On the tidal variation of the geopotential

In this paper analytical expressions are derived for the temporal variations ofJ ₂ andJ ₂₂ due to the tides of the solid Earth, taking into account only the deformation of the mantle, and employing a procedure already used by the authors in their Hamiltonian theory of the Earth's rotation, which obtain the necessary parameters in a direct way by integration of those provided by a selected model of Earth interior.Numerical tables giving the periodic variation of coefficients are given, as well as a new prediction for UT1. For J ₂ and J ₂₂ the amplitudes reach such a magnitude that both two variations should not be ignored in studies involving the analysis of highly precise satellite tracking data. Moreover, the possibility of improving our knowledge of the value of those harmonic coefficients in only a more exact digit appears as to be strongly dependent on the limitations in the theoretical modeling of the variations of the inertia tensor due to solid tides.     

On some problems of seismic crustal phase

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井下记录的PP和SS震相

本文在系统分析静海台井下地震记录图的基础上,发现并解决了具有一定实际和理论意义的两个问题:其一是证明了最初误认为是干扰的“双脉冲”图形实际上均是微地震。从而指出研究静海周围地区的地震活动性应考虑微震活动问题。其二确认静海周围地区微震波形的4个主要震相是P、PP、S和SS,并对地面反射波PP和SS能够观测到的条件作了初步分析,其结果进一步说明井下地震记录较之地面记录更为“逼真”,复杂和丰富。     

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.     

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。