Valérie Cayol

The use of earthquake rate changes as a stress meter at Kilauea volcano.

Stress changes in the Earths crust are generally estimated from model calculations that use near-surface deformation as an observational constraint. But the widespread correlation of changes of earthquake activity with stress has led to suggestions that stress changes might be calculated from earthquake occurrence rates obtained from seismicity catalogues. Although this possibility has considerable appeal, because seismicity data are routinely collected and have good spatial and temporal resolution, the method has not yet proven successful, owing to the nonlinearity of earthquake rate changes with respect to both stress and time. Here, however, we present two methods for inverting earthquake rate data to infer stress changes, using a formulation for the stress- and time-dependence of earthquake rates. Application of these methods at Kilauea volcano, in Hawaii, yields good agreement with independent estimates, indicating that earthquake rates can provide a practical remote-sensing stress meter.

Finding realistic dike models from interferometric synthetic aperture radar data: The February 2000 eruption at Piton de la Fournaise

Dike intrusions often cause complex ground displacements that are not sufciently explained by simple analytical models. We develop a method to nd complex and realistic dike geometries and overpressures from interferometric synthetic aperture radar (InSAR) data. This method is based on a combination of a boundary element method with realistic topography and a neighbourhood algorithm inversion. Dike model geometry is roughly a quadrangle with its top reaching the ground. The inversion has two stages: search and appraisal. The appraisal stage involves calculations of model marginal probability density functions using mist val- ues calculated during the search stage. The mist function takes into account the variance and correlation of data noise. Synthetic tests show that a model is successfully retrieved within predicted narrow condence intervals. We apply the method on InSAR data of the February 2000 ank eruption at Piton de la Fournaise and get a trapezoid dike dipping seaward (61.0 n 67.3 ) with its bottom passing 800n1000 m beneath the summit. A model with a basal slip plane does not better explain observed asymmetric displacements and thus this asymmetry is solely attributed to the dipping dike. The dike lies above a narrow band of pre-eruption seis- micity, suggesting that lateral magma propagation occurred. Neglecting topography results in poor modeling at depth and in overestimations of overpressure (or opening), height (both about 30%), and volume (about 20%).

Three‐dimensional modeling of the 1983–1984 eruption at Piton de la Fournaise Volcano, Réunion Island

Displacement vectors on 125 points over a 6-km 2 area were calculated [Zlotnicki et al., 1990] for Piton de la Fournaise volcano, Reunion Island, from photogrammetric surveys conducted in September 1981 and again in September 1984. An eruptive crisis with two episodes occurred during the 3 years between the surveys. We modeled the displacements from the photogrammetric surveys using a three-dimensional mixed boundary element method. The model shows that both eruptive episodes were fed by a single dike oriented 165° from north. As the dike approached the ground surface, it divided into segments that rotated into an en echelon pattern. The model that best fits all observations suggests that the stress state within the volcano is quasi-isotropic such that horizontal stresses equal the overburden. These high horizontal stresses are incompatible with an elastic edifice loaded merely by gravitational forces. However, they may be attributed to the cumulative effect of repeated dike intrusions.

Nyamulagira’s magma plumbing system inferred from 15 years of InSAR

Abstract Nyamulagira, located in the east of the Democratic Republic of Congo on the western branch of the East African rift, is Africa’s most active volcano, with an average of one eruption every 3 years since 1938. Owing to the socio-economical context of that region, the volcano lacks ground-based geodetic measurements but has been monitored by interferometric synthetic aperture radar (InSAR) since 1996. A combination of 3D Mixed Boundary Element Method and inverse modelling, taking into account topography and source interactions, is used to interpret InSAR ground displacements associated with eruptive activity in 1996, 2002, 2004, 2006 and 2010. These eruptions can be fitted by models incorporating dyke intrusions, and some (namely the 2006 and 2010 eruptions) require a magma reservoir beneath the summit caldera. We investigate inter-eruptive deformation with a multi-temporal InSAR approach. We propose the following magma plumbing system at Nyamulagira by integrating numerical deformation models with other available data: a deep reservoir (c. 25 km depth) feeds a shallower reservoir (c. 4 km depth); proximal eruptions are fed from the shallow reservoir through dykes while distal eruptions can be fed directly from the deep reservoir. A dyke-like conduit is also present beneath the upper southeastern flank of Nyamulagira.

Persistent uplift of the Lazufre volcanic complex (Central Andes): New insights from PCAIM inversion of InSAR time series and GPS data

We reanalyzed the surface displacements observed at the Lazufre volcanic complex in the Southern Andean Central Volcanic Zone using GPS measurements made between 2006 and 2008 and a large InSAR data set. We performed a detailed spatiotemporal analysis of the displacements using a principal component analysis inversion method (PCAIM). The PCAIM reveals a source with no significant changes in shape and dimension and with a remarkably linear strength increase over the whole period of observation (i.e., 2003–2010). Then we used a three-dimensional mixed boundary element method (MBEM) to invert the first component of surface displacement as obtained from PCAIM. We explored a continuum of geometries from a shallow elliptic crack to a deep massive truncated elliptical cone that could represent a sill or a large magma chamber, respectively. The best models indicate a large flat-topped source with a roof area between 40 and 670 km2 and a depth of between 2 and 14 km below ground surface. Lastly, on the basis of the limited data available for the thermomechanical structure of the crust in the Southern Andean Central Volcanic Zone, we consider some possible scenarios to explain the spatial and temporal pattern of displacements at Lazufre.

Hawaiian volcanoes : from source to surface

Contributors vii Preface xi About the Companion Website xiii 1. How and Why Hawaiian Volcanism Has Become Pivotal to Our Understanding of Volcanoes from Their Source to the Surface 1 Michael O. Garcia 2. Seismic Constraints on a Double Layered Asymmetric Whole Mantle Plume Beneath Hawai I 19 Cheng Cheng, Richard M. Allen, Rob W. Porritt, and Maxim D. Ballmer 3. Asymmetric Dynamical Behavior of Thermochemical Plumes and Implications for Hawaiian Lava Composition 35 Maxim D. Ballmer, Garrett Ito, and Cheng Cheng 4. Major Element and Isotopic Variations in Mauna Loa Magmas over 600 ka: Implications for Magma Generation and Source Lithology as Mauna Loa Transits the Hawaiian Plume 59 J. Michael Rhodes 5. Lithium Isotopic Signature of Hawaiian Basalts 79 Lauren Harrison, Dominique Weis, Diane Hanano, and Elspeth Barnes 6. Onset of Rejuvenated Stage Volcanism and the Formation of L hu e Basin: Kaua i Events That Occurred 3 4 Million Years Ago 105 David R. Sherrod, Scot K. Izuka, and Brian L. Cousens 7. Evidence for Large Compositional Ranges in Coeval Melts Erupted from K lauea s Summit Reservoir 125 Rosalind T. Helz, David A. Clague, Larry G. Mastin, and Timothy R. Rose 8. Petrologic Testament to Changes in Shallow Magma Storage and Transport During 30+ Years of Recharge and Eruption at K lauea Volcano, Hawai I 147 Carl R. Thornber, Tim R. Orr, Christina Heliker, and Richard P. Hoblitt 9. Shallow Magma Storage at Piton de la Fournaise Volcano After 2007 Summit Caldera Collapse Tracked in Pele s Hairs 189 Andrea Di Muro, Thomas Staudacher, Valerie Ferrazzini, Nicole Metrich, Pascale Besson, Christine Garofalo, and Benoit Villemant 10. Analysis of Seismicity Rate Changes and Tilt During Early Episodic Fountaining Stage of Pu u O o , Hawai i, Eruption: Implications for Magma Storage and Transport 213 Harmony V. Colella and James H. Dieterich 11. Episodic Deflation Inflation Events at Kilauea Volcano and Implications for the Shallow Magma System 229 Kyle R. Anderson, Michael P. Poland, Jessica H. Johnson, and Asta Miklius 12. Crustal Stress and Structure at K lauea Volcano Inferred from Seismic Anisotropy 251 Jessica H. Johnson, Donald A. Swanson, Diana C. Roman, Michael P. Poland, and Weston A. Thelen 13. Delicate Balance of Magmatic Tectonic Interaction at K lauea Volcano, Hawai i, Revealed from Slow Slip Events 269 Emily K. Montgomery Brown, Michael P. Poland, and Asta Miklius 14. From Reservoirs and Conduits to the Surface: Review of Role of Bubbles in Driving Basaltic Eruptions 289 Sylvie Vergniolle and Yves Gaudemer 15. Insights Into Mixing, Fractionation, and Degassing of Primitive Melts at K lauea Volcano, Hawai I 323 Marie Edmonds, Isobel Sides, and John Maclennan 16. Reticulite Producing Fountains From Ring Fractures in K lauea Caldera ca. 1500 CE 351 Michael May, Rebecca J. Carey, Donald A. Swanson, and Bruce F. Houghton 17. Hawaiian Fissure Fountains: Quantifying Vent and Shallow Conduit Geometry, Episode 1 of the 1969 1974 Mauna Ulu Eruption 369 Carolyn Parcheta, Sarah Fagents, Donald A. Swanson, Bruce F. Houghton, and Todd Ericksen 18. K lauea s 5 9 March 2011 Kamoamoa Fissure Eruption and Its Relation to 30+ Years of Activity From Pu u O o 393 Tim R. Orr, Michael P. Poland, Matthew R. Patrick, Weston A. Thelen, A. Jeff Sutton, Tamar Elias, Carl R. Thornber, Carolyn Parcheta, and Kelly M. Wooten 19. Onset of a Basaltic Explosive Eruption From Kilauea s Summit in 2008 421 Rebecca J. Carey, Lauren Swavely, Donald A. Swanson, Bruce F. Houghton, Tim R. Orr, Tamar Elias, and A. Jeff Sutton 20. Primitive Components, Crustal Assimilation, and Magmatic Degassing During the Early 2008 Kilauea Summit Eruptive Activity 439 Michael C. Rowe, Carl R. Thornber, and Tim R. Orr 21. FLOWGO 2012: An Updated Framework for Thermorheological Simulations of Channel Contained Lava 457 Andrew J. L. Harris and Scott K. Rowland 22. Lava Flows in 3D: Using Airborne Lidar and Preeruptive Topography To Evaluate Lava Flow Surface Morphology and Thickness in Hawai I 483 Hannah R. Dietterich, S. Adam Soule, Katharine V. Cashman, and Benjamin H. Mackey 23. Are Piton de la Fournaise (La Reunion) and K lauea (Hawai i) Really Analog Volcanoes ? 507 Aline Peltier, Michael P. Poland, and Thomas Staudacher 24. Points Requiring Elucidation About Hawaiian Volcanism 533 Michael P. Poland Index 563

Sheared sheet intrusions as mechanism for lateral flank displacement on basaltic volcanoes: Applications to Réunion Island volcanoes

Field work carried out on the Piton des Neiges volcano (Reunion Island) suggests that the injection of magma along detachments could trigger flank failure by conjugate opening and shear displacement. We use 3-D numerical models to compare the ability of purely opened sheet intrusions, sheared sheet intrusions, and normal faults to induce flank displacement on basaltic volcanoes. We assume that shear stress change on fractures results from stress anisotropy of the host rock under gravity. Exploring a large range of stress anisotropies, fracture dips, and fracture depth over length ratios, we determine that the amount of shear displacement is independent of the proximity to the ground surface. Sheared sheet intrusions are the most efficient slip medium on volcanoes. Consequently, the largest flank displacement is induced by the longest, deepest sheared intrusion dipping closest to 45° in a host rock with the highest stress anisotropy. Using our model in a forward way, we provide shear and normal displacements for buried fractures. Applying the model to a pile of sills at the Piton des Neiges volcano, we determine that the mean shear displacement caused by each intrusion was 3.7 m, leading to a total of a 180–260 m of lateral displacement for the 50 m high pile of sills. Using our model in an inverse way, we formulate a decision tree to determine some fracture characteristics and the host rock stress anisotropy from ratios of maximum surface displacements. This procedure provides a priori models, which can be used to bound the parameter space before it is explored through a formal inversion. Applying the decision tree to the 1.4 m coeruptive flank displacement recorded at Piton de la Fournaise in 2007, we find that it probably originated from a shallow eastward dipping subhorizontal normal fault.

Magma Pathways and Their Interactions Inferred from InSAR and Stress Modeling at Nyamulagira Volcano, D.R. Congo

A summit and upper flank eruption occurred at Nyamulagira volcano, Democratic Republic of Congo, from 2–27 January 2010. Eruptions at Nyamulagira during 1996–2010 occurred from eruptive fissures on the upper flanks or within the summit caldera and were distributed along the ~N155E rift zone, whereas the 2011–2012 eruption occurred ~12 km ENE of the summit. 3D numerical modeling of Interferometric Synthetic Aperture Radar (InSAR) geodetic measurements of the co-eruptive deformation in 2010 reveals that magma stored in a shallow (~3.5 km below the summit) reservoir intruded as two subvertical dikes beneath the summit and southeastern flank of the volcano. The northern dike is connected to an ~N45E-trending intra-caldera eruptive fissure, extending to an ~2.5 km maximum depth. The southern dike is connected to an ~N175E-trending flank fissure extending to the depth of the inferred reservoir at ~3.5 km. The inferred reservoir location is coincident with the reservoir that was active during previous eruptions in 1938–1940 and 2006. The volumetric ratio of total emitted magma (intruded in dikes + erupted) to the contraction of the reservoir (rv) is 9.3, consistent with pressure recovery by gas exsolution in the small, shallow modeled magma reservoir. We derive a modified analytical expression for rv, accounting for changes in reservoir volume induced by gas exsolution, as well as eruptive volume. By using the precise magma composition, we estimate a magma compressibility of 1.9–3.2 × 109 Pa−1 and rv of 6.5–10.1. From a normal-stress change analysis, we infer that intrusions in 2010 could have encouraged the ascent of magma from a deeper reservoir along an ~N45E orientation, corresponding to the strike of the rift transfer zone structures and possibly resulting in the 2011–2012 intrusion. The intrusion of magma to greater distances from the summit may be enhanced along the N45E orientation, as it is more favorable to the regional rift extension (compared to the local volcanic rift zone, trending N155E). Repeated dike intrusions beneath Nyamulagira’s SSE flank may encourage intrusions beneath the nearby Nyiragongo volcano.

Inversion of coeval shear and normal stress of Piton de la Fournaise flank displacement

The April 2007 eruption of Piton de la Fournaise was the biggest volcano eruptive crisis of the 20th and 21st centuries. Interferometric synthetic aperture radar (InSAR) captured a large coeruptive seaward displacement on the volcanos eastern flank, which continued for more than a year at a decreasing rate. Coeruptive uplift and posteruptive subsidence were also observed. While it is generally agreed that flank displacement is induced by fault slip, we suggest that this flank displacement might have been induced by a sheared sill, based on observations of sheared sills at Piton des Neiges. To test this hypothesis, we develop a new method to invert a quadrangular curved source submitted to simultaneous pressure and shear stress changes. This method, based on boundary elements, is applied to data acquired along six Envisat orbits covering a 14 month period subsequent to the April 2007 eruption. Posteruptive displacement is well explained by closure and slip of a large (5 km by 8 km) and shallow (500 m) trapezoidal fracture parallel to the flank and probably coincident with a lithological discontinuity. We investigate whether thermal contraction or degassing of a coeruptive sill can explain the displacement. Such a sill would have to be 10 times thicker than inferred from the coeruptive uplift and solidification time 10 times shorter (~20 days) than the duration of the posteruptive subsidence (24 to 33 months). Instead, we propose that the posteruptive eastern flank displacement is due to the compaction and ongoing slow slip on a shallow detachment fault.

XFEM-Based Fictitious Domain Method for Linear Elasticity Model with Crack

Reduction of computational cost of solutions is a key issue for crack identification or crack propagation problems. One of the solutions is to avoid remeshing the domain when the crack position changes or when the crack extends. To avoid remeshing, we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media. The approach is based on a fictitious domain method originally developed for Dirichlet conditions for the Poisson problem and for the Stokes problem, which is adapted to the Neumann boundary conditions of crack problems. The crack is represented by level-set functions. Numerical tests are made with a mixed formulation to emphasize the accuracy of the method, as well as its robustness with respect to the geometry enforced by a stabilization technique. In particular, an inf-sup condition is theoretically proven for the latter. A realistic simulation with a uniformly pressurized fracture inside a volcano is given for i...