Yakov Khazan

Bio: Yakov Khazan is an academic researcher from University of California, San Diego. The author has contributed to research in topics: Magma chamber & Resurgent dome. The author has an hindex of 5, co-authored 5 publications receiving 484 citations. Previous affiliations of Yakov Khazan include California Institute of Technology.

Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy

Abstract: We consider deformation due to sill-like magma intrusions using a model of a horizontal circular crack in a semi-infinite elastic solid. We present exact expressions for vertical and horizontal displacements of the free surface of a half-space, and calculate surface displacements for a special case of a uniformly pressurized crack. We derive expressions for other observable geophysical parameters, such as the volume of a surface uplift/subsidence, and the corresponding volume change due to fluid injection/withdrawal at depth. We demonstrate that for essentially oblate (i.e. sill-like) source geometries the volume change at the source always equals the volume of the displaced material at the surface of a half-space. Our solutions compare favourably to a number of previously published approximate models. Surface deformation due to a ‘point’ crack (that is, a crack with a large depth-to-radius ratio) differs appreciably from that due to an isotropic point source (‘Mogi model’). Geodetic inversions that employ only one component of deformation (either vertical or horizontal) are unlikely to resolve the overall geometry of subsurface deformation sources even in a simplest case of axisymmetric deformation. Measurements of a complete vector displacement field at the Earth's surface may help to constrain the depth and morphology of active magma reservoirs. However, our results indicate that differences in surface displacements due to various axisymmetric sources may be subtle. In particular, the sill-like and pluton-like magma chambers may give rise to differences in the ratio of maximum horizontal displacements to maximum vertical displacements (a parameter that is most indicative of the source geometry) that are less than 30 per cent. Given measurement errors in geodetic data, such differences may be hard to distinguish.

Fusion by earthquake fault friction: Stick or slip?

Abstract: Field observations of pseudotachylites, and experimental studies of high-speed friction indicate that melting on a slipping interface may sig- nificantly affect the magnitude of shear stresses resisting slip. We investigate the effects of rock melting on the dynamic friction using theoretical models of shear heating that couple heat transfer, thermodynamics of phase transitions, and fluid mechanics. Results of laboratory experiments conducted at high (order of m/s) slip velocities but low (order of MPa) normal stresses suggest that the onset of frictional melting may give rise to substantial increases in the effective fault strength, presumably due to viscous effects. However, extrapolation of the modeling results to in situ conditions suggests that the efficiency of viscous braking is significantly reduced under high normal and shear stresses. When transient increases in the dynamic fault strength due to fusion are not sufficient to inhibit slip, decreases in the effective melt viscosity due to shear heating and melting of clasts drastically decrease the dynamic friction, resulting in a nearly complete stress drop ("thermal runaway"). The amount of energy dissipation associated with the formation of pseudo- tachylites is governed by the temperature dependence of melt viscosity, and the average clast size in the fault gouge prior to melting. Clasts from a coarse- grained gouge have lower chances of survival in a pseudotachylite due to a higher likelihood of non-equilibrium overheating. The maximum temperature and energy dissipation attainable on the fault surface are ultimately limited by either the rock solidus (via viscous braking, and slip arrest), or liquidus (via thermal runaway, and vanishing resistance to sliding). Our modeling results indicate that the thermally-activated fault strengthening and rupture arrest are unlikely to occur in most mafic protoliths, but might be relevant for quartz-rich rocks, especially at shallow (< 5-7 km) depths where the driving shear stress is relatively low.

Finite source modelling of magmatic unrest in Socorro, New Mexico, and Long Valley, California

Abstract: SUMMARY We investigate surface deformation associated with currently active crustal magma bodies in Socorro, New Mexico, and Long Valley, California, USA. We invert available geodetic data from these locations to constrain the overall geometry and dynamics of the inferred deformation sources at depth. Our best-fitting model for the Socorro magma body is a sill with a depth of 19 km, an effective diameter of 70 km and a rate of increase in the excess magma pressure of 0.6 kPa yr x1 . We show that the corresponding volumetric inflation rate is y6r10 x3 km 3 yr x1 , which is considerably less than previously suggested. The measured inflation rate of the Socorro magma body may result from a steady influx of magma from a deep source, or a volume increase associated with melting of the magma chamber roof (i.e. crustal anatexis). In the latter case, the most recent major injection of mantle-derived melts into the middle crust beneath Socorro may have occurred within the last several tens to several hundreds of years. The Synthetic Interferometric Aperture Radar (InSAR) data collected in the area of the Long Valley caldera, CA, between June 1996 and July 1998 reveal an intracaldera uplift with a maximum amplitude of y11 cm and a volume of 3.5r10 x2 km 3 . Modelling of the InSAR data suggests that the observed deformation might be due to either a sill-like magma body at a depth of y12 km or a pluton-like magma body at a depth of y8 km beneath the resurgent dome. Assuming that the caldera fill deforms as an isotropic linear elastic solid, a joint inversion of the InSAR data and two-colour laser geodimeter data (which provide independent constraints on horizontal displacements at the surface) suggests that the inferred magma chamber is a steeply dipping prolate spheroid with a depth of 7‐9 km and an aspect ratio in excess of 2:1. Our results highlight the need for large radar look angles and multiple look directions in future InSAR missions.

Fracture criteria at the tip of fluid‐driven cracks in the Earth

Abstract: The effect of high confining pressure on fluid-filled crack growth is considered. Exact solutions are given for a two-dimensional horizontal crack in an infinite elastic body using the approximation of Dugdale-Barenblatt (DB) model. It is shown that for equilibrium cracks (i.e. for cracks on the verge of propagation) the large-scale crack characteristics, such as fluid overpressure, apparent fracture toughness, maximum opening of the crack and crack volume, grow with increase of confining pressure. These effects result from a pressure induced fracture resistance (PIFR). If basic parameters of the DB model (tensile strength and critical crack opening displacement) are independent of confining pressure then PIFR dominates over intrinsic rock strength starting from quite shallow depth (tens to hundreds of meters).

Why do kimberlites from different provinces have similar trace element patterns

Abstract: [1] Analysis of the trace element contents in kimberlites from various provinces around the world, including South Africa, India, and Yakutia (Siberia, Russia), reveals remarkable similarity of the maximum abundances. In addition, we find that abundances of the rare earth elements (REE) in the South African kimberlites are highly coherent between individual elements. We suggest that the observed similarity of the trace element patterns may result from a common physicochemical process operating in the kimberlite source region, rather than from peculiar source compositions and magmatic histories. The most likely candidates for such a process are (1) partial melting at very low melting degrees and (2) porous melt flow and diffusive exchange with the host rocks. These two processes can produce the same maximum trace element abundances and similar undersaturated patterns. We argue that the porous flow, and the associated chromatographic enrichment, is preferred because it allows high saturations at relatively large melt fractions of ∼1%. Observations of enrichment of the xenolith grain rims due to an exchange with metasomatizing melts of quasi-kimberlitic composition imply that the melt percolated beyond the source region, in agreement with basic assumptions of the percolation model. We demonstrate that the saturated REE patterns are in a good agreement with the maximum observed REE abundances in kimberlites from different provinces. The theoretical patterns are independent of the melt fraction and only weakly (if at all) depend on the source modal composition. Characteristic diverging fan-like patterns of trace elements predicted by the percolation model are identified in kimberlites from South Africa. We propose that a high coherency of the REE patterns in the South African kimberlites results from a general dependence of all REE abundances on the calcium content. According to this interpretation, the overall depletion of the source rocks in REE with temperature (and depth) postulated by our model is a natural consequence of a decrease in the calcium content along the lherzolite trend.

A new method for measuring deformation on volcanoes and other natural terrains using InSAR persistent scatterers

Abstract: [1] We present here a new InSAR persistent scatterer (PS) method for analyzing episodic crustal deformation in non-urban environments, with application to volcanic settings. Our method for identifying PS pixels in a series of interferograms is based primarily on phase characteristics and finds low-amplitude pixels with phase stability that are not identified by the existing amplitude-based algorithm. Our method also uses the spatial correlation of the phases rather than a well-defined phase history so that we can observe temporally-variable processes, e.g., volcanic deformation. The algorithm involves removing the residual topographic component of flattened interferogram phase for each PS, then unwrapping the PS phases both spatially and temporally. Our method finds scatterers with stable phase characteristics independent of amplitudes associated with man-made objects, and is applicable to areas where conventional InSAR fails due to complete decorrelation of the majority of scatterers, yet a few stable scatterers are present.

Segmented lateral dyke growth in a rifting event at Bárðarbunga volcanic system, Iceland

Abstract: Crust at many divergent plate boundaries forms primarily by the injection of vertical sheet-like dykes, some tens of kilometres long1. Previous models of rifting events indicate either lateral dyke growth away from a feeding source, with propagation rates decreasing as the dyke lengthens2, 3, 4, or magma flowing vertically into dykes from an underlying source5, 6, with the role of topography on the evolution of lateral dykes not clear. Here we show how a recent segmented dyke intrusion in the Barðarbunga volcanic system grew laterally for more than 45 kilometres at a variable rate, with topography influencing the direction of propagation. Barriers at the ends of each segment were overcome by the build-up of pressure in the dyke end; then a new segment formed and dyke lengthening temporarily peaked. The dyke evolution, which occurred primarily over 14 days, was revealed by propagating seismicity, ground deformation mapped by Global Positioning System (GPS), interferometric analysis of satellite radar images (InSAR), and graben formation. The strike of the dyke segments varies from an initially radial direction away from the Barðarbunga caldera, towards alignment with that expected from regional stress at the distal end. A model minimizing the combined strain and gravitational potential energy explains the propagation path. Dyke opening and seismicity focused at the most distal segment at any given time, and were simultaneous with magma source deflation and slow collapse at the Barðarbunga caldera, accompanied by a series of magnitude M > 5 earthquakes. Dyke growth was slowed down by an effusive fissure eruption near the end of the dyke. Lateral dyke growth with segment barrier breaking by pressure build-up in the dyke distal end explains how focused upwelling of magma under central volcanoes is effectively redistributed over long distances to create new upper crust at divergent plate boundaries.

A model for the origin of large silicic magma chambers: precursors of caldera-forming eruptions

Abstract: The relatively low rates of magma production in island arcs and continental extensional settings require that the volume of silicic magma involved in large catastrophic caldera-forming (CCF) eruptions must accumulate over periods of 105 to 106 years. We address the question of why buoyant and otherwise eruptible high-silica magma should accumulate for long times in shallow chambers rather than erupt more continuously as magma is supplied from greater depths. Our hypothesis is that the viscoelastic behavior of magma chamber wall rocks may prevent an accumulation of overpressure sufficient to generate rhyolite dikes that can propagate to the surface and cause an eruption. The critical overpressure required for eruption is based on the model of Rubin (1995a). An approximate analytical model is used to evaluate the controls on magma overpressure for a continuously or episodically replenished spherical magma chamber contained in wall rocks with a Maxwell viscoelastic rheology. The governing parameters are the long-term magma supply, the magma chamber volume, and the effective viscosity of the wall rocks. The long-term magma supply, a parameter that is not typically incorporated into dike formation models, can be constrained from observations and melt generation models. For effective wall-rock viscosities in the range 1018 to 1020 Pa s–1, dynamical regimes are identified that lead to the suppression of dikes capable of propagating to the surface. Frequent small eruptions that relieve magma chamber overpressure are favored when the chamber volume is small relative to the magma supply and when the wall rocks are cool. Magma storage, leading to conditions suitable for a CCF eruption, is favored for larger magma chambers (>102 km3) with warm wall rocks that have a low effective viscosity. Magma storage is further enhanced by regional tectonic extension, high magma crystal contents, and if the effective wall-rock viscosity is lowered by microfracturing, fluid infiltration, or metamorphic reactions. The long-term magma supply rate and chamber volume are important controls on eruption frequency for all magma chamber sizes. The model can explain certain aspects of the frequency, volume, and spatial distribution of small-volume silicic eruptions in caldera systems, and helps account for the large size of granitic plutons, their association with extensional settings and high thermal gradients, and the fact that they usually post-date associated volcanic deposits.

Intrusion triggering of the 2010 Eyjafjallajokull explosive eruption

Abstract: The ash cloud that brought chaos to European air traffic in April this year was the result of emissions from an Icelandic volcano that had been intermittently active for about 18 years. A combination of detailed space-based geodetic measurements and seismic monitoring of the Eyjafjallajkull volcano in the run-up to the ash-producing explosive summit eruption reveals an unusual deformation pattern that may be attributed to its off-rift setting with relatively cool subsurface structure and limited magma at shallow depth. As to the predictability of such a dramatic reawakening, the immediate precursors to the initial eruption of the volcano in 2010 were subtle and difficult to detect, but the clear signs of volcanic unrest during the weeks, months and years preceding it may provide better clues to the catastrophic explosion.

Recent advances in the understanding of fault zone internal structure: a review

Abstract: It is increasingly apparent that faults are typically not discrete planes but zones of deformed rock with a complex internal structure and three-dimensional geometry. In the last decade this has led to renewed interest in the consequences of this complexity for modelling the impact of fault zones on fluid flow and mechanical behaviour of the Earth's crust. A number of processes operate during the development of fault zones, both internally and in the sur- rounding host rock, which may encourage or inhibit continuing fault zone growth. The complexity of the evolution of a faulted system requires changes in the rheological properties of both the fault zone and the surrounding host rock volume, both of which impact on how the fault zone evolves with increasing displacement. Models of the permeability structure of fault zones emphasize the presence of two types of fault rock components: fractured conduits parallel to the fault and gran- ular core zone barriers to flow. New data presented in this paper on porosity- permeability relationships of fault rocks during laboratory deformation tests support recently advancing con- cepts which have extended these models to show that poro-mechanical approaches (e.g., critical state soil mechanics, fracture dilatancy) may be applied to predict the fluid flow behaviour of complex fault zones during the active life of the fault. Predicting the three-dimensional heterogen- eity of fault zone internal structure is important in the hydrocarbon industry for evaluating the retention capacity of faults in exploration contexts and the hydraulic behaviour in production contexts. Across-fault reservoir juxtaposition or non-juxtaposition, a key property in predicting retention or across-fault leakage, is strongly controlled by the three-dimensional complexity of the fault zone. Although algorithms such as shale gouge ratio greatly help predict capillary threshold pressures, quantification of the statistical variation in fault zone composition will allow estimations of uncertainty in fault retention capacity and hence prospect reserve estimations. Permeability structure in the fault zone is an important issue because bulk fluid flow rates through or along a fault zone are dependent on permeability variations, anisotropy and tortuosity of flow paths. A possible way forward is to compare numerical flow models using statistical variations of permeability in a complex fault zone in a given sandstone/shale context with field-scale estimates of fault zone permeability. Fault zone internal structure is equally important in understanding the seismogenic behaviour of faults. Both geometric and compositional complexities can control the nucleation, propagation and arrest of earthquakes. The presence and complex distribution of different fault zone materials of contrasting velocity-weakening and velocity-strengthening prop- erties is an important factor in controlling earthquake nucleation and whether a fault slips seismo- genically or creeps steadily, as illustrated by recent studies of the San Andreas Fault. A synthesis of laboratory experiments presented in this paper shows that fault zone materials which become stronger with increasing slip rate, typically then get weaker as slip rate continues to increase to seismogenic slip rates. Thus the probability that a nucleating rupture can propagate sufficiently to generate a large earthquake depends upon its success in propagating fast enough through these materials in order to give them the required velocity kick. This propagation success is hence controlled by the relative and absolute size distributions of velocity-weakening and vel- ocity-strengthening rocks within the fault zone. Statistical characterisation of the distribution of such contrasting properties within complex fault zones may allow for better predictive models of rupture propagation in the future and provide an additional approach to earthquake size fore- casting and early warnings.