outer sectors of the pile. The strength of the substrate, therefore, constrains the lateral position of detachment faults within the pile, and consequently, the geometry of gravitational failures. The simulations presented here, modeled after those of Morgan and McGovern (2005-a,b) for the lowest values of basal friction, yield comparable results. For l bas = 0.2, high angle normal faults intersect the upper flanks and underlie narrow flank synclines (Fig. 2). For l bas = 0.1, these high angle faults undercut the summit regions, defining inward-dipping fault scarps where they intersect the surface (Fig. 3). Summit subsidence is a dominant mode of deformation; the resulting downward motion drives the outward displacements of the flanks, leading to signature low slopes and concave up morphology. Overlapping piles lead to complicated stress fields that localize normal faulting adjacent to the topographic highs. These results can also be understood within the context of CCW theory, as the unstable flanks are forced to deform internally in order to regain stress equilibrium.

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Although these simple 2-D simulations do not incorporate all the elements of natural volcanic analogs, the kinematic results provide a new framework within which to examine characteristics of Hawaiian volcanoes that have been long debated. The results provide important insights into the internal structure and dynamics of active Hawaiian volcanoes, as detailed below. 6.2. Comparisons to volcanic spreading in Hawaidi 6.2.1. Surface slopes The subaerial slopes of Hawaiian volcanoes, constructed of basaltic surface flows, are remarkably low, typically 58 or less (Mark and Moore, 1987; Moore and Mark, 1992). Submarine slopes, constructed of pillow basalts and fragmental lavas, are higher, ranging from 88 to 118. Such low surface slopes have commonly been attributed to the dynamics of low-viscosity basaltic lava flows (e.g., Moore and Mark, 1992). From this study, we see that such low surface slopes can also develop if the edifice undergoes gravitational spreading, which may provide a more comprehensive explanation for the observed volcanic geometries. The relevance of CCW theory to the mechanics and low slopes of Kı¯lauea’s mobile flank has been noted previously (e.g., Dieterich, 1988; Thurber and Gripp, 1988; Delaney and Denlinger, 1999), although the DEM models provide a fuller representation of the complex, gravity driven behavior of volcanic wedges. Of the examples shown here, the surface slopes of spreading piles constructed above the weakest substrate of l bas = 0.1, provide the best fit to Hawaiian volcanoes, further supporting models of Hawaiian volcanic spreading above a weak basal de´collement (e.g., Swanson et al., 1976; Denlinger and Okubo, 1995). The modeled lower flanks lie at ~68 from horizontal (Fig. 7), slightly less than Kı¯lauea’s south flank and Mauna Loa’s west flank. The upper flanks are ~178, which is significantly greater than for Hawaiian volcanoes. Morgan and McGovern (2005-b) note that the slopes of the upper flanks of these simulated granular piles can be predicted by CCW theory; they define frictional extensional wedges at their blimitingQ taper as they slide along a horizontal de´collement. Wedges with steeper slopes will deform internally through normal faulting, until they attain this limiting taper (Dahlen, 1984). The lower flanks of the granular piles slide stably without internal faulting, and have surface slopes between the limiting taper and the bcriticalQ taper, i.e., contractional wedges deforming by thrust faulting (Davis et al., 1983; Dahlen, 1984). The differences between upper flank

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slopes in the simulations and observed slopes of Hawaiian volcanoes suggest that the cores of Hawaiian volcanoes exhibit a much more complex rheology than modeled here, probably due to the presence of weak ductile magma or dunite bodies that flow viscously as the summit subsides (e.g., Delaney et al., 1990; Clague and Denlinger, 1994, Gillard et al., 1996). 6.2.2. De´collement slip Geodetic and seismic evidence for seaward displacements of the south flank of Kı¯lauea volcano (e.g., Swanson et al., 1976; Got et al., 1994; Denlinger and Okubo, 1995; Owen et al., 1995, 2000; Delaney et al., 1998) is consistent with modeled slip along the basal de´collement in these simulations. For the weakest l bas condition, the flanks slide stably above this de´collement with little internal deformation (e.g., Figs. 7–9). Intermittent de´collement earthquakes, such as the 1975 M 7.2–7.9 Kalapana earthquake beneath Kı¯lauea’s south flank, equate to frictional stick-slip events that occur over discrete intervals of pile growth during the simulations (e.g., Fig. 9). Mauna Loa is also subject to gravitationally driven deformation, exhibiting flank creep, although at comparatively low rates (Miklius et al., 1995, 1997), and infrequent de´collement earthquakes. The great Kau earthquake of 1868, estimated at M. 8.0, that struck the southeast flank of Mauna Loa, may have caused seaward slip of Mauna Loa’s southeastern flank, and most of edifice of Kı¯lauea volcano (e.g., Wyss, 1988). An intriguing analogy to this event is provided by the simulated sequence of deformation for Test L22C, where incipient de´collement slip beneath the upper reaches of the buttressed right flank of the primary pile (Fig. 9c), propagated outward to merge with de´collement slip beneath the second pile, despite the buttressing effect of the second pile (Fig. 9d). Mauna Loa’s unbuttressed west flank has also experienced smaller earthquakes this century, consistent with seaward de´collement slip (Gillard et al., 1992; Wyss and Koyanagi, 1992). 6.2.3. Detachment geometries and catastrophic landsliding The ongoing debate about the depths and orientations of the several normal faults that intersect the surfaces of Hawaiian volcanoes may be partially resolved by the simulation results. The two low strength configurations modeled here yield high angle normal faults that cut deep into the pile flanks. For l bas = 0.1, detachment faults commonly extend beneath the summit regions, and mobilize the topographic summits as well as the flanks (Fig. 9b, c and d). Concurrently,

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shallower faults form along the pile slopes farther from the summit, defining shallow slump features (e.g., Fig. 9b). These numerical results provide a framework within which to interpret fault systems observed on Mauna Loa and Kı¯lauea. Fig. 12 presents a broken cross-section that passes through Mauna Loa’s west flank and summit, Kı¯lauea’s southwest rift zone close to the summit, and offshore flank (see Fig. 1 for location). The Kaoiki and Koae fault systems are well-positioned to accommodate subsidence of Kı¯lauea’s summit. Both sets of faults probably dip steeply beneath the active volcano; the Kaoiki fault system may reach the top of the oceanic plate; the Koae fault system could define an antithetic normal fault that intersects the seaward-dipping Kaoiki fault system (e.g., Borgia et al., 2000). Either or both fault systems may also intersect magma chambers at depth, which accommodate summit subsidence and spreading. The Hilina fault system is thought to bound an active submarine slump (e.g., Lipman et al., 1985). At this distance from Kı¯lauea’s summit, r I is likely to be slightly deflected from vertical (e.g., Fig. 3), resulting in a relatively shallow structure, consistent with several previous models (e.g., Swanson et al., 1976; Cannon and Bu¨rgmann, 2001; Cervelli et al., 2002; Morgan et al., 2003). The major fault scarps observed along Mauna Loa’s west flank (Fig. 1) may once have linked up to define a single through-going detachment fault responsible for catastrophic landsliding (Lipman et al., 1988; Lipman, 1995). These are projected into the plane of the section of Fig. 12 as two different faults, to denote their three dimensional geometries: the steeply dipping Kahuku fault is interpreted to cut high on the volcano’s slopes, consistent with its intersection with Mauna Loa’s southwest rift zone (Fig. 1); the Kealakekua fault is shown with a much lower dip near the shoreline. The distal reaches of both volcanoes’ flanks show evidence for uplift and overthrusting (e.g., Denlinger and Okubo,

1995; Morgan et al., 2000, 2003; Morgan and Clague, 2003), not unlike the structures that form when the simulated flanks impinge upon the lateral walls of the model (e.g., Fig. 9). The hypothesized slope failure that occurred along Mauna Loa’s west flank is thought to have been catastrophic in nature, and is interpreted to have occurred along a discrete detachment fault (e.g., Lipman et al., 1988, 1990). Subsequent to this event, subaerial lava flows from Mauna Loa’s southwest rift zone have flowed preferentially westward, gradually rebuilding the still oversteepened subaerial flank. The simulated thinning of strata along the unbuttressed left flank of Pile 1 is kinematically similar to catastrophic slope failure, but occurs incrementally along high-angle, deep-seated normal faults (e.g., Fig. 9). This deformation also tends to steepen the flank, making room for new deposits, which preferentially flow down the left flank (Fig. 9). 6.2.4. Subsidence Long-term summit and rift zone subsidence have been documented for Kı¯lauea volcano in historic times (Delaney et al., 1993, 1998; Miklius et al., 1997; Owen et al., 2000), and from geologic evidence (Walker, 1992; Quane et al., 2000). The DEM simulations of edifice growth upon low substrate strengths demonstrate the importance of high-angle, axial normal faults, which accommodate ongoing summit subsidence (e.g., Figs. 9–10), as has been argued previously (e.g., Borgia et al., 2000). It is this axial subsidence and associated flank spreading that accounts for low surface slopes and inward-dipping layers (e.g., Figs. 3a and 7). The discrepancy between higher upper flank slopes in the models, relative to the low slopes and broad summits at Kı¯lauea and Mauna Loa, however, indicates that additional factors come into play in the natural system. In particular, the active summit and rift zones are

Fig. 12. Cross-section across Mauna Loa and Kı¯lauea volcanoes’ submarine and subaerial flanks and summits, plotted with no vertical exaggeration, showing probable geometries of fault zones observed to intersect the volcano surfaces. (See Fig. 1 for location and key to fault zones.) Vertical lines denote the region comprising Kı¯lauea volcano. High angle normal faults underlie the summit regions and accommodate subsidence and axial extension. The subsiding edifices drive the unbuttressed flanks seaward along a weak de´collement. Fault dips decrease with distance from the summit, defining surficial slump features, for example, the Hilina fault zone (HFZ) along Kı¯lauea’s south flank. Overthrusting along the distal edges of the flanks leads to lateral shortening, uplift and formation of the mid-slope bench (MSB). Kı¯lauea volcano (vertical lines) has subsided into the underlying flank of Mauna Loa, partitioning the flank into stable upslope and mobile downslope regions. Concurrent magmatic intrusion at the cores of the volcanoes is shown schematically.

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presumed to be underlain by ductile material, either a deep magma body or thick accumulation of viscous cumulates, that facilitates axial subsidence and flank spreading (e.g., Delaney et al., 1990; Clague and Denlinger, 1994; Gillard et al., 1996). If correct, then the conjugate faults modeled here are restricted to the brittle shell of the volcano, and project downward into a ductile core undergoing subsidence and spreading that is kinematically equivalent to normal faulting (Fig. 12). The DEM simulations also demonstrate that subsidence of an overlapping volcanic edifice will have a pronounced effect on the structure of the underlying volcano. From the time of inception, the overlapping pile settles into the strata below, segregating the underlying flank into two parts: a stable upslope region, and a mobile downslope region that is incorporated into the spreading flank of the younger pile (e.g., Figs. 4, 7 and 8). Although the topographic expression is relatively modest, by the end of a simulation, the second pile has subsided and displaced much of the underlying flank. The volume of the younger pile, is therefore masked; surface exposures could lead to erroneous estimates of relative edifice size. The degree of subsidence of the second pile depends on the relative ages and sizes of the two edifices. These model observations may help to reconcile puzzling interpretations of recent submersible observations that suggest that Kı¯lauea is only a thin carapace on the dynamically more active Mauna Loa volcano (e.g., Lipman et al., 2006). Instead, much of the volume of Kı¯lauea volcano may be deeply buried within the underlying flank of Mauna Loa volcano (e.g., Fig. 12), following a long history of summit subsidence and seaward spreading. Furthermore, Kı¯lauea volcano may have partitioned Mauna Loa’s southeast flank into a landward portion that is effectively buttressed by the younger volcano, and a seaward portion, now entrained beneath Kı¯lauea’s mobile south flank. 6.2.5. Volcanic buttressing The proximity of Mauna Loa and Kı¯lauea raises important questions about the degree to which each one buttresses the other (e.g., Swanson et al., 1976; Lipman, 1980). Similarly, Lo¯dihi seamount lies offshore along Mauna Loa’s distal flank (Fig. 1), and may impart some resistance to flank spreading as well. The DEM simulations presented here graphically portray the buttressing effects between the two edifices. The addition of a second topographic feature has an immediate influence on edifice dynamics and deformation (Fig. 9a). The additional load perturbs the equilibrium between

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the topographic shear stresses driving spreading and the frictional resistance, governed by CCW theory. The added normal load increases frictional resistance along the base, impeding spreading of upslope regions, but at the same time, enhancing spreading of the downslope regions. Occasionally, shear stresses induced by the larger edifice may overwhelm the resistance generated by the new load, allowing for renewed slip along the inboard de´collement (e.g., Figs. 9 and 10). The degree to which even a small topographic perturbation can buttress the larger primary pile is surprising; a small pile built along the lower flanks of the primary pile not only inhibits sliding of the larger flank, but also causes back-slip along the de´collement (e.g. Fig. 10b). The increased horizontal compressive stresses at the junction of the two piles reflect this mutual resistance (Fig. 11b). It appears, therefore, that Kı¯lauea volcano should serve as an effective buttress for much of Mauna Loa’s southeast flank (Fig. 1), although the gravitational load of the larger edifice may occasionally rupture the basal de´collement beneath both Mauna Loa and, as hypothesized for the 1868 Kau earthquake (e.g., Wyss, 1988). As plotted in the broken cross-section in Fig. 12, the summit and upper reaches of Kı¯lauea’s southwest rift zone define a distinct topographic feature, lying downslope of Mauna Loa’s summit region. Lo¯dihi seamount (dashed in Fig. 12) lies in a more distal position along Mauna Loa’s southeast flank (Fig. 1) and effectively buttresses the southern reaches of the flank. Similarly, Hualalai (dashed in Fig. 12) buttresses and impedes spreading of Mauna Loa’s northwest flank. 6.2.6. Volcanic spreading at Kı¯lauea The DEM simulation results suggest that the topographic high produced by the growth of Kı¯lauea volcano may have been adequate to drive local volcanic spreading of Kı¯lauea’s south flank (e.g., Fig. 8). Over the lifespan of this volcano, this spreading has resulted in large seaward flank displacements that have caused distal uplift and overthrusting of the frontal bench (e.g., Borgia et al., 1990, 2000; Denlinger and Okubo, 1995; Morgan et al., 2000; Hills et al., 2002; Lipman et al., 2002). The thinning of strata within the right flank of Pile 1 due to subsidence of Pile 2 in Test L22C (Fig. 8e) requires displacements on the order of 15 to 25 km, consistent with estimates obtained from seismic reflection profiles over Kı¯lauea’s south flank (Morgan et al., 2000). Interestingly, the present day configuration of the broad midslope bench at the toe of Kı¯lauea’s sliding flank, now defines a distinct topographic high with steeper slopes than the surrounding submarine flank

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(Fig. 12). The frontal bench may have developed above a zone of increased basal sliding friction beneath the distal flank, in accordance with CCW theory (e.g., Morgan and McGovern, 2005-a). Now, however, the bench also serves to buttress Kı¯lauea’s upper flank, as well as the Hilina slump, possibly reducing the rate of seaward spreading of the mobile flank (e.g., Morgan et al., 2003). 6.3. Other processes The simple 2-D simulations presented here provide support for gravitational spreading models for Hawaiian volcanoes, demonstrating the important role of summit subsidence in driving (and resisting) flank displacements. Certainly, the assumption of Coulomb rheology for the entire volcanic edifice is simplistic, but it places an upper bound on the basal and internal friction conditions necessary to produce volcanic spreading, as well as the observed slopes and fault geometries. Magmatic processes may contribute to Hawaiian volcanotectonics in significant ways, by adding to the outward push on the flanks (e.g., Dieterich, 1988; Iverson, 1995), or by softening the core to allow axial subsidence, extension, and flank spreading (e.g., Delaney et al., 1990; Clague and Denlinger, 1994; Johnson, 1995). Substrate flexure beneath the growing piles will also modify the stress field throughout the edifice, enhancing lateral compressional stresses at the distal edges of the edifice, as well as near the summit regions (e.g., Dieterich, 1988; McGovern and Solomon, 1993; Martel, 2000). Finally, the complicated three-dimensional geometries of the overlapping volcanoes on the south portion of the Island of Hawaidi, and the coupled magmatic and tectonic processes, introduce another layer of complexity to be dealt with in future models. 7. Conclusions DEM simulations of granular piles constructed upon a weak substrate provide numerical analogs to active Hawaiian volcanoes, such as Mauna Loa and Kı¯lauea. The results demonstrate that gravity alone is capable of producing much of the observed edifice spreading under the right mechanical conditions. Here, the paired l int and l bas of 0.6 and 0.1 results in deep-seated volcanic spreading, accommodated by summit subsidence along conjugate normal faults, and stable flank sliding, much as is observed at Kı¯lauea today. The driving stresses for spreading arise from the progressive growth of the volcanic edifice, which increases the outward directed shear stresses that must be relieved by flank deforma-

tion, until balanced by frictional resistance. In the granular simulations, summit subsidence is accommodated along high-angle conjugate normal faults; in natural volcanoes, viscous flow of ductile materials beneath the summits and rift zones may accomplish similar subsidence, possibly manifested by normal faults within the shallow brittle crust of the edifice. The combination of summit subsidence and flank spreading in the models leads to characteristic low volcanic slopes observed on Hawaiian volcanoes. The inwarddipping strata generated along the distal flanks is also analogous to the landward-bedding dips interpreted above and within the frontal benches at Kı¯lauea and Mauna Loa (e.g., Morgan et al., 2003). The simulations demonstrate that edifice overlap can significantly alter a volcano’s dynamics. Generally, the flanks exist in a state of stress equilibrium; the topographic driving stresses are balanced by frictional resisting stresses. However, the addition of a topographic load, even a small one, perturbs this balance, causing local deformation to regain this critical balance. If the second edifice grows high upon the flanks of the primary pile, it contributes to the outward spreading of the underlying flank. If it is built low on the underlying flank, it resists the outward spreading of the buried flank, and locally, may even cause reverse slip on the basal de´collement. The growth of Kı¯lauea upon the preexisting flank of Mauna Loa, therefore, has probably served to buttress the larger volcano, although to differing degrees depending on the lateral positions and rates of growth of the two edifices. Certainly, however, Kı¯lauea volcano is likely to have generated sufficient gravitational stresses, in addition to magmatic pressures, to cause substantial local spreading of the volcanic edifice. Due to accompanying subsidence, the resulting mass of the younger volcano, therefore, probably lies deep within the older flank of Mauna Loa volcano. Acknowledgements This work was motivated by discussions with many colleagues about volcanic processes, and gravitational spreading at Kı¯lauea and Mauna Loa, and elsewhere, in particular, Andrea Borgia, Ben Brooks, Dave Clague, Roger Denlinger, Peter Lipman, Pat McGovern, Greg Moore, Jim Moore, Paul Okubo, John Smith, and Don Swanson. I thank Eric Cannon, Steve Martel, Michelle Coombs, and Peter Lipman for very thoughtful and thorough reviews of a previous version of this manuscript. This research was supported in part by NASA grant NAG5-12226.

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