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Fialko, Y, Khazan Y, Simons M.  2001.  Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy. Geophysical Journal International. 146:181-190.   10.1046/j.1365-246X.2001.00452.x   AbstractWebsite

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.

Guterman, VG, Fialko YA, Khazan YM.  1996.  Dome structures above sill-like crustal intrusions: A quantitative model fo preseismic uplift. Part 2. Geofizicheskii Zhurnal. 18:62-69.
Guterman, VG, Fialko YA, Khazan YM.  1996.  Dome structures above sill-like crustal intrusions: A quantitative model fo preseismic uplift. Part I. Geofizicheskii Zhurnal. 18:35-43.
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Fialko, Y, Rivera L, Kanamori H.  2005.  Estimate of differential stress in the upper crust from variations in topography and strike along the San Andreas fault. Geophysical Journal International. 160:527-532.   10.1111/j.1365-246X.2004.02511.x   AbstractWebsite

The major bends of the San Andreas fault in California are associated with significant variations in the along-fault topography. The topography-induced perturbations in the intermediate principal stress may result in the rotation of the fault with respect to the maximum compression axis provided that the fault is non-vertical, and the slip is horizontal. The progressive fault rotation may produce additional topography via thrust faulting in the adjacent crust, resulting in a positive feedback. The observed rotation of the fault plane due to the along-fault variations in topography is used to infer the magnitude of the in situ differential stress. Our results suggest that the average differential stress in the upper crust around the San Andreas fault is of the order of 50 MPa, implying that the effective fault strength is about a factor of two lower than predictions based on Byerlee's law and the assumption of hydrostatic pore pressure.

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Fialko, Y, Simons M, Khazan Y.  2001.  Finite source modelling of magmatic unrest in Socorro, New Mexico, and Long Valley, California. Geophysical Journal International. 146:191-200.   10.1046/j.1365-246X.2001.00453.x   AbstractWebsite

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 brst-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(-1). We show that the corresponding volumetric inflation rate is similar to6 x 10(-3) km(3) yr(-1), 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 map 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 similar to 11 cm and a volume of 3.5 x 10(-2) 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 similar to 12 km or a pluton-like magma body at a depth of similar to8 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-colons 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.

Khazan, YM, Fialko YA.  1995.  Fracture Criteria at the Tip of Fluid-Driven Cracks in the Earth. Geophysical Research Letters. 22:2541-2544.   10.1029/95gl02547   AbstractWebsite

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).

Fialko, Y, Khazan Y.  2005.  Fusion by earthquake fault friction: Stick or slip? Journal of Geophysical Research-Solid Earth. 110   10.1029/2005jb003869   AbstractWebsite

[1] Field observations of pseudotachylites and experimental studies of high-speed friction indicate that melting on a slipping interface may significantly 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 pseudotachylites 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 nonequilibrium 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.

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Kaneko, Y, Fialko Y, Sandwell DT, Tong X, Furuya M.  2013.  Interseismic deformation and creep along the central section of the North Anatolian Fault (Turkey): InSAR observations and implications for rate-and-state friction properties. Journal of Geophysical Research-Solid Earth. 118:316-331.   10.1029/2012jb009661   AbstractWebsite

We present high-resolution measurements of interseismic deformation along the central section of the North Anatolian Fault (NAF) in Turkey using interferometric synthetic aperture radar data from the Advanced Land Observing Satellite and Envisat missions. We generated maps of satellite line-of-sight velocity using five ascending Advanced Land Observing Satellite tracks and one descending Envisat track covering the NAF between 31.2 degrees E and 34.3 degrees E. The line-of-sight velocity reveals discontinuities of up to similar to 5 mm/yr across the Ismetpasa segment of the NAF, implying surface creep at a rate of similar to 9 mm/yr; this is a large fraction of the inferred slip rate of the NAF (21-25 mm/yr). The lateral extent of significant surface creep is about 75 km. We model the inferred surface velocity and shallow fault creep using numerical simulations of spontaneous earthquake sequences that incorporate laboratory-derived rate and state friction. Our results indicate that frictional behavior in the Ismetpasa segment is velocity strengthening at shallow depths and transitions to velocity weakening at a depth of 3-6 km. The inferred depth extent of shallow fault creep is 5.5-7 km, suggesting that the deeper locked portion of the partially creeping segment is characterized by a higher stressing rate, smaller events, and shorter recurrence interval. We also reproduce surface velocity in a locked segment of the NAF by fault models with velocity-weakening conditions at shallow depth. Our results imply that frictional behavior in a shallow portion of major active faults with little or no shallow creep is mostly velocity weakening. Citation: Kaneko, Y., Y. Fialko, D. T. Sandwell, X. Tong, and M. Furuya (2013), Interseismic deformation and creep along the central section of the North Anatolian Fault (Turkey): InSAR observations and implications for rate-and-state friction properties, J. Geophys. Res. Solid Earth, 118, 316-331, doi: 10.1029/2012JB009661.

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Kaneko, Y, Fialko Y.  2011.  Shallow slip deficit due to large strike-slip earthquakes in dynamic rupture simulations with elasto-plastic off-fault response. Geophysical Journal International. 186:1389-1403.   10.1111/j.1365-246X.2011.05117.x   AbstractWebsite

Slip inversions of geodetic data from several large (magnitude similar to 7) strike-slip earthquakes point to coseismic slip deficit at shallow depths (< 3-4 km), that is, coseismic slip appears to decrease towards the Earth surface. While the inferred slip distribution may be consistent with laboratory-derived rate and state friction laws suggesting that the uppermost brittle crust may be velocity strengthening, there remains a question of how the coseismic slip deficit is accommodated throughout the earthquake cycle. The consequence of velocity-strengthening fault friction at shallow depths is that the deficit of coseismic slip is relieved by post-seismic afterslip and interseismic creep. However, many seismic events with inferred shallow slip deficit were not associated with either resolvable shallow interseismic creep or robust shallow afterslip. Hence, the origin of shallow 'slip deficit' remains uncertain. In this study, we investigate whether inelastic failure in the shallow crust due to dynamic earthquake rupture can explain the inferred deficit of shallow slip. Evidence for such failure is emerging from geologic, seismic and geodetic observations. We find that the amount of shallow slip deficit is proportional to the amount of inelastic deformation near the Earth surface. Such deformation occurs under a wide range of parameters that characterize rock strength in the upper crust. However, the largest magnitude of slip deficit in models accounting for off-fault yielding is 2-4 times smaller than that inferred from kinematic inversions of geodetic data. To explain this discrepancy, we further explore to what extent assumptions in the kinematic inversions may bias the inferred slip distributions. Inelastic deformation in the shallow crust reduces coseismic strain near the fault, introducing an additional 'artificial' deficit of up to 10 per cent of the maximum slip in inversions of geodetic data that are based on purely elastic models. The largest magnitude of slip deficit in our models combined with the bias in inversions accounts for up to 25 per cent of shallow slip deficit, which is comparable, but still smaller than 3060 per cent deficit inferred from kinematic inversions. We discuss potential mechanisms that may account for the remaining discrepancy between slip deficit predicted by elasto-plastic rupture models and that inferred from inversions of space geodetic data.

Hamiel, Y, Katz O, Lyakhovsky V, Reches Z, Fialko Y.  2006.  Stable and unstable damage evolution in rocks with implications to fracturing of granite. Geophysical Journal International. 167:1005-1016.   10.1111/j.1365-246X.2006.03126.x   AbstractWebsite

We address the relation between the rock rigidity and crack density by comparing predictions of a viscoelastic damage rheology model to laboratory data that include direct microscopic mapping of cracks. The damage rheology provides a generalization of Hookean elasticity to a non-linear continuum mechanics framework incorporating degradation and recovery of the effective elastic properties, transition from stable to unstable fracturing, and gradual accumulation of irreversible deformation. This approach is based on the assumption that the density of microcracks is uniform over a length scale much larger than the length of a typical crack, yet much smaller than the size of the entire deforming domain. For a system with a sufficiently large number of cracks, one can define a representative volume in which the crack density is uniform and introduce an intensive damage variable for this volume. We tested our viscoelastic damage rheology against sets of laboratory experiments done on Mount Scott granite. Based on fitting the entire stress-strain records the damage variable is constrained, and found to be a linear function of the crack density. An advantage of these sets experiments is that they were preformed with different loading paths and explicitly demonstrated the existence of stable and unstable fracturing regimes. We demonstrate that the viscoelastic damage rheology provides an adequate quantitative description of the brittle rock deformation and simulates both the stable and unstable damage evolution under various loading conditions. Comparison between the presented data analysis of experiments with Mount Scott granite and previous results with Westerly granite and Berea sandstone indicates that granular or porous rocks have lower seismic coupling. This implies that the portion of elastic strain released during a seismic cycle as brittle deformation depends on the lithology of the region. Hence, upper crustal regions with thick sedimentary cover, or fault zones with high degree of damage are expected to undergo a more significant inelastic deformation in the interseismic period compared to 'intact' crystalline rocks.

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Khazan, YM, Fialko YA.  2001.  Tensile and shear cracks in the Dugdale-Barenblatt model. Geofizicheskii Zhurnal. 23:13-30.
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Khazan, Y, Fialko Y.  2005.  Why do kimberlites from different provinces have similar trace element patterns? Geochemistry Geophysics Geosystems. 6   10.1029/2005gc000919   AbstractWebsite

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 similar to 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.