Scattering of elastic waves by a fracture zone containing randomly distributed cracks

We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ ^–1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ ^–1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ ^–1 is proportional tok ^–1 independently of model parameters and the wave modes. If the seismological observation thatQ ^–1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.     

弹性波的三维有限元模拟

本文讨论了弹性波瞬态传播问题的三维有限元计算方法及当前存在的实际困难.针对要求计算机内存大和计算时间长的问题,采取了改进措施.由于采用了集中质量矩阵和修正的中心差分时间积分显格式相结合的方法,可以使计算机内存和计算时间大为减少;由于采用结点定位法,最适合用于目前发展的并行计算机系统,可使计算速度大大增快;还采用了有效激发震源法,有效激发区是随时间步进的增加而逐步增大,这不仅能节省计算时间,而且使波场的传播过程一目了然,本文计算了由两种介质组成的三维楔形问题,得到若干典型剖面的瞬时波场图及随时间变化的合成地震图.     

Computation of Large Anisotropic Seismic Heterogeneities (CLASH)

A general tomographic technique is designed in order (i) to operate in anisotropic media; (ii) to account for the uneven seismic sampling and (iii) to handle massive data sets in a reasonable computing time. One modus operandi to compute a 3-D body wave velocity model relies on surface wave phase velocity measurements. An intermediate step, shared by other approaches, consists in translating, for each period of a given mode branch, the phase velocities integrated along ray paths into local velocity perturbations. To this end, we develop a method, which accounts for the azimuthal anisotropy in its comprehensive form. The weakly non-linear forward problem allows to use a conjugate gradient optimization. The Earth's surface is regularly discretized and the partial derivatives are assigned to the individual grid points. Possible lack of lateral resolution, due to the inescapable uneven ray path coverage, is taken into account through the a priori covariances on parameters with laterally variable correlation lengths. This method allows to efficiently separate the 2ψ and the 4ψ anisotropic effects from the isotropic perturbations. Fundamental mode and overtone phase velocity maps, derived with real Rayleigh wave data sets, are presented and compared with previous maps. The isotropic models concur well with the results of Trampert & Woodhouse. Large 4ψ heterogeneities are located in the tectonically active regions and over the continental lithospheres such as North America, Antarctica or Australia. At various periods, a significant 4ψ signature is correlated with the Hawaii hotspot track. Finally, concurring with the conclusions of Trampert & Woodhouse, our phase velocity maps show that Rayleigh wave data sets do need both 2ψ and 4ψ anisotropic terms.     

Calculated Phase Relations in the System Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O with Applications to UHP Eclogites and Whiteschists

Pressure–temperature grids in the system Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O and its subsystems have been calculatedin the range 15–45 kbar and 550–900°C, usingan internally consistent thermodynamic dataset and new thermodynamicmodels for amphibole, white mica, and clinopyroxene, with thesoftware THERMOCALC. Minerals considered for the grids includegarnet, omphacite, diopside, jadeite, hornblende, actinolite,glaucophane, zoisite, lawsonite, kyanite, coesite, quartz, talc,muscovite, paragonite, biotite, chlorite, and plagioclase. Compatibilitydiagrams are used to illustrate the phase relationships in thegrids. Coesite-bearing eclogites and a whiteschist from Chinaare used to demonstrate the ability of pseudosections to modelphase relationships in natural ultrahigh-pressure metamorphicrocks. Under water-saturated conditions, chlorite-bearing assemblagesin Mg- and Al-rich eclogites are stable at lower temperaturesthan in Fe-rich eclogites. The relative temperature stabilityof the three amphiboles is hornblende > actinolite > glaucophane(amphibole names used sensu lato). Talc-bearing assemblagesare stable only at low temperature and high pressure in Mg-and Al-rich eclogites. For most eclogite compositions, talccoexists with lawsonite, but not zoisite, in the stability fieldof coesite. Water content contouring of pressure–temperaturepseudosections, along with appropriate geotherms, provides newconstraints concerning dehydration of such rocks in subductingslabs. Chlorite and lawsonite are two important H₂O-carriersin subducting slabs. Depending on bulk composition and pressure–temperaturepath, amphibole may or may not be a major H₂O-carrier to depth.In most cases, dehydration to make ultrahigh-pressure eclogitestakes place gradually, with H₂O content controlled by divariantor higher variance assemblages. Therefore, fluid fluxes in subductionzones are likely to be continuous, with the rate of dehydrationchanging with changing pressure and temperature. Further, eclogitesof different bulk compositions dehydrate differently. Dehydrationof Fe-rich eclogite is nearly complete at relatively shallowdepth, whereas Mg- and Al-rich eclogites dehydrate continuouslydown to greater depth. KEY WORDS: dehydration; eclogites; phase relations; THERMOCALC; UHP metamorphism; whiteschists     

Calculated Phase Relations in the System NCKFMASH (Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O) for High-Pressure Metapelites

Petrogenetic grids in the system NCKFMASH (Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O)and the subsystems NCKMASH and NCKFASH calculated with the softwareTHERMOCALC 3.1 are presented for the P–T range 7–30kbar and 450–680°C, for assemblages involving garnet,chloritoid, biotite, carpholite, talc, chlorite, kyanite, staurolite,paragonite, glaucophane, jadeite, omphacite, diopsidic pyroxene,plagioclase, zoisite and lawsonite, with phengite, quartz/coesiteand H₂O in excess. These grids, together with calculated compatibilitydiagrams and P–T and T–X_Ca and P–X_Ca pseudosectionsfor different bulk-rock compositions, show that incorporationof Ca into the NKFMASH system leads to many of the NKFMASH invariantequilibria moving to lower pressure and/or lower temperature,which results, in most cases, in the stability of jadeite andgarnet being enlarged, but in the reduction of stability ofglaucophane, plagioclase and AFM phases. The effect of Ca onthe stability of paragonite is dependent on mineral assemblageat different P–T conditions. The calculated NCKFMASH diagramsare powerful in delineating the phase equilibria and P–Tconditions of natural pelitic assemblages. Moreover, contoursof the calculated phengite Si isopleths in P–T and P–X_Capseudosections confirm that phengite barometry in NCKFMASH isstrongly dependent on mineral assemblage. KEY WORDS: phase relations; metapelites; NCKFMASH; THERMOCALC; phengite geobarometry     

地震信号的相位恢复及误差分析

常见的几种地震子波有:零相位子波、最小相位子波、最大相位子波和混合相位子波。以不同类型的信号为激发子波,对不同地层模型合成地震道。仅用原始合成地震道记录的振幅谱来恢复原始记录,讨论不同方法下,由于激发子波的不同,对比分析原始记录与恢复记录的差异,及其恢复效果。     

微量相X射线衍射定量分析的一种简便方法

阐述了关于微量相X射线衍射定量分析的一种简便方法———近似线性关系法,它适用于二相体系(或基体吸收系数基本恒定的多相体系)材料中微量相的定量分析。该方法不需要在待测样品中加入参考物相,分析时仅需对一条衍射线进行测定,因而分析时间很短,其测定结果与实际含量的相对误差为-10.2%～ 21.4%,与外标法和内标法的测量结果的精度相当。     

三种类型烃-烃不混溶包裹体组合的特征和热力学条件的计算

在自然界广泛分布着烃-烃不混溶体系中捕获的流体包裹体,由于这些包裹体具有复杂的组成和相态,因此不混溶包裹体组合的判别和热力学参数的计算常常难以进行。根据烃-烃不混溶体系中两个端员组分流体包裹体室温下的相态特征和在温度-压力平面图上等容线交点显示的位置,划分成三种类型流体包裹体组合,本介绍了三种类型流体包裹体组合特征,叙述了不混溶烃-烃包裹体组合的测定和判别方法,并且阐述均一化包裹体相态方程和气-液平衡常数原理和方法与此同时列举了自然界简单的三种类型不混溶烃-烃包裹体组合的测定、判别和计算的几个实例,利用相态方程和气-液平衡常数,不但精确地计算出包裹体均一压力,并且精确地计算出流体密度和体积等热力学参数。最后,利用均一成气相和液相的两种包裹体在 p-T 平面图上等容线交点同样计算出流体包裹体组合的捕获温度和压力。