Effect of frictional heating and thermal advection on pre-seismic sliding: a numerical simulation using a rate-, state- and temperature-dependent friction law

Laboratory experiments on simulated faults in rocks clearly show the temperature dependence of dynamic rock friction. Since rocks surrounding faults are permeable, we have developed a numerical method to describe the thermo-mechanical evolution of the pre-seismic sliding phase which takes into account both the rate-, state- and temperature-dependent friction law and the heat advection term in the energy equation. We consider a laminar fluid motion perpendicular to a vertical fault plane and assume that fluids move away from the fault plane. A semi-analytical temperature solution which accounts for the variability of slip velocity and stress on the fault has been found. This solution has been generalized to the case of a time varying fluid velocity and then was used to include the thermal pressurization effect. After discretizing the temperature solution, the evolution of the system is obtained by the solution of a system of first order differential equations which allows us to determine the evolution of slip, slip rate, friction coefficient, effective normal stress, temperature and fluid velocity. The numerical solutions are found using a Runge-Kutta method with an adaptative stepsize control in time. When the thermal pressurization effects can be neglected, the heat advection effect gives rise to a delay, with respect to the purely conductive case, of the earthquake occurrence time. This delay increases with increasing permeability H of the system. When the thermal pressurization effects are taken into account the situation is opposite, i.e. the onset of instability tends to precede that of the purely conductive case. The advance in the time of occurrence of instability increases with increasing coefficient of thermal pressurization. In the small permeability range (H ≤ 10^?18 m²), the seismic moment and nucleation length of the pre-seismic phase are significantly smaller than those predicted by the purely conductive model.     

The role of magma chamber-fault interaction in caldera forming eruptions

This paper examines the role of the position and orientation of a regional fault in the roof of a magma chamber on stress distribution, mechanical failure, and dyking using 2D finite element numerical simulations. The study pertains to the magma chamber behavior in the relatively short time intervals of several hundreds to thousand of years. The magma chamber is represented as an elliptical inclusion (eccentricity, a/b = 0.12) at a relative depth, H/a, of 0.9. The fault has a 45° dip and is represented by a frictionless fracture. The temperature field in the host rock is calculated assuming a quasisteady-state thermal regime that develops through periodic episodes of magma supply. The rheology of the surrounding rocks is treated using viscoelasticity with temperature activated strain-rate dependent viscosity. Strain weakening of the rocks in the ductile zone is described within the frame of the Dynamic Power Law model . The magma pressure is coupled with the deformation of the rock mass hosting the chamber, including the fault. The variation of magma pressure in response to magma supply and chamber deformation is calculated in the elastic and viscoelastic regimes. The latter corresponds to slow filling, while the former represents a filling time much less than the viscous relaxation time scale. The resulting “equation of state” for the magma chamber couples the magma pressure with the chamber volume in the elastic regime, and with the filling rate for the viscoelastic regime. Analysis of stresses is used to predict dyke propagation conditions, and the mechanical failure of the chamber roof for different fault positions and magma overpressures. Results show that an outward dipping fault located on the periphery of the chamber roof hinders the propagation of dykes to the surface, causing magma to accumulate under the footwall of the fault. At high to moderate overpressures (30–40 MPa), the fault causes localized shear failure and chamber roof collapse that might lead to the first stage of a caldera-forming eruption.     

Zircon U–Pb ages of plutonic rocks in the southern Abukuma Mountains: Implications for Cretaceous geotectonic evolution of the Abukuma Belt

Plutonic rocks in the southern Abukuma Mountains include gabbro and diorite, fine‐grained diorite, hornblende–biotite granodiorite (Ishikawa, Samegawa, main part of Miyamoto and Tabito, Kamikimita and Irishiken Plutons), biotite granodiorite (the main part of Hanawa Pluton and the Torisone Pluton), medium‐ to coarse‐grained biotite granodiorite and leucogranite, based on the lithologies and geological relations. Zircon U–Pb ages of gabbroic rocks are 112.4 ±1.0 Ma (hornblende gabbro, Miyamoto Pluton), 109.0 ±1.1 Ma (hornblende gabbro, the Hanawa Pluton), 102.7 ±0.8 Ma (gabbronorite, Tabito Pluton) and 101.0 ±0.6 Ma (fine‐grained diorite). As for the hornblende–biotite granodiorite, zircon U–Pb ages are 104.2 ±0.7 Ma (Ishikawa Pluton), 112.6 ±1.0 Ma (Tabito Pluton), 105.2 ±0.8 Ma (Kamikimita Pluton) and 105.3±0.8 Ma (Irishiken Pluton). Also for the medium‐ to fine‐grained biotite granodiorite, zircon U–Pb ages are 106.5±0.9 Ma (Miyamoto Pluton), 105.1 ±1.0 Ma (Hanawa Pluton) and the medium‐ to coarse‐grained biotite granodiorite has zircon U–Pb age of 104.5 ±0.8 Ma. In the case of the leucogranite, U–Pb age of zircon is 100.6 ±0.9 Ma. These data indicate that the intrusion ages of gabbroic rocks and surrounding granitic rocks ranges from 113 to 101 Ma. Furthermore, K–Ar ages of biotite and or hornblende in the same rock samples were dated. Accordingly, it is clear that these rocks cooled down rapidly to 300 °C (Ar blocking temperature of biotite for K–Ar system) after their intrusion. These chronological data suggest that the Abukuma plutonic rocks in the southern Abukuma Mountains region uplifted rapidly around 107 to 100 Ma after their intrusion.     

The Elastic Strain Energy of Damaged Solids with Applications to Non-Linear Deformation of Crystalline Rocks

Laboratory and field data indicate that rocks subjected to sufficiently high loads clearly deviate from linear behavior. Non-linear stress–strain relations can be approximated by including third and higher-order terms of the strain tensor in the elastic energy expression (e.g., the Murnaghan model). Such classical non-linear models are successful for calculating deformation of soft materials, for example graphite, but cannot explain with the same elastic moduli small and large non-linear deformation of stiff rocks, such as granite. The values of the third (higher-order) Murnaghan moduli estimated from acoustic experiments are one to two orders of magnitude above the values estimated from stress–strain relations in quasi-static rock-mechanics experiments. The Murnaghan model also fails to reproduce an abrupt change in the elastic moduli upon stress reversal from compression to tension, observed in laboratory experiments with rocks, concrete, and composite brittle material samples, and it predicts macroscopic failure at stress levels lower than observations associated with granite. An alternative energy function based on second-order dependency on the strain tensor, as in the Hookean framework, but with an additional non-analytical term, can account for the abrupt change in the effective elastic moduli upon stress reversal, and extended pre-yielding deformation regime with one set of elastic moduli. We show that the non-analytical second-order model is a generalization of other non-classical non-linear models, for example “bi-linear”, “clapping non-linearity”, and “unilateral damage” models. These models were designed to explain the abrupt changes of elastic moduli and non-linearity of stiff rocks under small strains. The present model produces dilation under shear loading and other non-linear deformation features of the stiff rocks mentioned above, and extends the results to account for gradual closure of an arbitrary distribution of initial cracks. The results provide a quantitative framework that can be used to model simultaneously, with a small number of coefficients, multiple observed aspects of non-linear deformation of stiff rocks. These include, in addition to the features mentioned above, stress-induced anisotropy and non-linear effects in resonance experiments with damaged materials.     

An empirical function to estimate the depths of linear hot sources: Laboratory modeling and field measurements of lava tubes

Estimating depths of buried lava tubes is important for determining the thermal budgets and effusion rates of basaltic volcanic systems. This research used a laboratory experiment scaled to a lava tube system to measure the 3D temperature field surrounding a hot viscous fluid flowing through a buried glass tube while varying conditions such as flow rate and temperature. The depth of the glass tube was changed for different experimental runs. Numerical techniques were applied to model the laboratory experiment. The surface thermal distributions from 166 thermal traverses, constrained to a depth to width ratio of 0.6 to 1.6, were analyzed to empirically derive a depth estimation function using regression techniques. This “Linear Anomaly Surface Transect (LAST)” depth function is a scaleable depth estimation technique which can be solved with thermal imaging data alone. The minimum temperature, maximum temperature and width of a Lorentzian distribution fit to a surface thermal transect, are the only inputs required for the LAST function to estimate the depths of the hot source. The input parameters were then applied to non-laboratory situations including the Kuhio lava tube system in Hawai’i. The LAST function produced depth estimates of ∼ 0.3 m for the Kuhio lava tube in Hawai’i, which did not agree with observations on the ground. This is the result of the complex composition and geometry of an actual lava tube where heat transfer is controlled by more than a simple fluid filling a tube, but also by convection of gasses and fluids in a partially filled passage. Though not effective for lava tubes at this time, the model provides promising results for simple cases applied to engineering and underground coal fires.     

Fumarole monitoring with a handheld infrared camera: Volcán de Colima,Mexico, 2006–2007

This paper describes a methodology for the monitoring of fumarole temperatures at medium ranges (~ 6 km) using a handheld infrared camera (wavelength range: 8–13.5 µm). As a relationship between fumarole temperatures, gas flux and volcanic activity has been demonstrated by a number of studies, fumarole temperature data has a potential use as a monitoring tool. Volcán de Colima is an andesitic stratovolcano with a 300 m diameter summit crater formed by the destruction of the 2004 lava dome by a series of explosions in 2005. Between January 2006 and August 2007, sequences of thermal images were recorded from a viewpoint 6 km to the north during regular 24–48 hour monitoring excursions. The temperatures of fumaroles on the crater rim and the ground surface on the volcano's flanks were measured. A methodology was developed to remove data affected by clouds or volcanic water vapour based on rates of temperature change and scatter within the data. For the remaining data, it is demonstrated mathematically that at this range, typical variations in atmospheric transmissivity will affect the apparent temperatures by +/− 2 °C, while a 25% change in fumarole heat flux would change it by 5–10 °C. The mean night-time apparent temperature of the fumaroles was calculated for each excursion and showed an irregular decline over the 19 month period. Subtracting the radiant heat flux of flank rocks from those of the fumaroles removes seasonal variations and gives the clearest view of trends in the fumarole heat flux. A sharp drop in fumarole temperature during February 2007 coincided with the emergence of a lava dome in the crater. The declining fumarole temperature is interpreted to reflect decreasing gas flux from the crater in line with a change in eruptive regime from frequent, small, ash-rich explosions to slow effusion of lava.     

A THREE-DIMENSIONAL NUMERICAL BOTTOM-HOLE TEMPERATURE STABILIZATION MODEL*

The heat flow equation in cylindrical coordinates is solved numerically for any general distribution of thermal diffusivity. The temperature stabilization of a borehole is considered, and solutions for the case where thermal diffusivity is a function of radial distance from the borehole are obtained and compared to solutions for uniform diffusivity. The results are discussed in terms of thermal diffusivities that are different for the well contents and for the surrounding material. It is found that the approach to formation temperature is affected by differences between well contents and the surrounding region.     

Evaluation of approximations in modelling the cooling of magmatic bodies

The cooling of a magmatic intrusion is simulated by a simple model of a non-homogeneous earth, with thermal properties depending on temperature, in which heat transfer is assumed to take place by conduction only. The mathematical problem consists in solving a non-linear partial differential equation with continuity conditions on temperature and heat flux imposed at the contacts between different rocks. This has been done numerically by a finite difference method. The model is then adopted as “reality” against which a number of commonly used approximations are tested. It is found that the effect of latent heat liberation can be reasonably taken into account by attributing an effective initial temperature to the magma (errors within 20°C for t > 10⁵ years, when the temperature of the magma is still as high as 600°C); the effective specific heat approximation does not work as well. The dependence of thermal conductivity and specific heat on temperature may be eliminated by maintaining the errors within 30°C for t < 5 × 10⁵ years. The assumption that magma and country rocks have the same thermal properties allows an estimate of the temperature field in the host rocks with errors of 50°C at most. The assumption that all rocks have the same constant conductivity yields results that are far from “reality” (errors of 100–200°C even at shallow depth).     

Thermal diffusivity of seasonal snow determined from temperature profiles

Thermal diffusivity of snow is an important thermodynamic property associated with key hydrological phenomena such as snow melt and heat and water vapor exchange with the atmosphere. Direct determination of snow thermal diffusivity requires coupled point measurements of thermal conductivity and density, which continually change due to snow metamorphism. Traditional methods for determining these two quantities are generally limited by temporal resolution. In this study we present a method to determine the thermal diffusivity of snow with high temporal resolution using snow temperature profile measurements. High resolution (between 2.5 and 10 cm at 1 min) temperature measurements from the seasonal snow pack at the Plaine-Morte glacier in Switzerland are used as initial conditions and Neumann (heat flux) boundary conditions to numerically solve the one-dimensional heat equation and iteratively optimize for thermal diffusivity. The implementation of Neumann boundary conditions and a t-test, ensuring statistical significance between solutions of varied thermal diffusivity, are important to help constrain thermal diffusivity such that spurious high and low values as seen with Dirichlet (temperature) boundary conditions are reduced. The results show that time resolved thermal diffusivity can be determined from temperature measurements of seasonal snow and support density-based empirical parameterizations for thermal conductivity.     

An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system

A mathematical model is developed for predicting the temperature distribution in an aquifer thermal energy storage (ATES) system, which consists of a confined aquifer bounded from above and below by the rocks of different geological properties. The main transfer processes of heat include the conduction and advection in the aquifer and the conduction in the rocks. The semi‐analytical solution in dimensionless form for the model is developed by Laplace transforms and its corresponding time‐domain solution is evaluated by the modified Crump method. Field geothermal property data are used to simulate the temperature distribution in an ATES system. The results show that the heat transfer in the aquifer is fast and has a vast effect on the vicinity of the wellbore. However, the aquifer temperature decreases with increasing radial and vertical distances. The temperature in the aquifer may be overestimated when ignoring the effect of thermal conductivity. The temperature distribution in an ATES system depends on the vertical thermal conduction in the rocks and the horizontal advection and thermal conduction in the aquifer. The present solution is useful in designing and simulating the heat injection facility in the ATES systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Long-term underground temperature measurements at Syowa Station, East Antarctica

Underground temperature measurements in two shallow boreholes have been carried out by the Japanese Antarctic Research Expedition at Syowa Station, East Antarctica from April, 1981 to January, 1985. Two quartz thermometers were installed in the first borehole at depths of 2 and 5 m and three were in the second one at depths of 1, 4 and 6.8 m. The mean underground temperatures in the first borehole were −8.181 and −8.843°C at depths of 2 and 5 m, and in the second one −8.242 and −8.220°C at depths of 4 and 6.8 m. As the mean air temperature at Syowa Station was −10.8°C, the underground temperature in the 2 −6.8 m depth range is about two degrees higher than the air temperature. The thermal diffusivities of the observation area are determined by the same principle of the Ångström method, using long-term underground temperature records. The thermal diffusivity around Syowa Station is established to be about two times larger than those of ordinary igneous and metamorphic rocks measured in the laboratory. The thermal conductivity of the drilled cores and surrounding outcropping rocks are also measured by the transient method with temperature conditions at +23°C and −20°C. The thermal conductivities measured in various samples at −20°C are about 7% larger than those at +23°C. Thes tendency is consistent with the results of holocrystalline rock experiments.     

Near‐surface temperatures and heat balance of bare outcrops exposed to solar radiation

Subsurface temperatures in rocks naturally fluctuate under the influence of local meteorological conditions. These fluctuations play a role in mechanical weathering, thus creating the environmental conditions conducive to natural hazards such as rockfalls and providing important sediment source terms for landscape evolution. However, the physics that control heat penetration into rocks are not fully understood, which makes the underground thermal state difficult to interpret when temperature measurements are available and even more difficult to estimate for unmonitored sites. This is an important lacuna given possible impacts of future climate change on mechanical weathering processes. The natural daily variations of subsurface temperatures were investigated on a bare gneiss outcrop exposed to solar radiation, where temperatures at various depths (up to 50 cm), as well as the solar radiation reaching a pyranometer, were monitored hourly for several months. This detailed times series of thermal data was used to gain insight into the heat balance at the inclined free surface of the rock mass. Attention was focused on two major contributors to the heat balance; the heat flux entering the rock mass through conduction and the incoming shortwave (solar) radiation. A Fourier decomposition of the temperature measurements provided an estimate of the in situ thermal conductivity of the rock and was used to calculate the conductive term. The shortwave radiation term was determined on the basis of the pyranometer measurements adjusted to account for the angle of incidence of the sun. It is shown that, throughout clear‐sky periods, heat exchanges at the surface are mainly controlled by direct solar radiation during the day, and by a roughly constant outgoing heat flux during the night. Subsurface temperatures can be reliably estimated with a semi‐infinite medium model whose boundary condition is derived from an analytical insolation model that takes atmospheric attenuation into account. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of high-pressures on the electrical resistivity of natural zeolites from Deccan Trap, Maharashtra, India

We report here the electrical resistivity measurements on two natural zeolites–natrolite and scolecite (from the Killari borehole, Maharashtra, India) as a function of pressure up to 8 GPa at room temperature. High-pressure electrical resistivity studies on hydrous alumino-silicate minerals are very helpful in understanding the role of water in deep crustal conductivities obtained from geophysical models. The results obtained by magneto-telluric (MT) soundings and direct current resistivity surveys, along with the laboratory data on the electrical resistivity of minerals and rocks at high-pressure–temperature are used to determine the electrical conductivity distribution in continental lithosphere. The electrical resistivity of natural natrolite decreases continuously from 2.9 × 10⁹ Ω cm at ambient condition to 7.64 × 10² Ω cm at 8 GPa, at room temperature. There is no pressure-induced first order structural phase transitions in natrolite, when it is compressed in non-penetrating pressure transmitting medium up to 8 GPa. On the other hand scolecite exhibits a pressure-induced transition, with a discontinuous decrease of the electrical resistivity from 2.6 × 10⁶ to 4.79 × 10⁵ Ω cm at 4.2 to 4.3 GPa. The observed phase transition in scolecite is found to be irreversible. Vibrational spectroscopic and X-ray diffraction studies confirm the amorphous nature of the high-pressure phase. The results of the present high-pressure studies on scolecite are in good agreement with the high-pressure Raman spectroscopic data on scolecite. The thermo gravimetric studies on the pressure-quenched samples show that the samples underwent a pressure-induced partial dehydration. Such a pressure-induced partial dehydration, which has been observed in natural scolecite could explain the presence of high conductive layers in the earth's deep-crust.     

Geodetic and seismic constraints on recent activity at Long Valley Caldera,California: evidence for viscoelastic rheology

Long Valley Caldera is an active volcanic region in east central California. Surface deformation on the resurgent dome within the caldera was an order of magnitude higher for the five-month period September 1997 through January 1998 compared to the previous three-year average. However, the location of the immediate (shallow) source of deformation remained essentially constant, 5–7 km beneath the dome, near the top of a region of probable magma accumulation defined by seismic data. Similarly, although the rate of seismic moment release increased dramatically, earthquake locations remained similar to earlier periods. The rate of deformation increased exponentially between April–May 1997 and late November 1997 with a time constant of ∼55–65 days, after which it decreased exponentially with about the same time constant. We develop a model consistent with these observations and also consistent with independent constraints on sub-surface rheology from thermal, geochemical and laboratory data. Deformation at sites on the resurgent dome most sensitive to the shallow deformation source are well fit by a model with a single pressure source at 6 km depth which experienced a pressure pulse that began in late 1996, peaked in November 1997, close to the time of major seismic moment release, and essentially ended in mid-1999. The pressure source in our model is surrounded by a 1 km thick “shell” of Maxwell viscoelastic material (shell viscosity 10¹⁶ Pa s) within an elastic half space, and has peak values that are much lower than corresponding purely elastic half space models. The shell viscosity is characteristic of a weak, deformable solid, e.g. quartz-bearing country rock surrounding the magma chamber at temperatures in the range 500–600°C, i.e. above the brittle–ductile transition, and/or largely crystallized rhyolite near its solidus temperature of ∼670°C, material that probably exists near the top of the zoned magma chamber at Long Valley.     

塔里木盆地现今地热特征

地温梯度和大地热流是揭示盆地现今热状态的重要参数,它们对理解盆地的构造-热演化过程及油气资源评价等方面均具有重要意义.利用塔里木盆地约470口井的地层测试温度资料和941块岩石热导率数据,本文计算了塔里木盆地38个新的大地热流数据,进而揭示了该盆地现今地热分布特征.研究表明,塔里木盆地现今地温梯度变化范围为17～32 ℃/km,平均为22.6±3.0 ℃/km;大地热流变化范围为26.2～65.4 mW/m²,平均为43.0±8.5 mW/m².与我国其他大中型沉积盆地相比,它表现为低地温、低大地热流的冷盆的热状态,但仍具有与世界上典型克拉通盆地相似的地热背景.整体而言,盆地隆起区地温梯度和热流相对较高,坳陷区地温梯度和热流则偏低.此外,我们还发现塔里木盆地现有的油气田区一般位于高地温梯度区域,这可能与下部热流体的向上运移和聚集有关.影响塔里木盆地现今地热特征的因素包括盆地深部结构、构造演化、岩石热物理性质、盆地基底构造形态和烃类聚集等.     

On the heat budget of the moon and the surface temperature variation during a lunar eclipse

Summary The analysis of surface temperature variations of the moon is based on the equations of heat conduction and heat continuity in the interior of the moon andStefan's law. During a well-defined process, as exemplified by a lunar eclipse, the local heat budget equation establishes a boundary condition at the moon surface which must be satisfied by solutions of the thermal diffusion equation in the interior. Three simplified models of the general case are discussed. They are characterized by special assumptions regarding the depth and time dependency of the thermic qualities of the material underlying the moon's surface. In short, the thermal diffusivity is assumed to be constant in the first model, a linear depth function in the second and a time function in the third. A unique solution can be obtained for model No. I such that the absolute surface temperature is approximately inversely proportional to the 6th root of time during the phase of total eclipse.Epstein's conclusion that the average surface of the moon might consist of highly porous rocks or fine dust is confirmed by the order of magnitude of the heat conductivity which produces the best fit between the theoretical curves and a plot ofPettit's observational data during the lunar eclipse of 1939. Existing differences between the observed and theoretical curves during the totality phase of the eclipse can be reduced by the employment of the second model. A crude estimate shows that the average dust cover resting on more solid ground of lunar rocks might possibly have a thickness of approximately 0.5 meters.     

Mylonites of the South Armorican Shear Zone: Insights for crustal-scale fluid flow and water–rock interaction processes

Mylonites display petrographical and geochemical characteristics that can be related to syn-deformation fluid circulation. The South Armorican Shear Zone, a major structural feature of the Armorican Massif (France), is outlined by the presence of mylonitic rocks cropping out mostly in open quarries. These mylonites were essentially formed at the expense of peraluminous granitic bodies. Deformation occurred from ductile conditions in the biotite stability field (>400 °C) down to lower greenschist cataclasis and brecciation, where carbonation developed. U–Pb analyses on zircon and monazite define a minimum duration of 15 Ma for the deformation and hydrothermal history, between 315 Ma and 300 Ma. Fluid circulations are well documented, by way of petrographic observation (chlorite and carbonate crystallization), mineralogical composition analysis (muscovite chemistry), erratic mobility behavior of some elements (As, Sn, U for instance), and stable isotope composition analysis of the infiltrated rocks. High temperature deformation is not accompanied by alteration of the O isotope system, which implies either low fluid/rock ratio and/or the involvement of δ¹⁸O crustal fluids with a composition similar to that of the rocks. On the other hand, some low temperature mylonites show a drastic decrease in the δ¹⁸O values, which has to be related to the influx of surface derived waters. The heat source necessary for this crustal scale downward infiltration of fluids followed by upward motion was likely provided by the exhumation of lower crustal units in the South Armorican domain.     

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic–viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown–Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown–Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz–clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks.     

结构面分布特征对隧道围岩变形影响的数值模拟分析

结构面对隧道围岩变形及稳定性起着决定性作用。运用三维离散元方法（3DEC）研究结构面分布特征,重点是结构面线密度1/λ、强度和倾角对隧道围岩变形的影响,总结了结构面分布与围岩变形特征的关系。结果表明,在结构面强度较低的情况下,结构面线密度对隧道变形的影响较大,其影响可分为两种情况：①λ≤0.2时,围岩的弯曲变形大于沿结构面的剪切变形,属于应力型大变形;②0.2〈λ≤0.4时,沿结构面的剪切变形大于围岩的弯曲变形,属于结构型大变形。结构面倾角主要影响围岩大变形发生的位置。将数值模拟结果与国内工程实例实测变形资料相对比,发现一致性较好。本研究结果对隧道支护结构的设计以及施工设计具有借鉴意义与指导作用。     

A thin elastic core can control large-scale patterns of lithosphere shortening

Peak lithospheric strength should reside in the rocks that, under the applied stress, cannot either creep (due to low temperature) or break (due to high confining pressure). The greatest resistance comes from dry olivine/pyroxene-rich upper mantle/lowermost crust at Moho conditions (400–600 °C and > 1 GPa). We have conducted laboratory experiments to investigate the importance of the unbreakable core of the lithosphere in between its brittle and ductile parts and conclude that it can control the large-scale lithospheric deformation pattern under shortening. Regardless of the thickness of the unbreakable core, it acts as a restraining layer that is easily flexed but is unstretchable. This eliminates large scale brittle faulting or homogeneous thickening as available shortening modes and results in irregular wrinkling of the unbreakable layer. We discuss geodynamic implications of our laboratory experiments and advocate studies of large scale buckling of the lithosphere as a relevant shortening mode.