Absolute S-velocity estimation from receiver functions
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Ocean Surface Current Analysis (OSCAR) Third Degree Resolution User’s HandbookCopyright 2009 California Institute of Technology.All rights reserved.TABLE OF CONTENTSDATA PRODUCT ABSTRACT (1)1. INVESTIGATOR’S NAME AND CREDIT (1)2. DATA DESCRIPTION (1)2.1 FILENAMING CONVENTION (1)2.2 FILE FORMAT (1)2.3 TEMPORAL COVERAGE AND RESOLUTION (1)2.4 SPATIOAL COVEAGE AND RESOLUTION (2)2.5 DATA PARAMETERS AND FORMAT (2)2.6 SAMPLE DATA RECORD (3)2.7 SAMPLE GLOBAL ATTRIBUTES (4)3. AVAILABLE READ SOFTWARE (4)4. PROCESSING METHODS (4)5. CALIBRATION INFORMATION (5)6. SOURCES OF ERROR (5)7. KNOWN PROBLEMS (5)8. DIFFERENCES BETWEEN 1/3° AND 1° OSCAR (6)9. REFERENCES (6)10. ACRONYMS (7)11. CONTACT INFORMATION (8)12. DOCUMENT INFORMATION (8)13. ACKNOWLEDGEMENTS (8)DATA PRODUCT ABSTRACTThis product contains global near-surface current estimates, derived using quasi-linear and steady flow momentum equations. The horizontal velocity is directly estimated from sea surface height, surface vector wind and sea surface temperature, these data were collected from various satellites and in situ instruments (see processing methods). The model formulation combines geostrophic, Ekman and Stommel shear dynamics, and a complementary term from the surface buoyancy gradient [1].The ocean surface velocity files are in netCDF format which contain zonal (u) and meridional (v) velocitiesINVESTIGATOR’S NAME AND CREDITThe OSCAR product was developed by Gary Lagerloef, Fabrice Bonjean andKathleen Dohan from Earth and Space Research (ESR).If you use OSCAR data in publications, please include the following citation:The OSCAR data were obtained from JPL Physical Oceanography DAAC anddeveloped by ESR.Also, ESR would appreciate receiving a preprint and/or reprint of publicationsutilizing these data for inclusion in the OSCAR bibliography. These publications should be sent to:OSCAR Project OfficeEarth and Space Research2101 Fourth Avenue, Suite 1310Seattle, WA 98121DATA DESCRIPTIONFILENAMING CONVENTIONThe file names have a naming convention of oscar_velNNNN.ncoscar – name of productvel – velocity product calculated from altimetry, scatterometer winds, and sst.NNNN – year of the data or a single day’s worth of data with NNNN thenumber of days since October 5, 1992FILE FORMATThe data are in NetCDF files and have a maximum size of 480 MB whenzipped.TEMPORAL COVERAGE AND RESOLUTIONOne file consists of an entire year’s worth of data, except for the present year.The time resolution within each file is 1/72 year ≈ 5 days, or half a Jason-1 or TOPEX/Poseidon cycle. For the present year, data are added as it comes in. SPATIAL COVERAGE AND RESOLUTIONThe data covers -80° to 80° latitude and 0° to 360° longitude. However thedata represents longitude as 20° to 420°, i.e. the entire Earth is representedin the data as 20° to 380°, and the data repeats itself from 380.33° to 420°.Thus 390° is actually 30°. This range for longitude was chosen so that themajor ocean basins would not be broken, but continuous.The resolution is 1/3° in each direction.DATA PARAMETERS AND FORMATLatitudeDefinition: LatitudeDimension: 481Unit: degrees NorthElement type: doubleLongitudeDefinition: LongitudeDimension: 1201Unit: degrees EastElement type: doubleTimeDefinition: TimeDimension: 72Unit: days since 1992-10-05 00:00:00Element type: integerYearDefinition: Time in yearsDimension: 72Unit: time in fractional yearElement type: floatDepthDefinition: DepthDimension: 1Unit: metersElement type: floatUmDefinition: Ocean surface Zonal currents maximum maskDimension: time, depth, latitude, longitudeUnit: m/sElement type: doubleVmDefinition: Ocean surface Meridional currents maximum maskDimension: time, depth, latitude, longitudeUnit: m/sElement type: doubleUDefinition: Zonal VelocityDimension: time, depth, latitude, longitudeUnit: m/sElement type: doubleMissing value: nanVDefinition: Meridional VelocityDimension: time, depth, latitude, longitudeUnit: m/sElement type: doubleMissing value: nanSAMPLE DATA RECORDThese data are from oscar_vel2008.nclatitude = 80, 79.6666666666667, 79.3333333333333, 79,78.6666666666667longitude = 20, 20.3333333333333, 20.6666666666667, 21,21.3333333333333time = 5566, 5571, 5576, 5581, 5586year = 2008, 2008.014, 2008.027, 2008.041, 2008.055depth = 15um = nan, nan, nan, nan, nanvm = nan, nan, nan, nan, nanu = nan, nan, nan, nan, nanv = nan, nan, nan, nan, nanSAMPLE GLOBAL ATTRIBUTESThese global attributes come from oscar_vel2008.nc.:VARIABLE = "Ocean Surface Currents" ;:DATATYPE = "1/72 YEAR Interval" ;:DATASUBTYPE = "unfiltered" ;:GEORANGE = "20 to 420 -80 to 80" ;:PERIOD = "Jan.01,2008 to Dec.26,2008" ;:year = "2008" ;:description = "OSCAR Third Degree Sea Surface Velocity" ;:CREATION_DATE = "18:41 24-Mar-2009" ;:version = 2009.f ;:source="GaryLagerloef,ESR(*************)andKathleenDohan,ESR (**************)";:contact="KathleenDohan(**************)orJohnT.Gunn(************)";:company = "Earth & Space Research, Seattle, WA" ;:reference = "Bonjean F. and G.S.E. Lagerloef, 2002 ,Diagnostic model and analysis of the surface currents in the tropical Pacific ocean, J. Phys.Oceanogr., 32, 2,938-2,954" ;AVAILABLE READ SOFTWARERead software are available from PO.DAAC’s anonymous ftp site for IDL and Matlab at /pub/ocean_currents/OSCAR/software.Unidata also has software available to read NetCDF files with the ncdump command at /downloads/netcdf/index.jsp PROCESSING METHODSThe near-surface velocity is directly derived from sea surface height (ssh),wind stress (τ) and sea surface temperature (sst). It is the sum of the geostrophic, Ekman-Stommel and thermal wind currents, whereg – gravity accelerationζ - sea surface displacementh – depthθ - buoyancy forceτ - wind stressA – eddy viscosityU’ – vertical shear.The total velocity is the vertical average over a surface layer thickness of 30 m [2].The data used to calculate the velocity are:- TOPEX/POSEIDON, Jason-1, Jason-2, ERS1-2, GFO and ENVISAT ssh anomalies, merged into a gridded product (AVISO). An absolute ssh product is obtained by adding to the anomalies a mean dynamic topography which is a combined product recovering 7 years(1993-1999) based on GRACE mission, altimetry and in situ data (hydrologic and drifters data)[2], [3]- wind velocity from SSM/I [4] October 1992 to July 1999 and QScat [5] August 1999 to present.- sst from weekly Reynolds Smith O.I.v2 [6].The altimeter data are initially gridded on a “Mercator” grid (variable, from1/3°x1/3° at the equator to higher latitude resolution poleward), and horizontal gradients are calculated onto a 1/3°x1/3° grid with a temporal sampling of ≈5 days. Winds and sst are on the same temporal and 1/3°x1/3° grid as described above.For more detailed information on the processing methods refer to Bonjean and Lagerloef 2002 [1] and /methodology.html.CALIBRATION INFORMATIONValidation information on this product can be found in Johnson et al. 2007 [7]. Note: since the Johnson et al. (2007) article was published, a new OSCAR dataset corresponding to the one described on this web page has been released with significant improvements, notably the implementation of the new AVISO merged altimetry product (2006) into the OSCAR processing. Updated validation results can be found at /~bonjean/oscar/global_validation/ .SOURCES OF ERRORThis section only concerns the source datasets used to estimate surface velocity. High winds and rain can cause anomalous readings in SSM/I and QScat. Errors in the satellite altimetry product can come from residual orbit errors and long wavelength errors. All gridded products are also subject to formal mapping errors. KNOWN PROBLEMSThese near-surface currents are estimated through a simplified diagnostic model of the surface circulation. Notably, local acceleration and non-linearities are not represented. As shown in [7], the present velocity field is best used for description of large scale and low frequency variations of surface flow (T>=20 days, L>=5°longitude). ESR currently provides the scientific community with an unfiltered velocity field (no post-processing), on a 1/3° X 1/3° grid with a 5 day resolution. Smoothing may have been induced only by the processing of the source data, that is ssh [2], W [4,5] and sst [6]; also some smoothing inherent to the method itself was caused by calculation of spatial gradient (for geostrophic and thermal-wind currents only). When comparing OSCAR to the drifter data, smoothing can also just be implied by the interpolation from the 1/3° X 1/3° per 5-day grid to the drifter locations and times. This sort of indirect smoothing effect is lessened in the 1/3°OSCAR from the 1° OSCAR product. ESR encourages researchers to make comparisons between this velocity field and in-situ observations on meso to short scales. As this surface current estimation is a work in progress, we are interested in any result involving the present velocity field, and we remain available for any help and discussion.DIFFERENCES BETWEEN 1/3° AND 1° OSCARSurface currents are extended closer to the coasts in the 1/3° than 1° OSCAR. The Maximum Mask velocity (Um, Vm) is the maximum possible extent of the data per day. The data, given in U and V, are confined by the spatial extent of all satellite data on each day. The Maximum Mask velocity uses the geostrophic component for velocity at all points, along with the buoyancy-driven and wind-driven components, where they are available. This is done since sea surface height satellite data extends closer to the coast than wind and temperature at some locations, and the geostrophic component is an order of magnitude larger than the other components outside of the equator. This field is intended for testing purposes only.The model for equatorial velocities has been changed. The equatorial solution is now used within +/- 5 degrees of the equator. The turbulence parameterization is modified to blend from equatorial empirical values to global empirical values.The method for calculating gradients has also been changed to suit the higher resolution data, and produces much better comparisons with in situ data.A filtered velocity is not available in the 1/3° product since the 1° OSCAR filtered velocity is still provided.Velocities over 3m/s are removed without any further processing.REFERENCES1. Bonjean, F., and G. S. E. Lagerloef, 2002. Diagnostic model and analysis ofthe surface currents in the tropical Pacific Ocean. J. Phys. Oceanogr., vol.32, pg. 2938-2954./documents/bonjean/bl2002/bl2002.pdf2. SALP-MU-P-EA-21065-CLS, Edition 1.9, June 2008 Ssalto/Duacs UserHandbook : (M)SLA and (M)ADT Near-Real Time and Delayed TimeProducts(/fileadmin/documents/data/tools/hdbk_duacs.pdf )3. Rio, M. H. and F. Hernandez, 2004. A mean dynamic topography computedover the world ocean from altimetry, in situ measurements, and a geoidmodel. J. Geophys. Res., 109, C12032, doi:10.1029/2003JC002226.4. Atlas, R., R. Hoffman, S. Bloom, J. Jusem, and J. Ardizzone, 1996. A multi-year global surface wind velocity dataset using SSM/I wind observations.Bull. Amer. Meteor. Soc., vol. 77, pg. 869-882.5. Pegion, P. J., M. A. Bourassa, D. M. Legler, and J. J. O'Brien, 2000:Objectively-derived daily "winds" from satellite scatterometer data. Mon.Wea. Rev., 128, 3150-3168.(/scatterometry/Qscat/gcv_glob_L2B_1x1.html ) 6.Reynolds, R.W., N.A. Rayner, T.M. Smith, D.C. Stokes, and W. Wang.2002. An Improved In Situ and Satellite SST Analysis for Climate. J. Clim.vol. 15, pg. 1609-1625.(/research/cmb/sst_analysis/)7. Johnson, E. S., F. Bonjean, G. S. E. Lagerloef, and J. T. Gunn, 2007.Validation and error analysis of OSCAR sea surface currents. J. Atm.Ocean. Tech., vol. 24, pg. 688-701.ACRONYMSAVISO Archiving, Validation and Interpretation of SatelliteOceanographic dataCHAMP Challenging Mini-Satellite Payload for Geophysical Researchand ApplicationDh Dynamic heightESR Earth and Space ResearchGDR Geophysical Data RecordGRACE Gravity Recovery and Climate ExperimentJPL Jet Propulsion LaboratoryNetCDF Network Common Data FormOSCAR Ocean Surface Current AnalysisPO.DAAC Physical Oceanography Distributed Active Archive Center QScat QuikSCAT- Quick ScatterometerSSH Sea Surface HeightSSM/I Special Sensor Microwave ImagerSST Sea Surface TemperatureWOA World Ocean AtlasCONTACT INFORMATIONQuestions or comments about this data product should be directed via email to the PhysicalOceanographyDAAC:*****************.DOCUMENT INFORMATIONJessica Hausman, PO.DAACFabrice Bonjean, ESRKathleen Dohan, ESRMay 2009ACKNOWLEDMENTSThe research described in this handbook was carried out at Earth Space Research and written at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration and the National Oceanic and Atmospheric Administration.。
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line磁感应线magneticmaterial磁性材料magnetic needle磁针magnetic pole磁极magnetics 磁学magnetism 磁学magneti zation 磁化magnet 磁体magnifi cation 放大率magnifi er 放大镜,放大器manom eter 流体压强计mass质量massdefect质量亏损mass-energyequation 质能方程matter物质matterwave物质波Maxwell'sequations 麦克斯韦方程组meanspeed平均速率meanvelocity平均速度measurement测量mechanicalenergy机械能mechanicalmotion机械运动mechanicalvibration 机械振动mechanics 力学medium介质meltingfusion熔化melting point 熔点metre rule 米尺microde tector 灵敏电流计microm eter caliper 螺旋测微器microsc ope 显微镜microscopicparticle微观粒子mirrorreflection 镜面反射mirror镜mixedunitsystem混合单位制modernphysics现代物理学molarvolume摩尔体积molecularspectrum 分子光谱molecularstructure 分子结构momentof force力矩momentum ofelectromagnetic field电磁场的动量momentum 动量motor电动机multimeter 多用[电]表musical quality 音色N pole 北极natural frequen cy 固有频率natural light 自然光negativ e charge负电荷negativecrystal负晶体negative ion 负离子negative plate负极板network网络neutralization中和neutron中子newton牛顿(力的单位)Newtonfirst law牛顿第一定律Newtonsecondlaw 牛顿第二定律Newtonthirdlaw 牛顿第三定律nonequilibriumstate 非平衡态northpole 北极nucleusforce 核力nucleusofcondensation 凝结核object 物object distance 物距object height 物高objectiv e 物镜observa tion 观察Oersted' s experim ent 奥斯特实验ohm欧姆Ohmlaw 欧姆定律ohmmeter 欧姆计Ohm'slaw 欧姆定律opencircuit开路opticalbench光具座opticalcentreof lens透镜光心opticalfiber 光导纤维opticalglass 光学玻璃opticalinstrument 光学仪器opticallever 光杠杆opticalpathdifference 光程差opticalpath 光程(路)opticallydensermedium光密介质opticallythinnermedium 光疏介质optics 光学orbit 轨道order 有序oscillog raph 示波器output 输出overwei ght 超重parallelconnection ofcondensers 电容器的并联parallelogramrule 平行四边形定律parallel-resonancecircuit并联谐振电路parameter 参量particle质点,粒子Pascallaw 帕斯卡定律path路程peak 峰值pendulum 摆penumbra 半影perfectconductor 理想导体perfectelasticcollision 完全弹性碰撞perfectinelasticcollision 完全非弹性碰撞periodic ity 周期性period 周期perisco pe 潜望镜perman ent magnet 永磁体permitti vity of vacuum 真空介电常数permittivity 电容率phase位相phenomenon 现象photocurrent 光电流photoelectriccell 光电管photoelectriceffect光电效应photoelectron光电子photography 照相术photon光子physicalbalance物理天平physicalquantity物理量physics物理学piezometer 压强计pitch 音调Planckconstant 普朗克常量plasma等离子体pointcharge 点电荷polariza tion 偏振polarize d light 偏振光polycry stal 多晶体poor conduct or 不良导体positive charge 正电荷positivecrystal正晶体positiveion 正离子positiveplate 正极板positron正电子potential energy势能potentiometer电位差计power功率pressure 压强,压力primarycoil 原线圈principle ofconstancy oflightvelocity光速不变原理prism棱镜projectile 抛体projectilemotion抛体运动projector 投影仪proton质子pulley滑轮pulley block 滑轮组quantity of heat 热量quantiz ation 量子化quantu m 量子quantu m mechan ics 量子力学quantu mnumber量子数radar 雷达radioactivesource放射源radiusofgyration 回旋半径randommotion无规则运动range量程ratedvoltage额定电压reactingforce 反作用力realimage实像realobject实物reasoning 推理recoil反冲rectilinearmotion直线运动reference frame参考系,坐标系referencesystem参考系reflected angle反射角reflecte d ray 反射线reflecti on coeffici ent 反射系数reflecti on law 反射定律reflecti vity 反射率refracte d angle 折射角refracted ray 折射线refraction law折射定律refractioncoefficient 折射系数refractiveindex折射率relativeacceleration 相对加速度relativeerror 相对误差relativemotion相对运动relativevelocity相对速度relativity 相对论resistance 电阻resistance box电阻箱resistivity 电阻率resistor电阻[器]resolution offorce 力的分解resolution of velocity 速度的分解resonan ce 共振,共鸣resonan t frequen cy 共振频率resultan t force 合力resultan t velocity合速度reversibility ofopticalpath 光路可逆性reversibleprocess可逆过程rheostat变阻器right-handscrewrule 右手螺旋定则rocker火箭rotatingmagnetic field旋转磁场rotation自转,转动Rutherfordscattering 卢瑟福散射Rutherford[α-particlescattering]experiment 卢瑟福[α散射]实验Spole 南极saturation 饱和scalar 标量scalar field 标量场scanner 扫描器second cosmic velocity 第二宇宙速度selectiv e absorpti on 选择吸收self-inducedelectromotiveforce 自感电动势self-inductance 自感self-inductionphenomenon 自感系数semiconductor半导体semi-transparent film半透膜sensitivegalvanometer灵敏电流计sensitivity 灵敏度sensitometer感光计sensor传感器seriesconnection ofcondensers 电容器的串联series-resonancecircuit串联谐振电路shortcircuit短路shortsight 近视shunt resistor 分流电阻signific ant figure 有效数字simple harmon ic motion (SHM) 简谐运动simpleharmonic wave简谐波simplependulum 单摆singlecrystal(monocrystal)单晶体singleslitdiffraction 单缝衍射sinusoidalalternatingcurrent简谐交流电sinusoidalcurrent正弦式电流slidingfriction滑动摩擦slit狭缝solarcell 太阳能电池solenoid 螺线管solidification 凝固solidifyingpoint 凝固点solid 固体solution溶液solvatio n 溶解sonar 声纳sound source 声源sound velocity 声速sound wave 声波sound 声[音]source 电源southpole 南极space空间sparkdischarge 火花放电specialrelativity 狭义相对论specificheatcapacity 比热容spectacles 眼镜spectralanalysis光谱分析spectralline[光]谱线spectrograph摄谱仪spectrography摄谱学spectroscopy 光谱学spectrum 光谱speed速率sphericalmirror球面镜spontaneousradiation 自发辐射springbalance 弹簧秤stability 稳定性stabiliz ed current supply 稳流电源stabiliz ed voltage supply 稳压电源standar d atmosp hericpressure 标准大气压standard cell标准电池standing wave驻波staticfriction静摩擦stationary state定态steadycurrent恒定电流steadycurrentsource恒流源steadyvoltagesource恒压源steampoint 汽点stiffness劲度[系数]stimulatedradiation 受激辐射stopwatch停表sublimation 升华superconductivity 超导[电]性superco nductor 超导体superpo sition principl e of electric field 电场强度叠加原理superpo sition theorem 叠加定律supersat uration过度饱和supersonicspeed超声速supersonicwave超声波supplytransformer 电源变压器surfaceresistance 表面电阻switch开关systemofconcurrentforces共点力系systemofparticles 质点系systemof units单位制systematic error系统误差telescope 望远镜temperature 温度tension张力the lawofgravity万有引力定律theorem 原理theorem of kinetic energy 动能定理theorem of moment um 动量定理theoreti cal physics 理论物理学theory理论thermalcapacity 热容[量]thermalequilibrium 热平衡thermalmotion热运动thermaltransmission 传热thermodynamic scale[oftemperature]热力学温标thermodynamictemperature 热力学温度thermometer温度计thermometricscale 温标thermonuclearreaction热核反应thicklens 厚透镜thinlens 薄透镜thirdcosmicvelocity 第三宇宙速度three-phase alternati ng current 三相[交变]电流time时间timer 定时器,计时器torsionbalance扭秤totalreflection 全反射trajectory 轨道transformer 变压器transistor 晶体管transition 跃迁translation 平移transmissionline 传输线transmissivity透射率transverse wave横波triboelectrification 摩擦起电triode三极管trough波谷tuningfork 音叉turbulent flow湍流ultrasoundwave超声波ultraviolet ray紫外线umbra本影undulatory propert y 波动性uniform dielectri c 均匀电介质uniform motion 匀速运动unit 单位unit system 单位制univers al constant 普适常量universalgravitation 万有引力universal meter多用[电]表vacuumtube 真空管vacuum真空value ofamplitude 幅值vaporization 汽化variable变量vector矢量velocityof light光速velocity速度verification 验证vernier游标verniercaliper游标卡尺vibration 振动viewingangle视角viewingfield 视场virtualimage 虚像virtual object 虚物virtual value 有效值visibilit y 可见度visible light 可见光voltage 电压voltage division circuit分压电路voltaiccell 伏打电池voltmeter 伏特计voltmeter-ammetermethod伏安法volt 伏特volume体积vortexelectricfield 涡旋电场watt 瓦特waveequation 波动方程wavetheory波动说wavelength 波长wave-particledualism波粒二象性wave波weight重量weightlessness失重whitelight 白光work功workfunctio n 逸出功X-ray X 射线Young experim ent 杨氏实验zero line 零线α -decay α衰变α -particle α粒子α -ray α射线β -decay β衰变β -ray β射线γ -decay γ衰变γ -ray γ射线。
Robust Control and Estimation Robust control and estimation are two critical aspects of control engineering that have been extensively studied over the years. These two concepts areessential in ensuring that a system can operate optimally in the presence of uncertainties and disturbances. In this response, we will explore the concept of robust control and estimation from multiple perspectives, including its importance, key principles, and applications. From a general perspective, robust control and estimation are essential in ensuring that a system can operate optimally in the presence of uncertainties and disturbances. In many engineering applications, itis often challenging to predict the exact behavior of a system due to external factors such as noise, disturbances, and other uncertainties. As such, robust control and estimation techniques are used to design control systems that can operate efficiently under these conditions. By incorporating robust control and estimation principles into a system's design, engineers can ensure that the system can maintain its performance and stability even when subjected to disturbances and uncertainties. One of the key principles of robust control is the use of feedback control. Feedback control is a control technique that uses measurements of a system's output to adjust its input in real-time. By using feedback control, engineers can design control systems that are more robust to disturbances and uncertainties. For example, in a temperature control system, feedback control can be used to adjust the heater's output based on the temperature measurements taken from the system. This allows the system to maintain its temperature setpoint even when subjected to external disturbances such as changes in ambient temperature. Another important principle of robust control is the use of model-based control. Model-based control involves using a mathematical model of the system being controlled to design a control system that can operate optimally under different conditions. By using a model-based approach, engineers can design control systems that are more robust to uncertainties and disturbances. For example, in a robotic arm control system, a mathematical model of the arm's dynamics can be used to design a control system that can maintain the arm's position and orientation even when subjected to external disturbances. Robust estimation is another critical aspect of control engineering that is closely related to robust control. Robustestimation involves using statistical techniques to estimate a system's state or parameters in the presence of uncertainties and disturbances. By using robust estimation techniques, engineers can ensure that a system can accurately estimate its state or parameters even when subjected to external disturbances. For example, in a navigation system, robust estimation techniques can be used to estimate the position and velocity of a vehicle even when subjected to external disturbances such as wind and road conditions. The applications of robust control and estimation are diverse, ranging from aerospace and automotive systems toindustrial automation and robotics. In aerospace applications, robust control and estimation are used to design control systems for aircraft that can maintain their stability and performance even when subjected to external disturbances such as turbulence and wind gusts. In automotive applications, robust control and estimation are used to design control systems for vehicles that can maintain their stability and performance even when subjected to external disturbances such as road conditions and wind gusts. In industrial automation and robotics, robust control and estimation are used to design control systems for machines and robots that can operate optimally under different conditions. For example, in a manufacturing plant, robust control and estimation can be used to design control systems for machines that can maintain their performance and stability even when subjected to external disturbances such as changes in material properties and environmental conditions. In robotics, robust control and estimation can be used to design control systems for robots that can maintain their position and orientation even when subjected to external disturbances such as collisions and changes in payload. In conclusion, robust control and estimation are two critical aspects of control engineering that have been extensively studied over the years. By incorporating robust control and estimation principles into a system's design, engineers can ensure that the system can maintain its performance and stability even when subjected to disturbances and uncertainties. The principles of feedback control and model-based control are essential in designing robust control systems, while robust estimation techniques are essential in accurately estimating a system's state or parameters in the presence of uncertainties and disturbances.The applications of robust control and estimation are diverse, ranging from aerospace and automotive systems to industrial automation and robotics.。
Static ['stætɪk]静力Dynamic [daɪ'næmɪk]动力Explicit[ɪk'splɪsɪt]∙显示adj. 明确的;清楚的;直率的;详述的∙Time period ~ ['pɪrɪəd]n. 周期,期间;时期;月经;课时;(语法学)句点,句号时间长度Nlgeom 几何非线性Include adiabatic heating effects∙~(adiabatic[,ædɪə'bætɪk]adj. [物] 绝热的;隔热的)['hitɪŋ]~包括绝热效应Incrementation∙(increment['ɪŋkrɪm(ə)nt]n. [数] 增量;增加;增额;盈余)增量Automatic['ɔtə'mætɪk]自动Stable increment estimator∙['steɪb(ə)l]稳定~['estɪmeɪtə]n. [统计] 估计量;评价者稳定增量步数Unlimited[ʌn'lɪmɪtɪd]无限制的Use scaled mass and “throughoutstep”definitions∙(throughout[θrʊ'aʊt]整个,adv. 自始至终,到处;全部;prep. 贯穿,遍及∙definition [defɪ'nɪʃ(ə)n]n. 定义;[物] 清晰度;解说) 使用前一分析步的缩放系数和“整个分析步”定义Contact['kɑntækt]接触Tangential behavior[tæn'dʒenʃ(ə)l][bɪ'hevjɚ]切向行为Normal behavior['nɔrml]~法向行为Frictionless[f'rɪkʃnles]∙(friction['frɪkʃən]n. 摩擦,[力] 摩擦力)无摩擦∙Penalty['pen(ə)ltɪ]n. 罚款,罚金;处罚罚Friction formulation∙(formulation[fɔːmjʊ'leɪʃn]n. 构想,规划;公式化;简洁陈述)摩擦公式Directionality[daɪrɛkʃə'næləti]方向性Isotropic[,aɪsə'trɑpɪk]各向同性Anisotropic[,ænaɪsə'trɑpɪk]各向异性Use slip-rate-dependent data∙(rate[reɪt]n. 比率,率;速度;价格;等级∙Dependent[dɪ'pɛndənt]adj. 依靠的;从属的;取决于…的)使用基于滑动率的数据Use contact-pressure-dependent data 使用依赖接触压力的数据摩擦系数Friction coeff∙(coeff[kəuf]n. 多项式系数)Shear stress[ʃɪə]~剪应力压力过盈Pressure-overclosure ~[əʊvək'ləʊʒər]∙(closure ['kləʊʒə]n. 关闭;终止,结束∙vt. 使终止)Constraint enforcement method约束执行方法∙(enforcement [ɪn'forsmənt]n. 执行,实施;强制∙Method ['meθəd]n. 方法;条理;类函数∙adj. 使用体验派表演方法的)Allow separation after contact允许接触后分离∙(Allow[ə'laʊ]vt. 允许;给予;认可vi. 容许;考虑∙Separation [sepə'reɪʃ(ə)n]n. 分离,分开;间隔,距离;[法] 分居;缺口)Coupling['kʌplɪŋ]耦合Contact domain接触领域∙(domain [də(ʊ)'meɪn]n. 领域;域名;产业;地产)排除的表面对Excluded surface pairs∙(Exclude [ɪk'skluːd; ek-]vt. 排除;排斥;拒绝接纳;逐出)Exterior[ɪk'stɪərɪə; ek-]∙adj. 外部的;表面的;外在的∙n. 外部;表面;外型;外貌Segments['segm(ə)nt]∙vi. 分割n. 段;部分vt. 分割属性指派Attribute assignment∙(Attribute [ə'trɪbjut]n. 属性;特质∙vt. 归属;把…归于∙assignment[ə'saɪnmənt]n. 分配;任务;作业;功课)力学约束公式化Machanical constraint formulation(Machanical[məˈkænɪkl]adj. 机械的,机械学的; 呆板的; 体力的; 手工操作的;Kinematic contact method运动摩擦法∙(Kinematic[,kɪnə'mætɪk]adj. [力] 运动学上的,[力] 运动学的)有限滑移Finite sliding∙(Finite ['faɪnaɪt]adj. 有限的;限定的n. 有限之物∙Sliding ['slaɪdɪŋ]∙Clearance['klɪrəns]n. 清除;空隙过盈量∙Procedure[prə'sidʒɚ]n. 程序,手续;步骤步骤∙Frequency['frikwənsi]n. 频率;频繁频率∙Interval['ɪntəv(ə)l]n. 间隔;间距;幕间休息间隔场输出:S, Stress components and invariantsS,应力分量和不便量∙(component [kəm'ponənt]adj. 组成的,构成的∙n. 成分;组件;[电子] 元件∙invariant [ɪn'veərɪənt]adj. 不变的∙n. [数] 不变量;[计] 不变式PE,塑性应变分量PE, Plastic strain components∙(Plastic ['plæstɪk]adj. 塑料的;(外科)造型的;可塑的;n. 塑料制品;整形;可塑体PEEQ,等效塑性应变PEEQ, Equivalent plastic strain∙(Equivalent [ɪ'kwɪvələnt]adj. 等价的,相等的;同意义的∙n. 等价物,相等物PEMAG, Plastic strain magnitudePEMAG,塑性应变∙(magnitude ['mæɡnɪtud]n. 大小;量级;[地震] 震级;重要;光度LE,对数应变分量LE, Logarithmic strain components∙(Logarithmic [lɔɡə'rɪðmɪk]adj. 对数的位移、速度、加速度Displacement/Velocity/Acceleration∙(Velocity [və'lɑsəti]n. [力] 速率;迅速;周转率∙Acceleration [əkselə'reɪʃ(ə)n]n. 加速,促进;[物]加速度U,位移和转动U,Translation and rotations∙(rotation [rə(ʊ)'teɪʃ(ə)n]n. 旋转;循环,轮流UT,Translations UT,平移UR,Rotations UR,旋转作用力/反作用力Forces/Reactions∙(Reaction [rɪ'ækʃən]n. 反应,感应;反动,复古;反作用RF,Reaction forces and moments RF,反作用力和力矩CF,Concentrated forces and momentsCF,集中力和弯矩∙(Concentrate ['kɑnsn'tret]vi. 集中;浓缩;全神贯注;聚集∙vt.集中;浓缩∙n. 浓缩,精选;浓缩液CSTRESS, Contact stress CSTRESS,接触应力CDISP,接触位移CDISP, Contact displacements∙(Contact ['kɑntækt]n. 接触,联系∙vt.使接触∙vi. 联系,接触Evenly spaced time intervals均匀时间间隔∙(Evenly ['ivnli]adv. 均匀地;平衡地;平坦地;平等地∙Spaced [spest]adj. 隔开的;以规定距离排列的;间隔排列的∙v. 隔开;空出(space的过去分词)每x个时间单位Every x units of time∙(unit ['junɪt]n. 单位,单元;装置;[军] 部队;部件Concentrated force 集中力Moment 弯矩Pressure 压力Surface traction表面载荷∙(traction ['trækʃən]n. 牵引;[机][车辆] 牵引力∙Gravity['ɡrævəti]n. 重力,地心引力;严重性;庄严重力线性摄动Linear perturbation∙(perturbation [,pɜːtə'beɪʃ(ə)n]n. [数][天] 摄动;不安;扰乱∙Individually[ˌɪndɪˈvɪdʒuəli]adv. 个别地,单独地逐个对称/反对称/完全固定Symmetry/Antisymmetry/Encastre∙(Symmetry ['sɪmətri]n. 对称(性);整齐,匀称Antisymmetry['æntɪsɪmɪtrɪ]n.反对称性Encastre[en'kɑ:stər]n. 端部固定∙Maintain[men'ten]∙vt. 维持;继续;维修;主张;供养Subsequent['sʌbsɪkwənt]∙adj. 后来的,随后的Active ['æktɪv]∙adj. 积极的;活跃的;主动的;有效的;现役的Applicable ['æplɪkəbl]∙adj. 可适用的;可应用的;合适的Allocation [,ælə'keʃən]∙n. 分配,配置;安置estimate['estɪmeɪt]估计∙vi. 估计,估价∙n. 估计,估价;判断,看法∙vt.估计,估量;判断,评价Parallelization[pærəlɪlaɪ'zeɪʃn]并行Use multiple processors运行多个处理器∙(multiple ['mʌltəpl]adj. 多重的;多样的;许多的∙n. 倍数;[电] 并联∙processor ['prɑsɛsɚ]n. [计] 处理器;处理程序;加工者精度∙Precision[prɪ'sɪʒ(ə)n]n. 精度,[数] 精密度;精确∙adj. 精密的,精确的提交∙Submit[səb'mɪt]vt.使服从;主张;呈递∙vi. 提交;服从监控∙Monitor['mɒnɪtə]n. 监视器;监听器;监控器;班长∙vt.监控边界条件:速度/角速度Velocity/Angular velocity∙(Velocity [və'lɑsəti]n. [力] 速率;迅速;周转率∙Angular ['æŋgjʊlə]adj. [生物] 有角的;生硬的,笨拙的;瘦削的Acceleration/Angular acceleration 加速度/角加速度可视化:Render['rendə]渲染风格Wireframe['waiəfreim]线框变形缩放系数Deformation scale factor∙(Deformation [,diːfɔː'meɪʃ(ə)n]n. 变形Uniform['junɪfɔrm]一致Nonumiform 不一致可见边Visible edges∙(Visible ['vɪzəbl]adj. 明显的;看得见的;现有的;可得到的∙n. 可见物;进出口贸易中的有形项目外部边Exterior edges∙(Exterior [ɪk'stɪərɪə; ek-]adj. 外部的;表面的;外在的∙n. 外部;表面;外型;外貌ODB display options:Refinement level细化精度∙(Refinement [rɪ'faɪnmənt]n. 精制;文雅;[化工][油气][冶] 提纯∙Level ['lev(ə)l]n. 水平;标准;水平面∙adj. 水平的;平坦的;同高的∙vi. 瞄准;拉平;变得平坦∙vt.使同等;对准;弄平∙Coarse[kɔrs]adj. 粗糙的;粗俗的;下等的稍粗极粗Extra coarse∙(Extra ['ekstrə]adv. 特别地,非常;另外∙n. 临时演员;号外;额外的事物;上等产品∙adj. 额外的,另外收费的;特大的中∙Medium['midɪəm]adj. 中间的,中等的;半生熟的∙n. 方法;媒体;媒介;中间物Fine 稍细Extra fine 极细辅助显示∙Idealizations[aɪ'dɪəlɪ'zeʃən]n. 理想化;理想化的事物考虑未激活的单元Account for deactivated elements∙(Account [ə'kaʊnt]n. 账户;解释;账目,账单;理由vi. 解释;导致;报账∙vt.认为;把…视为∙deactivate[di'æktə,vet]vt.使无效;使不活动;遣散;复员Mirror/Pattern镜像/图样∙(Pattern ['pæt(ə)n]n. 模式;图案;样品∙vt.模仿;以图案装饰∙vi. 形成图案Pattern 模式Pattern CSYS 阵列坐标系∙Rectangular[rek'tæŋgjʊlə]adj. 矩形的;成直角的直角Circular 圆形云图绘制选项:Contour type 云图类型Isosurface 等值表面离散∙Discrete[dɪ'skrit]adj. 离散的,不连续的∙n. 分立元件;独立部件Interval type 间隔类型Log 对数User-defined用户定义∙(defined [dɪ'faɪnd]adj. 有定义的,确定的;清晰的,轮廓分明的∙v. 使明确;给...下定义;使...的轮廓分明(define的过去分词)显示位置Show location∙(location [lə(ʊ)'keɪʃ(ə)n]n. 位置(形容词locational);地点;外景拍摄场地动画Animation[ænɪ'meɪʃ(ə)n]∙n. 活泼,生气;激励;卡通片绘制Use limits from all frames使用所有桢的最大最小值∙(frame [freɪm]n. 框架;结构;[电影] 画面∙vt.设计;建造;陷害;使…适合∙vi. 有成功希望∙adj. 有木架的;有构架的Animate scale factor 动画缩放系数Animate harmonic动画:谐振∙(harmonic [hɑr'mɑnɪk]adj. 和声的;谐和的;音乐般的∙n. [物] 谐波;和声动画选项:Frame rate 帧频率显示帧计数Show frame counter∙(counter ['kaʊntə]n. 柜台;对立面;计数器;(某些棋盘游戏的)筹码∙vt.反击,还击;反向移动,对着干;反驳,回答∙vi. 逆向移动,对着干;反驳∙adj. 相反的∙adv. 反方向地;背道而驰地积分点Integration point∙(Integration [ɪntɪ'greɪʃ(ə)n]n. 集成;综合质心Centroid['sentrɒɪd]∙n. 图心单元结点Element nodal∙(nodal ['nodl]adj. 节的;结的;节似的唯一结点的Unique nodal∙(Unique [jʊ'nik]adj. 独特的,稀罕的;[数] 唯一的,独一无二的∙n. 独一无二的人或物网格:近似全局尺寸Approximate global size∙(Approximate [ə'prɑksɪmət]vt.近似;使…接近;粗略估计∙vi. 接近于;近似于∙adj. [数] 近似的;大概的Curvature control曲率控制∙(Curvature ['kɜːvətʃə]n. 弯曲,[数] 曲率Maximum deviation factor最大偏离因子∙(deviation [diːvɪ'eɪʃ(ə)n]n. 偏差;误差;背离By fraction of global size按占全局尺寸的比例∙(fraction['frækʃ(ə)n]n. 分数;部分;小部分;稍微By absolute value 按绝对值∙(absolute['æbsəlut]adj. 绝对的;完全的;专制的∙n. 绝对;绝对事Hex 六面体Hex-dominated六面体为主∙(dominated['dɔmineitid]adj. 占主导地位的;强势的;占统治地位的;[数] 受控的∙v. 控制,支配;处于支配地位(dominate的过去式Tet 四面体楔形Wedge[wedʒ]∙vt.楔入;挤进;楔住∙vi. 楔入;挤进∙n. 楔子;楔形物;导致分裂的东西技术Technique[tek'niːk]∙n. 技巧,技术;手法结构Structured['strʌktʃəd]∙adj. 有结构的;有组织的∙v. 组织;构成(structure的过去分词);建造Medial axis 中性轴算法Appropriate [ə'prəʊprɪət]∙adj. 适当的∙vt.占用;拨出Linear 线性二次Quadratic[kwɑ'drætɪk]∙adj. [数] 二次的∙n. 二次方程式杂交公式Hybrid formulation∙(Hybrid['haɪbrɪd]n. 杂种,混血儿;混合物∙adj. 混合的;杂种的∙formulation[fɔːmjʊ'leɪʃn]n. 构想,规划;公式化;简洁陈述Reduced integration 减缩积分Incompatible modes 非协调模式Hourglass stiffness 沙漏刚度Viscosity 粘性Kinematic split 运动裂纹Second-order accuracy 二阶精度Distortion control 扭曲控制Hourglass control 沙漏控制Enhanced 增强Relax stiffness 松弛刚度Stiffness 刚度Viscous 粘性Combined 组合Element deletion 单元删除Max Degradation 最大下降Scaling factors 缩放系数Linear bulk viscosity 线性体积粘性Quadratic bulk viscosity 二次体积粘度优化:Freeze load regions 冻结载荷区域Freeze boundary condition regions 冻结边界条件区域Density update strategy 密度更新策略Conservative 保守Aggressive 激进Initial density 初始密度Maximun change per design cycle 每个设计循环的最大改变Convergence criteria 收敛准则首次设计循环作为评价标准First design cycle used to evaluatecriteriaCriteria to be fulfilled 要适应的准则Objective function delta criterion 目标函数delta准则Algorithm 算法Sensitivity-based 基于敏度Condition-based optimization 基于条件的优化Method 方法Material interpolation technique 材料内插技术Volume 体积Frozen area 冻结区域Member size 构件尺寸Memold control 脱模控制Rotational symmetry 轴对称Cyclic symmetry 循环对称Operator 运操作符Comparison operation 对比操作Previous iteration 前一次迭代Modify reference value by factor 按因子修改参考值Displacement by addition of material 有材料增加引起的位移Reduction 减少Total absolute displacement 总觉得位移Equivalent stress 等效应力任务区域内约束点的等效应力Equivalent stress of restricted pointsin task region载荷里的速度。
Aabscissa 横坐标absence rate 缺勤率absolute number 绝对数absolute value 绝对值accident error 偶然误差accumulated frequency 累积频数alternative hypothesis 备择假设analysis of data 分析资料analysis of variance(ANOV A) 方差分析arith-log paper 算术对数纸arithmetic mean 算术均数assumed mean 假定均数arithmetic weighted mean 加权算术均数asymmetry coefficient 偏度系数average 平均数average deviation 平均差Bbar chart 直条图、条图bias 偏性binomial distribution 二项分布biometrics 生物统计学bivariate normal population 双变量正态总体Ccartogram 统计图case fatality rate(or case mortality) 病死率census 普查chi-sguare(X2) test 卡方检验central tendency 集中趋势class interval 组距classification 分组、分类cluster sampling 整群抽样coefficient of correlation 相关系数coefficient of regression 回归系数coefficient of variability(or coefficieut of variation) 变异系数collection of data 收集资料column 列(栏)combinative table 组合表combined standard deviation 合并标准差combined variance(or poolled variance) 合并方差complete survey 全面调查completely correlation 完全相关completely random design 完全随机设计confidence interval 可信区间,置信区间confidence level 可信水平,置信水平confidence limit 可信限,置信限constituent ratio 构成比,结构相对数continuity 连续性control 对照control group 对照组coordinate 坐标correction for continuity 连续性校正correction for grouping 归组校正correction number 校正数correction value 校正值correlation 相关,联系correlation analysis 相关分析correlation coefficient 相关系数critical value 临界值cumulative frequency 累积频率Ddata 资料degree of confidence 可信度,置信度degree of dispersion 离散程度degree of freedom 自由度degree of variation 变异度dependent variable 应变量design of experiment 实验设计deviation from the mean 离均差diagnose accordance rate 诊断符合率difference with significance 差别不显著difference with significance 差别显著discrete variable 离散变量dispersion tendency 离中趋势distribution 分布、分配Eeffective rate 有效率eigenvalue 特征值enumeration data 计数资料equation of linear regression 线性回归方程error 误差error of replication 重复误差error of type II Ⅱ型错误,第二类误差error of type I Ⅰ型错误,第一类误差estimate value 估计值event 事件experiment design 实验设计experiment error 实验误差experimental group 实验组extreme value 极值Ffatality rate 病死率field survey 现场调查fourfold table 四格表freguency频数freguency distribution 频数分布GGaussian curve 高斯曲线geometric mean 几何均数grouped data 分组资料Hhistogram直方图homogeneity of variance 方差齐性homogeneity test of variances 方差齐性检验hypothesis test 假设检验hypothetical universe 假设总体Iincidence rate 发病率incomplete survey 非全面调检indepindent variable 自变量indivedual difference 个体差异infection rate 感染率inferior limit 下限initial data 原始数据inspection of data 检查资料intercept 截距interpolation method 内插法interval estimation 区间估计inverse correlation 负相关Kkurtosis coefficient 峰度系数Llatin sguare design 拉丁方设计least significant difference 最小显著差数least square method 最小平方法,最小乘法leptokurtic distribution 尖峭态分布leptokurtosis 峰态,峭度linear chart 线图linear correlation 直线相关linear regression 直线回归linear regression eguation 直线回归方程link relative 环比logarithmic normal distribution 对数正态分布logarithmic scale 对数尺度lognormal distribution 对数正态分布lower limit 下限Mmatched pair design 配对设计mathematical statistics 数理统计(学)maximum value 极大值mean 均值mean of population 总体均数mean square 均方mean variance 均方,方差measurement data 讲量资料median 中位数medical statistics 医学统计学mesokurtosis 正态峰method of least squares 最小平方法,最小乘法method of grouping 分组法method of percentiles 百分位数法mid-value of class 组中值minimum value 极小值mode 众数moment 动差,矩morbidity 患病率mortality 死亡率Nnatality 出生率natural logarithm 自然对数negative correlation 负相关negative skewness 负偏志no correlation 无相关non-linear correlation 非线性相关non-parametric statistics 非参数统计normal curve 正态曲线normal deviate 正态离差normal distribution 正态分布normal population 正态总体normal probability curve 正态概率曲线normal range 正常范围normal value 正常值normal kurtosis 正态峰normality test 正态性检验nosometry 患病率null hypothesis 无效假设,检验假设Oobserved unit 观察单位observed value 观察值one-sided test 单测检验one-tailed test 单尾检验order statistic 顺序统计量ordinal number 秩号ordinate 纵坐标Ppairing data 配对资料parameter参数percent 百分率percentage 百分数,百分率percentage bar chart 百分条图percentile 百分位数pie diagram 园图placebo 安慰剂planning of survey 调查计划point estimation 点估计population 总体,人口population mean 总体均数population rate 总体率population variance 总体方差positive correlation 正相关positive skewness 正偏态power of a test 把握度,检验效能prevalence rate 患病率probability 概率,机率probability error 偶然误差proportion 比,比率prospective study 前瞻研究prospective survey 前瞻调查public health statistics 卫生统计学Qquality eontrol 质量控制quartile 四分位数Rrandom 随机random digits 随机数字random error 随机误差random numbers table 随机数目表random sample 随机样本random sampling 随机抽样random variable 随机变量randomization 随机化randomized blocks 随机区组,随机单位组randomized blocks analysis of variance 随机单位组方差分析randomized blocks design 随机单位组设计randomness 随机性range 极差、全距range of normal values 正常值范围rank 秩,秩次,等级rank correlation 等级相关rank correlation coefficent 等级相关系数rank-sum test 秩和检验rank test 秩(和)检验ranked data 等级资料rate 率ratio 比recovery rate 治愈率registration 登记regression 回归regression analysis 回归分析regression coefficient 回归系数regression eguation 回归方程relative number 相对数relative ratio 比较相对数relative ratio with fixed base 定基比remainder error 剩余误差replication 重复retrospective survey 回顾调查Ridit analysis 参照单位分析Ridit value 参照单位值Ssample 样本sample average 样本均数sample size 样本含量sampling 抽样sampling error 抽样误差sampling statistics 样本统计量sampling survay 抽样调查scaller diagram 散点图schedule of survey 调查表semi-logarithmic chart 半对数线图semi-measursement data 半计量资料semi-guartile range 四分位数间距sensitivity 灵敏度sex ratio 性比例sign test 符号检验significance 显著性,意义significance level 显著性水平significance test 显著性检验significant difference 差别显著simple random sampling 单纯随机抽样simple table 简单表size of sample 样本含量skewness 偏态slope 斜率sorting data 整理资料sorting table 整理表sources of variation 变异来源square deviation 方差standard deviation(SD) 标准差standard error (SE) 标准误standard error of estimate 标准估计误差standard error of the mean 均数的标准误standardization 标准化standardized rate 标化率standardized normal distribution 标准正态分布statistic 统计量statistics 统计学statistical induction 统计图statistical inference 统计归纳statistical map 统计推断statistical method 统计地图statistical survey 统计方法statistical table 统计调查statistical test 统计表statistical treatment 统计检验stratified sampling 统计处理stochastic variable 分层抽样sum of cross products of 随机变量deviation from mean 离均差积和sum of ranks 秩和sum of sguares of deviation from mean 离均差平方和superior limit 上限survival rate 生存率symmetry对称(性)systematic error 系统误差systematic sampling 机械抽样Tt-distribution t分布t-testt检验tabulation method 划记法test of normality 正态性检验test of one-sided 单侧检验test of one-tailed 单尾检验test of significance 显著性检验test of two-sided 双侧检验test of two-tailed 双尾检验theoretical frequency 理论频数theoretical number 理论数treatment 处理treatment factor 处理因素treatment of date 数据处理two-factor analysis of variance 双因素方差分析two-sided test 双侧检验two-tailed test 双尾检验type I error 第一类误差type II error 第二类误差typical survey 典型调查Uu test u检验universe 总体,全域ungrouped data 未分组资料upper limit 上限Vvariable 变量variance 方差,均方variance analysis 方差分析variance ratio 方差比variate 变量variation coefficient 变异系数velocity of development 发展速度velocity of increase 增长速度Wweight 权数weighted mean 加权均数Zzero correlation 零相关unit onedivision of labor 劳动分工commodity money 商品货币legal tender 法定货币fiat money 法定通货a medium of exchange交换媒介legal sanction法律制裁face value面值liquid assets流动资产illiquidl assets非流动资产the liquidity scale 流动性指标real estate 不动产checking accounts,demand deposit,checkable deposit 活期存款time deposit 定期存款negotiable order of withdrawal accounts 大额可转让提款单money market mutual funds 货币市场互助基金repurchase agreements 回购协议certificate of deposits存单bond 债券stock股票travelers\'checks 旅行支票small-denomination time deposits小额定期存款large-denomination time deposits大额定期存款bank overnight repurchase agreements 银行隔夜回购协议bank long-term repurchase agreements 银行长期回购协议thrift institutions 存款机构financial institution 金融机构commercial banks商业银行a means of payment 支付手段a store of value储藏手段a standard of value价值标准unit tworeserve 储备note 票据discount贴现circulate流通central bank 中央银行the Federal Reserve System联邦储备系统credit union 信用合作社paper currency 纸币credit creation 信用创造branch banking 银行分行制unit banking 单一银行制out of circulation 退出流通capital stock股本at par以票面价值计electronic banking电子银行banking holding company 公司银行the gold standard金本位the Federal Reserve Board 联邦储备委员会the stock market crash 股市风暴reserve ratio 准备金比率unit threedeficit 亏损roll展期wholesale批发default不履约auction拍卖collateralize担保markup价格的涨幅dealer交易员broker经纪人pension funds 养老基金face amount面值commerical paper商业票据banker\'s acceptance银行承兑汇票Fed fund 联邦基金eurodollar欧洲美元treasury bills 国库券floating-rate 浮动比率fixed-rate 固定比率default risk 拖欠风险credit rating信誉级别tax collection税收money market货币市场capital market资本市场original maturity 原始到期期限surplus funds过剩基金回复引用举报返回顶部2#admin发表于2006-11-24 08:49 |只看该作者unit four管理员premium 升水 discount 贴水par 平价deficit 赤字future 期货capital movements 资本流动foreign exchange dealings 外汇交易balance of payment 国际收支eurodollar market 欧洲美元市场spot rate 即期汇率 forward rate 远期汇率 cross rate 交叉汇率 arbitrage transation 套汇交易space arbitrage 地点套汇 time arbitrage 时间套汇 interest arbitrage 套利 direct quotation 直接标价法indirect quotation 间接标价法decimal system 十进制 long position 多头 short position 空头 swedish kronor 瑞典克郎 Sfr 瑞士法郎DM 德国马克FFr 法国法郎Dkr 丹麦克郎Nkr 挪威克郎Yen 日元Can $加拿大元 £英镑Lit 意大利里拉 Aus $澳大利亚元 DG 荷兰盾BF 比利时法郎unit fivethe society for worldwidetelecommunication(SWIFT)环球银行金融电讯协会the clearing houseinterbank paymentssystem(CHIPS)纽约银行同业清算系统over-the-counter market场外交易市场invoice发票,发货单portfolio债务,投资组合turnover总成交额not-for-profitcooperative非盈利性组织triangular arbitrage三角套汇unit sixquota 配额guaratee保函fixed exchange rate固定汇率balance of paymentdeficit国际收支逆差international reserve国际储备credit tranche drawing信贷份额借款credit tranche信贷份额credit tranche facilities信贷份额贷款便利international payment国际收支buffer stock缓冲存货extended facilities补偿信贷便利government borrowing国债;政府借款price fluctuation价格波动,价格涨落export earning 出口收益enlarged access policy 延期进入政策credit policy信用政策组,债务调整Bretton Woods Agreement布雷顿森林协议International MonetaryFund 国际货币基金组织International Bank forResonstruction andDevelopment(IBRD)国际复兴与开发银行InternationalDevelopment Association(I.D.A.)国际开发协会International FincanceCorporation(I.F.C.)国际金融公司financial intermediary金融中介concessional terms特惠条件trade credit商业信贷earning capacity收益能力Bank for InternationalSettlements(B.I.S.)国际清算银行financial settlement财务清算接着来:unit sevensyndication辛迪加underwrite包销,认购hedge对冲买卖、套期保值innovation到期交易spread利差principal本金swap掉期交易eurobond market 欧洲债券市场euronote欧洲票据Federal Reserve Bank(FRB)联邦储备银行unsecured credit无担保贷款定期支付存款lead bank牵头银行neogotiabletime deposit议付定期存款inter-bank money market银行同业货币市场medium term loan 中期贷款syndicated credit银团贷款merchant bank商业银行portfolio management 有价债券管理lease financing租赁融资note issurance facility票据发行安排bearer note不记名票价underwriting facility包销安排floating-rate note 浮动利率票据bond holder债券持持有者London Interbank OfferedRate(LIBOR)伦敦同业优惠利率back-up credit line备用信贷额promissorynote(P.N..p/n)本票revolving cerdit 循环信用证,即revolving letterof creditnon interest-bearingreserves无息储备金interest rate controls 利率管制interest rate ceiling 利率上限interest rate floor 利率下限deposit insurance 存款保险。
我最喜欢的出行方式中国高铁英语作文全文共3篇示例,供读者参考篇1My Favorite Way to Travel - China's High-Speed RailWhooosh! The high-speed train zips past cities, villages, and wide open fields. It's my absolute favorite way to travel! Riding on these awesome super-fast trains is always an exciting adventure.Last summer, my family took an amazing trip from Beijing to Shanghai on one of China's high-speed rail lines. Just the idea of rocketing between those two huge cities at crazy speeds over 300 km/h (186 mph) had me bouncing off the walls with anticipation! The morning of our journey, I could barely sit still as we waited in the sleek, modern station.When our sparkly white г¤ёと⌐ train pulled in, my jaw dropped. It looked like a super-cool futuristic rocket ship on rails! As we stepped onboard into the bright, spotless cabins, I feltlikе a space explorer venturing somewhere out of this world. The seats were incredibly comfy with their soft cushions and leg rests.There were screens to watch movies, and electrical outlets for my video games too.Finally, we were underway and picking up speed fast. In just minutes, the suburbs turned into a blur. Before I knew it, we were in the countryside just flying by the scenery. I pressed my face up to the window, wide-eyed watching farmers tilling fields and water buffaloes grazing lazily as we whooshed past at warp speed. Probably faster than a cheetah can run! Apartment buildings in the distance looked like toy blocks.Riding a high-speed train is awesome for so many reasons. First off, they're safe and comfortable with a super smooth ride. You barely feel any bumps or turns at all, even when blazing ahead at top speeds over 300 km/h. Watching the landscape rapidly transform out your window is a total thrill ride!Plus, these trains have amenities galore to keep you entertained for hours. You get to pick from tons of snacks from the food carts, check out shows on your personal TV, or even walk around and explore other cabins. Some of the fancier trains have awesome stuff like viewing cars with big panoramic windows. On others, there are designated family rooms for little kids to play in. What could be better? It's like a hotel onsuper-fast wheels!Another amazing thing about China's high-speed rail is how far and fast you can travel using it. The network of high-speed lines now stretches for over 40,000 km across the country! That means you can get to almost any major city without having to go to an airport or sit in traffic on a highway. It's mind-blowing how quickly you can connect between far-away places.On my family's recent journey from Beijing to Shanghai, we made it there in just 4.5 smooth, comfortable, high-speed hours. If we drove, it would have taken us over 12 long, tedious hours of being stuck in a car. No thanks! And traveling by plane would have meant hauling luggage through airports and dealing with security lines. With the high-speed train, we pulled into city centers without any of those annoying hassles.High-speed rail is also kinder to the planet than driving or flying too. These electric trains run on renewable energy sources like wind, hydro, and solar power. That means they leave behind a way smaller carbon footprint compared to cars or planes. China's commitment to growing its high-speed rail network instead of expanding airports and highways helps the whole world by fighting air pollution and climate change. How awesome is that?I absolutely loved every second of my high-speed rail experience in China, from the modern stations to the crazy-fast speeds to all the amazing amenities onboard. I'm already begging my parents to plan our next high-speed adventure. Maybe we could make it all the way from Beijing to Guangzhou next time, which would take us less than 9 hours! Or we could go east to Shanghai and keep riding the rails all the way down to Hong Kong after that.Wherever we end up going, I just hope it's on one of those sleek, incredible high-speed trains again. There's nothing as fun and convenient as being able to zip across the country at over 300 km/h, watching the scenery rapidly blur past your window. Airplanes and cars don't even come close. China's high-speed rail lets me go on fantastic journeys while feeling like I'm aboard a space ship from the future. Now that's how you travel in serious style!篇2My Favorite Way to Travel - China's High-Speed RailWhenever my parents ask me how I want to travel for our next family vacation, I always give the same excited answer - "Let's take the high-speed rail!" You see, I absolutely love ridingon China's super-fast bullet trains. They are simply the coolest way to get around in my opinion.First off, high-speed rail is incredibly convenient. The trains connect so many major cities across our vast country. Instead of having to go through the hassle of an airport, we can just hop on a train right in the heart of the city center. No extra travel time or costs to get to a faraway airport. Just walk to the beautiful railway station near our home.Speaking of railway stations, they are marvels of architecture and engineering themselves. The soaring glass and steel terminals are like palaces for trains. Waiting areas are clean, modern and comfortable with plenty of shops and restaurants. Watching the sleek trains glide in and out of the platforms never gets old for me.Once onboard, the high-speed rail experience begins! The trains themselves are works of art with their aerodynamic designs and pristine interiors. The seats are incredibly roomy, at least from my perspective as a kid. Big windows give panoramic views of the outdoors. Some trains even have monitoring rooms where you can watch live feeds from cameras on the front of the locomotive!Then the real fun starts as the whistle blows and the powerful electric engines start propelling us forward, quickly ramping up to incredible speeds. I still vividly remember my first high-speed rail journey and theawa I felt as the super-train effortlessly bolted to over 300 km/h in what felt like just a few seconds. The acceleration still takes my breath away every time!Watching the amazing scenery fly by at such unbelievable speeds is just mesmerizing. One moment you're in a crowded city, then in an instant you've zoomed into wide open countryside. Forests, farms, rivers and mountains whizz past in a beautiful blur. It's almost like the train is teleporting you across the vast distances between cities.Despite traveling at such an intense velocity, the ride itself is incredibly smooth and quiet thanks to the advanced engineering and construction of the railbeds and tracks. You tend to forget just how rapidly you are rocketing across the landscape. Only when zipping through tunnels do you get a rush from the compressed air and noise.High-speed rail makes it so easy to hop between major cities in just a matter of hours. Journeys that used to take an entire day of traveling can now be completed with time to spare. I've beenable to see so many more destinations this way compared to before the high-speed rail system expanded everywhere.For example, just this past Spring Festival holiday my family took the bullet train from Beijing all the way down to Guangzhou to visit relatives, a trip of over 2,000 kilometers! Yet it only took around 8 hours of total travel time thanks to the incredible speeds. We could leave in the morning and arrive before dinner with no hassles whatsoever.Even over slightly shorter distances, the high-speed rail beats taking a car or bus hands down in my book. The trips just fly by in pure comfort and safety. No getting stuck in tons of traffic or having to constantly swap drivers. We can just sit back, relax, walk around if we want, and let the skilled rail engineers do their thing in getting us to our destination quickly.I love watching the display screens that showcase our train's route and realtime speed, which often tops 300 km/h for long stretches between stops. Seeing the intermediate station times lets me calculate just how rapidly we are traversing the terrain compared to other transportation.Sometimes I imagine the rail workers managing the complicated logistics to keep all the trains running across China's vast high-speed rail network of over 40,000 kilometers ofdedicated tracks. It's like a sophisticated choreography getting thousands of trains safely across the country each day according to their precise schedules. Just thinking about that boggles my young mind!Of course, the high-speed rail system is not only useful for traveling between cities, but within many of China's major metropolitan areas too. For instance, when visiting my cousins in Shanghai, we can easily hop on the metropolitan rapid transit system which has several high-speed lines zipping across the huge city in a fraction of the time it would take by car or bus.I find it fascinating how the rapid transit lines thread their way both above and underneath Shanghai's densely packed urban sprawl of skyscapers and neighborhoods. We'll be riding along an elevated viaduct one moment, then dive down into tunnels brilliantly illuminated with decorative lighting displays the next stretch. The intricate rail overpasses and underground stations are like futuristic ant colonies that us humans get to be temporarily be part of during our journeys.My parents sometimes get weary from the almost dizzying speed of the rapid transit system within Shanghai compared to the slightly more relaxed pacing of the inter-city high-speed rail lines. But for me it's an absolute thrill ride! I'll be bouncing in myseat as the electric train tears around tight curves and dives through tunnels at over 100 km/h, zipping us across the immense urban landscape.No matter if it's a long-distance high-speed rail journey or short hop on rapid transit, I love every minute of the experience. The sights, the sounds, the incredible velocities - it's all amazing to me. Watching China's rail feats of engineering and technology in action never gets old.Perhaps I have an abnormally strong fascination forhigh-speed rail for someone my age. But it's born from a deep sense of pride and appreciation for what China has accomplished in building the most advanced rapid train system in the world. Whenever I see a bright white high-speed train streak by, I know I'm witnessing something incredibly special on the move - the future!So while other kids my age may want to take an airplane or car for vacation, you can be certain I'll always vote forhigh-speed rail. It's simply the fastest, safest, most efficient and coolest way to travel in my book. Riding China's vanguard rail technology at breathtaking speeds across our vast homeland is an experience I cherish and hope to do for many more years to come.Who knows, maybe I'll even get to be a high-speed rail engineer when I grow up! Now that would be the dream...篇3My Favorite Way to Travel: China's High-Speed RailDo you know what my favorite way to travel is? It's China's amazing high-speed rail system! Riding on these super-fast trains is the best experience ever. Let me tell you all about it.First off, these trains are insanely fast! The top operational speed is over 350 km/h (217 mph). Can you believe that? They go sooo much faster than a car on the highway. Just watching the landscapes whizz by through the window is an adventure in itself. Tree? Zooooom - it's gone! House? Zooooom - blink and you'll miss it! It's like everything is on fast-forward.The acceleration is crazy too. When the train starts moving, you get pushed back into your seat a little bit. And when it slows down for a stop, you kind of get that bouncy feeling in your stomach like a little roller coaster. But don't worry, it's totally safe! The rides are actually really smooth and comfortable overall.Speaking of comfortable, the seats on these trains are awesome. They're big with plenty of legroom, and they recline pretty far back so you can relax. Some even have little footreststhat pop out! On longer trips, the attendants come around with food carts selling all kinds of yummy snacks and drinks too.Another cool thing is all the awesome technology on board. The trains have great wifi so you can watch videos, play games, or message your friends the whole ride. There are also TV screens and speakers at each seat with tons of movies and shows to watch if you get bored. And at the front and back of each car, there are huge window view areas where you can go stand and watch the scenery flying by. It's like having a viewing deck just for train riders!But someof my favorite parts about high-speed rail are actually at the stations. These place are huge! The biggest ones have giant curved roofs and sleek designs that make them look like spaceships. And the waiting areas inside feel more like airports than traditional train stations. There are places to eat, shops to explore, and even gardens and aquariums in some of them! It's like an adventure just getting on the train.Then there's the efficiency of the whole system. The trains run on time down to the second, so you never have to worry about being late. As soon as one pulls into the station, another is right behind it waiting to whisk you off to the next destination. No waiting around forever or missing your ride. And the stationsare conveniently located right in the heart of cities, not out in the middle of nowhere.I could go on and on about how great China's high-speed rail is, but I don't want this essay to be a million pages long! Let's just say riding these trains makes any trip an absolute blast. You get from place to place quickly, safely, comfortably, and in style. What's not to love?So next time you're planning a journey, skip the plane, forget about a car, and take the bullet train instead. It's guaranteed to be the most fun method of transportation you've ever experienced. Trust me, I'm basically an expert! I ride these awesome high-speed railways all the time with my family. We've been all over - Beijing, Shanghai, Guangzhou, you name it. And I have to say, beating the countryside views from my cozy window seat never gets old.In fact, I've already started my summer vacation countdown because my parents promised we'd take the high-speed rail somewhere cool again this year. Maybe we'll visit some place with beautiful mountains or beaches! Honestly, I don't really care where we go as long as we get to ride China's high-speed rail to get there. Those lightning-quick, high-tech, crazy-smooth trainsmake the journey as epic as the destination. That's why they're my absolute favorite way to travel. End of story!。
液氨安全基础知识培训液氨安全基础知识培训液氨是什么?(What is ammonia ?)(1)液氨是一种沸点在零下33摄氏度的比空气轻的气体(Ammonia is a gas lighter than Air at temperaturesabove minus 33°C);(2)液氨会与水剧烈反应,释放大量的热量(Ammonia reacts quite violently with water. A lot of heat isevolved);(3)液氨有严重刺激性气味,5-10ppm的浓度下人可以直接吸入(Ammonia has a heavy pungent smell, it can be smelled from 5-10 ppm);(4)液氨可以被探测器探测到或者直接从其气味被闻到。
由于液氨的这种气味可以让人在造成损伤之前被直接嗅到,这样给了液氨一定的安全度(Ammonia can be detected by ammonia detectors or by its smell. The smell gives to this chemical a kind of intrinsic safety since it can be smelled long before it is getting dangerous);(5)液氨是由空气中的氮气和氢气在金属催化剂和高温高压下生成的(Produced by reacting Nitrogen from the air with hydrogen on an iron based catalyst at high temperature and pressure);(6)以氢气为原料的合成氨法中的氢气是由煤或者是其他碳氢化合物经过气化重整过程得到的(The hydrogen used in the ammonia synthesis is produced by means of the steam reforming process with coal or other hydrocarbons as raw material);(7)全球年产液氨大约一亿两千万吨(2006年数据)(World production of ammonia ~ 120 million metric tonnes (2006))。
统计学术语中英文对照Absolute deviation 绝对离差Absolute number 绝对数Absolute residuals 绝对残差Acceleration array 加速度立体阵Acceleration in an arbitrary direction 任意方向上的加速度Acceleration normal 法向加速度Acceleration space dimension 加速度空间的维数Acceleration tangential 切向加速度Acceleration vector 加速度向量Acceptable hypothesis 可承受假设Accumulation 累积Accuracy 准确度Actual frequency 实际频数Adaptive estimator 自适应估计量Addition 相加Addition theorem 加法定理Additivity 可加性Adjusted rate 调整率Adjusted value 校正值Admissible error 容许误差Aggregation 聚集性Alternative hypothesis 备择假设Among groups 组间Amounts 总量Analysis of correlation 相关分析Analysis of covariance 协方差分析Analysis of regression 回归分析Analysis of time series 时间序列分析Analysis of variance 方差分析Angular transformation 角转换ANOVA 〔analysis of variance〕方差分析ANOVA Models 方差分析模型Arcing 弧/弧旋Arcsine transformation 反正弦变换Area under the curve 曲线面积AREG 评估从一个时间点到下一个时间点回归相关时的误差ARIMA 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper 算术格纸Arithmetic mean 算术平均数Arrhenius relation 艾恩尼斯关系Assessing fit 拟合的评估Associative laws 结合律Asymmetric distribution 非对称分布Asymptotic bias 渐近偏倚Asymptotic efficiency 渐近效率Asymptotic variance 渐近方差Attributable risk 归因危险度Attribute data 属性资料Attribution 属性Autocorrelation 自相关Autocorrelation of residuals 残差的自相关Average 平均数Average confidence interval length 平均置信区间长度Average growth rate 平均增长率Bar chart 条形图Bar graph 条形图Base period 基期Bayes' theorem Bayes定理Bell-shaped curve 钟形曲线Bernoulli distribution 伯努力分布Best-trim estimator 最好切尾估计量Bias 偏性Binary logistic regression 二元逻辑斯蒂回归Binomial distribution 二项分布Bisquare 双平方Bivariate Correlate 二变量相关Bivariate normal distribution 双变量正态分布Bivariate normal population 双变量正态总体Biweight interval 双权区间Biweight M-estimator 双权M估计量Block 区组/配伍组BMDP(Biomedical puter programs) BMDP统计软件包Boxplots 箱线图/箱尾图Breakdown bound 崩溃界/崩溃点Canonical correlation 典型相关Caption 纵标目Case-control study 病例对照研究Categorical variable 分类变量Catenary 悬链线Cauchy distribution 柯西分布Cause-and-effect relationship 因果关系Cell 单元Censoring 终检Center of symmetry 对称中心Centering and scaling 中心化和定标Central tendency 集中趋势Central value 中心值CHAID -χ2 Automatic Interaction Detector 卡方自动交互检测Chance 机遇Chance error 随机误差Chance variable 随机变量Characteristic equation 特征方程Characteristic root 特征根Characteristic vector 特征向量Chebshev criterion of fit 拟合的切比雪夫准那么Chernoff faces 切尔诺夫脸谱图Chi-square test 卡方检验/χ2检验Choleskey deposition 乔洛斯基分解Circle chart 圆图Class interval 组距Class mid-value 组中值Class upper limit 组上限Classified variable 分类变量Cluster analysis 聚类分析Cluster sampling 整群抽样Code 代码Coded data 编码数据Coding 编码Coefficient of contingency 列联系数Coefficient of determination 决定系数Coefficient of multiple correlation 多重相关系数Coefficient of partial correlation 偏相关系数Coefficient of production-moment correlation 积差相关系数Coefficient of rank correlation 等级相关系数Coefficient of regression 回归系数Coefficient of skewness 偏度系数Coefficient of variation 变异系数Cohort study 队列研究Column 列Column effect 列效应Column factor 列因素bination pool 合并binative table 组合表mon factor 共性因子mon regression coefficient 公共回归系数mon value 共同值mon variance 公共方差mon variation 公共变异munality variance 共性方差parability 可比性parison of bathes 批比拟parison value 比拟值partment model 分部模型passion 伸缩plement of an event 补事件plete association 完全正相关plete dissociation 完全不相关plete statistics 完备统计量pletely randomized design 完全随机化设计posite event 联合事件posite events 复合事件Concavity 凹性Conditional expectation 条件期望Conditional likelihood 条件似然Conditional probability 条件概率Conditionally linear 依条件线性Confidence interval 置信区间Confidence limit 置信限Confidence lower limit 置信下限Confidence upper limit 置信上限Confirmatory Factor Analysis 验证性因子分析Confirmatory research 证实性实验研究Confounding factor 混杂因素Conjoint 联合分析Consistency 相合性Consistency check 一致性检验Consistent asymptotically normal estimate 相合渐近正态估计Consistent estimate 相合估计Constrained nonlinear regression 受约束非线性回归Constraint 约束Contaminated distribution 污染分布Contaminated Gausssian 污染高斯分布Contaminated normal distribution 污染正态分布Contamination 污染Contamination model 污染模型Contingency table 列联表Contour 边界限Contribution rate 奉献率Control 对照Controlled experiments 对照实验Conventional depth 常规深度Convolution 卷积Corrected factor 校正因子Corrected mean 校正均值Correction coefficient 校正系数Correctness 正确性Correlation coefficient 相关系数Correlation index 相关指数Correspondence 对应Counting 计数Counts 计数/频数Covariance 协方差Covariant 共变Cox Regression Cox回归Criteria for fitting 拟合准那么Criteria of least squares 最小二乘准那么Critical ratio 临界比Critical region 拒绝域Critical value 临界值Cross-over design 穿插设计Cross-section analysis 横断面分析Cross-section survey 横断面调查Crosstabs 穿插表Cross-tabulation table 复合表Cube root 立方根Cumulative distribution function 分布函数Cumulative probability 累计概率Curvature 曲率/弯曲Curvature 曲率Curve fit 曲线拟和Curve fitting 曲线拟合Curvilinear regression 曲线回归Curvilinear relation 曲线关系Cut-and-try method 尝试法Cycle 周期Cyclist 周期性D test D检验Data acquisition 资料收集Data bank 数据库Data capacity 数据容量Data deficiencies 数据缺乏Data handling 数据处理Data manipulation 数据处理Data processing 数据处理Data reduction 数据缩减Data set 数据集Data sources 数据来源Data transformation 数据变换Data validity 数据有效性Data-in 数据输入Data-out 数据输出Dead time 停滞期Degree of freedom 自由度Degree of precision 精细度Degree of reliability 可靠性程度Degression 递减Density function 密度函数Density of data points 数据点的密度Dependent variable 应变量/依变量/因变量Dependent variable 因变量Depth 深度Derivative matrix 导数矩阵Derivative-free methods 无导数方法Design 设计Determinacy 确定性Determinant 行列式Determinant 决定因素Deviation 离差Deviation from average 离均差Diagnostic plot 诊断图Dichotomous variable 二分变量Differential equation 微分方程Direct standardization 直接标准化法Discrete variable 离散型变量DISCRIMINANT 判断Discriminant analysis 判别分析Discriminant coefficient 判别系数Discriminant function 判别值Dispersion 散布/分散度Disproportional 不成比例的Disproportionate sub-class numbers 不成比例次级组含量Distribution free 分布无关性/免分布Distribution shape 分布形状Distribution-free method 任意分布法Distributive laws 分配律Disturbance 随机扰动项Dose response curve 剂量反响曲线Double blind method 双盲法Double blind trial 双盲试验Double exponential distribution 双指数分布Double logarithmic 双对数Downward rank 降秩Dual-space plot 对偶空间图DUD 无导数方法Duncan's new multiple range method 新复极差法/Duncan新法Effect 实验效应Eigenvalue 特征值Eigenvector 特征向量Ellipse 椭圆Empirical distribution 经历分布Empirical probability 经历概率单位Enumeration data 计数资料Equal sun-class number 相等次级组含量Equally likely 等可能Equivariance 同变性Error 误差/错误Error of estimate 估计误差Error type I 第一类错误Error type II 第二类错误Estimand 被估量Estimated error mean squares 估计误差均方Estimated error sum of squares 估计误差平方和Euclidean distance 欧式距离Event 事件Event 事件Exceptional data point 异常数据点Expectation plane 期望平面Expectation surface 期望曲面Expected values 期望值Experiment 实验Experimental sampling 试验抽样Experimental unit 试验单位Explanatory variable 说明变量Exploratory data analysis 探索性数据分析Explore Summarize 探索-摘要Exponential curve 指数曲线Exponential growth 指数式增长EXSMOOTH 指数平滑方法Extended fit 扩大拟合Extra parameter 附加参数Extrapolation 外推法Extreme observation 末端观测值Extremes 极端值/极值F distribution F分布F test F检验Factor 因素/因子Factor analysis 因子分析Factor Analysis 因子分析Factor score 因子得分Factorial 阶乘Factorial design 析因试验设计False negative 假阴性False negative error 假阴性错误Family of distributions 分布族Family of estimators 估计量族Fanning 扇面Fatality rate 病死率Field investigation 现场调查Field survey 现场调查Finite population 有限总体Finite-sample 有限样本First derivative 一阶导数First principal ponent 第一主成分First quartile 第一四分位数Fisher information 费雪信息量Fitted value 拟合值Fitting a curve 曲线拟合Fixed base 定基Fluctuation 随机起伏Forecast 预测Four fold table 四格表Fourth 四分点Fraction blow 左侧比率Fractional error 相对误差Frequency 频率Frequency polygon 频数多边图Frontier point 界限点Function relationship 泛函关系Gamma distribution 伽玛分布Gauss increment 高斯增量Gaussian distribution 高斯分布/正态分布Gauss-Newton increment 高斯-牛顿增量General census 全面普查GENLOG (Generalized liner models) 广义线性模型Geometric mean 几何平均数Gini's mean difference 基尼均差GLM (General liner models) 通用线性模型Goodness of fit 拟和优度/配合度Gradient of determinant 行列式的梯度Graeco-Latin square 希腊拉丁方Grand mean 总均值Gross errors 重大错误Gross-error sensitivity 大错敏感度Group averages 分组平均Grouped data 分组资料Guessed mean 假定平均数Half-life 半衰期Hampel M-estimators 汉佩尔M估计量Happenstance 偶然事件Harmonic mean 调和均数Hazard function 风险均数Hazard rate 风险率Heading 标目Heavy-tailed distribution 重尾分布Hessian array 海森立体阵Heterogeneity 不同质Heterogeneity of variance 方差不齐Hierarchical classification 组内分组Hierarchical clustering method 系统聚类法High-leverage point 高杠杆率点HILOGLINEAR 多维列联表的层次对数线性模型Hinge 折叶点Histogram 直方图Historical cohort study 历史性队列研究Holes 空洞HOMALS 多重响应分析Homogeneity of variance 方差齐性Homogeneity test 齐性检验Huber M-estimators 休伯M估计量Hyperbola 双曲线Hypothesis testing 假设检验Hypothetical universe 假设总体Impossible event 不可能事件Independence 独立性Independent variable 自变量Index 指标/指数Indirect standardization 间接标准化法Individual 个体Inference band 推断带Infinite population 无限总体Infinitely great 无穷大Infinitely small 无穷小Influence curve 影响曲线Information capacity 信息容量Initial condition 初始条件Initial estimate 初始估计值Initial level 最初水平Interaction 交互作用Interaction terms 交互作用项Intercept 截距Interpolation 内插法Interquartile range 四分位距Interval estimation 区间估计Intervals of equal probability 等概率区间Intrinsic curvature 固有曲率Invariance 不变性Inverse matrix 逆矩阵Inverse probability 逆概率Inverse sine transformation 反正弦变换Iteration 迭代Jacobian determinant 雅可比行列式Joint distribution function 分布函数Joint probability 联合概率Joint probability distribution 联合概率分布K means method 逐步聚类法Kaplan-Meier 评估事件的时间长度Kaplan-Merier chart Kaplan-Merier图Kendall's rank correlation Kendall等级相关Kinetic 动力学Kolmogorov-Smirnove test 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis 峰度Lack of fit 失拟Ladder of powers 幂阶梯Lag 滞后Large sample 大样本Large sample test 大样本检验Latin square 拉丁方Latin square design 拉丁方设计Leakage 泄漏Least favorable configuration 最不利构形Least favorable distribution 最不利分布Least significant difference 最小显著差法Least square method 最小二乘法Least-absolute-residuals estimates 最小绝对残差估计Least-absolute-residuals fit 最小绝对残差拟合Least-absolute-residuals line 最小绝对残差线Legend 图例L-estimator L估计量L-estimator of location 位置L估计量L-estimator of scale 尺度L估计量Level 水平Life expectance 预期期望寿命Life table 寿命表Life table method 生命表法Light-tailed distribution 轻尾分布Likelihood function 似然函数Likelihood ratio 似然比line graph 线图Linear correlation 直线相关Linear equation 线性方程Linear programming 线性规划Linear regression 直线回归Linear Regression 线性回归Linear trend 线性趋势Loading 载荷Location and scale equivariance 位置尺度同变性Location equivariance 位置同变性Location invariance 位置不变性Location scale family 位置尺度族Log rank test 时序检验Logarithmic curve 对数曲线Logarithmic normal distribution 对数正态分布Logarithmic scale 对数尺度Logarithmic transformation 对数变换Logic check 逻辑检查Logistic distribution 逻辑斯特分布Logit transformation Logit转换LOGLINEAR 多维列联表通用模型Lognormal distribution 对数正态分布Lost function 损失函数Low correlation 低度相关Lower limit 下限Lowest-attained variance 最小可达方差LSD 最小显著差法的简称Lurking variable 潜在变量Main effect 主效应Major heading 主辞标目Marginal density function 边缘密度函数Marginal probability 边缘概率Marginal probability distribution 边缘概率分布Matched data 配对资料Matched distribution 匹配过分布Matching of distribution 分布的匹配Matching oftransformation 变换的匹配Mathematical expectation 数学期望Mathematical model 数学模型Maximum L-estimator 极大极小L 估计量Maximum likelihood method 最大似然法Mean 均数Mean squares between groups 组间均方Mean squares within group 组内均方Means (pare means) 均值-均值比拟Median 中位数Median effective dose 半数效量Median lethal dose 半数致死量Median polish 中位数平滑Median test 中位数检验Minimal sufficient statistic 最小充分统计量Minimum distance estimation 最小距离估计Minimum effective dose 最小有效量Minimum lethal dose 最小致死量Minimum variance estimator 最小方差估计量MINITAB 统计软件包Minor heading 宾词标目Missing data 缺失值Model specification 模型确实定Modeling Statistics 模型统计Models for outliers 离群值模型Modifying the model 模型的修正Modulus of continuity 连续性模Morbidity 发病率Most favorable configuration 最有利构形Multidimensional Scaling (ASCAL) 多维尺度/多维标度Multinomial Logistic Regression 多项逻辑斯蒂回归Multiple parison 多重比拟Multiple correlation 复相关Multiple covariance 多元协方差Multiple linear regression 多元线性回归Multiple response 多重选项Multiple solutions 多解Multiplication theorem 乘法定理Multiresponse 多元响应Multi-stage sampling 多阶段抽样Multivariate T distribution 多元T分布Mutual exclusive 互不相容Mutual independence 互相独立Natural boundary 自然边界Natural dead 自然死亡Natural zero 自然零Negative correlation 负相关Negative linear correlation 负线性相关Negatively skewed 负偏Newman-Keuls method q检验NK method q检验No statistical significance 无统计意义Nominal variable 名义变量Nonconstancy of variability 变异的非定常性Nonlinear regression 非线性相关Nonparametric statistics 非参数统计Nonparametric test 非参数检验Nonparametric tests 非参数检验Normal deviate 正态离差Normal distribution 正态分布Normal equation 正规方程组Normal ranges 正常范围Normal value 正常值Nuisance parameter 多余参数/讨厌参数Null hypothesis 无效假设Numerical variable 数值变量Objective function 目标函数Observation unit 观察单位Observed value 观察值One sided test 单侧检验One-way analysis of variance 单因素方差分析Oneway ANOVA 单因素方差分析Open sequential trial 开放型序贯设计Optrim 优切尾Optrim efficiency 优切尾效率Order statistics 顺序统计量Ordered categories 有序分类Ordinal logistic regression 序数逻辑斯蒂回归Ordinal variable 有序变量Orthogonal basis 正交基Orthogonal design 正交试验设计Orthogonality conditions 正交条件ORTHOPLAN 正交设计Outlier cutoffs 离群值截断点Outliers 极端值OVERALS 多组变量的非线性正规相关Overshoot 迭代过度Paired design 配对设计Paired sample 配对样本Pairwise slopes 成对斜率Parabola 抛物线Parallel tests 平行试验Parameter 参数Parametric statistics 参数统计Parametric test 参数检验Partial correlation 偏相关Partial regression 偏回归Partial sorting 偏排序Partials residuals 偏残差Pattern 模式Pearson curves 皮尔逊曲线Peeling 退层Percent bar graph 百分条形图Percentage 百分比Percentile 百分位数Percentile curves 百分位曲线Periodicity 周期性Permutation 排列P-estimator P估计量Pie graph 饼图Pitman estimator 皮特曼估计量Pivot 枢轴量Planar 平坦Planar assumption 平面的假设PLANCARDS 生成试验的方案卡Point estimation 点估计Poisson distribution 泊松分布Polishing 平滑Polled standard deviation 合并标准差Polled variance 合并方差Polygon 多边图Polynomial 多项式Polynomial curve 多项式曲线Population 总体Population attributable risk 人群归因危险度Positive correlation 正相关Positively skewed 正偏Posterior distribution 后验分布Power of a test 检验效能Precision 精细度Predicted value 预测值Preliminary analysis 预备性分析Principal ponent analysis 主成分分析Prior distribution 先验分布Prior probability 先验概率Probabilistic model 概率模型probability 概率Probability density 概率密度Product moment 乘积矩/协方差Profile trace 截面迹图Proportion 比/构成比Proportion allocation in stratified random sampling 按比例分层随机抽样Proportionate 成比例Proportionate sub-class numbers 成比例次级组含量Prospective study 前瞻性调查Proximities 亲近性Pseudo F test 近似F检验Pseudo model 近似模型Pseudosigma 伪标准差Purposive sampling 有目的抽样QR deposition QR分解Quadratic approximation 二次近似Qualitative classification 属性分类Qualitative method 定性方法Quantile-quantile plot 分位数-分位数图/Q-Q图Quantitative analysis 定量分析Quartile 四分位数Quick Cluster 快速聚类Radix sort 基数排序Random allocation 随机化分组Random blocks design 随机区组设计Random event 随机事件Randomization 随机化Range 极差/全距Rank correlation 等级相关Rank sum test 秩和检验Rank test 秩检验Ranked data 等级资料Rate 比率Ratio 比例Raw data 原始资料Raw residual 原始残差Rayleigh's test 雷氏检验Rayleigh's Z 雷氏Z值Reciprocal 倒数Reciprocal transformation 倒数变换Recording 记录Redescending estimators 回降估计量Reducing dimensions 降维Re-expression 重新表达Reference set 标准组Region of acceptance 承受域Regression coefficient 回归系数Regression sum of square 回归平方和Rejection point 拒绝点Relative dispersion 相对离散度Relative number 相对数Reliability 可靠性Reparametrization 重新设置参数Replication 重复Report Summaries 报告摘要Residual sum of square 剩余平方和Resistance 耐抗性Resistant line 耐抗线Resistant technique 耐抗技术R-estimator of location 位置R估计量R-estimator of scale 尺度R估计量Retrospective study 回忆性调查Ridge trace 岭迹Ridit analysis Ridit分析Rotation 旋转Rounding 舍入Row 行Row effects 行效应Row factor 行因素RXC table RXC表Sample 样本Sample regression coefficient 样本回归系数Sample size 样本量Sample standard deviation 样本标准差Sampling error 抽样误差SAS(Statistical analysis system ) SAS统计软件包Scale 尺度/量表Scatter diagram 散点图Schematic plot 示意图/简图Score test 计分检验Screening 筛检SEASON 季节分析Second derivative 二阶导数Second principal ponent 第二主成分SEM (Structural equation modeling) 构造化方程模型Semi-logarithmic graph 半对数图Semi-logarithmic paper 半对数格纸Sensitivity curve 敏感度曲线Sequential analysis 贯序分析Sequential data set 顺序数据集Sequential design 贯序设计Sequential method 贯序法Sequential test 贯序检验法Serial tests 系列试验Short-cut method 简捷法Sigmoid curve S形曲线Sign function 正负号函数Sign test 符号检验Signed rank 符号秩Significance test 显著性检验Significant figure 有效数字Simple cluster sampling 简单整群抽样Simple correlation 简单相关Simple random sampling 简单随机抽样Simple regression 简单回归simple table 简单表Sine estimator 正弦估计量Single-valued estimate 单值估计Singular matrix 奇异矩阵Skewed distribution 偏斜分布Skewness 偏度Slash distribution 斜线分布Slope 斜率Smirnov test 斯米尔诺夫检验Source of variation 变异来源Spearman rank correlation 斯皮尔曼等级相关Specific factor 特殊因子Specific factor variance 特殊因子方差Spectra 频谱Spherical distribution 球型正态分布Spread 展布SPSS(Statistical package for the social science) SPSS统计软件包Spurious correlation 假性相关Square root transformation 平方根变换Stabilizing variance 稳定方差Standard deviation 标准差Standard error 标准误Standard error of difference 差异的标准误Standard error of estimate 标准估计误差Standard error of rate 率的标准误Standard normal distribution 标准正态分布Standardization 标准化Starting value 起始值Statistic 统计量Statistical control 统计控制Statistical graph 统计图Statistical inference 统计推断Statistical table 统计表Steepest descent 最速下降法Stem and leaf display 茎叶图Step factor 步长因子Stepwise regression 逐步回归Storage 存Strata 层〔复数〕Stratified sampling 分层抽样Stratified sampling 分层抽样Strength 强度Stringency 严密性Structural relationship 构造关系Studentized residual 学生化残差/t化残差Sub-class numbers 次级组含量Subdividing 分割Sufficient statistic 充分统计量Sum of products 积和Sum of squares 离差平方和Sum of squares about regression 回归平方和Sum of squares between groups 组间平方和Sum of squares of partial regression 偏回归平方和Sure event 必然事件Survey 调查Survival 生存分析Survival rate 生存率Suspended root gram 悬吊根图Symmetry 对称Systematic error 系统误差Systematic sampling 系统抽样Tags 标签Tail area 尾部面积Tail length 尾长Tail weight 尾重Tangent line 切线Target distribution 目标分布Taylor series 泰勒级数Tendency of dispersion 离散趋势Testing of hypotheses 假设检验Theoretical frequency 理论频数Time series 时间序列Tolerance interval 容忍区间Tolerance lower limit 容忍下限Tolerance upper limit 容忍上限Torsion 扰率Total sum of square 总平方和Total variation 总变异Transformation 转换Treatment 处理Trend 趋势Trend of percentage 百分比趋势Trial 试验Trial and error method 试错法Tuning constant 细调常数Two sided test 双向检验Two-stage least squares 二阶最小平方Two-stage sampling 二阶段抽样Two-tailed test 双侧检验Two-way analysis of variance 双因素方差分析Two-way table 双向表Type I error 一类错误/α错误Type II error 二类错误/β错误UMVU 方差一致最小无偏估计简称Unbiased estimate 无偏估计Unconstrained nonlinear regression 无约束非线性回归Unequal subclass number 不等次级组含量Ungrouped data 不分组资料Uniform coordinate 均匀坐标Uniform distribution 均匀分布Uniformly minimum variance unbiased estimate 方差一致最小无偏估计Unit 单元Unordered categories 无序分类Upper limit 上限Upward rank 升秩Vague concept 模糊概念Validity 有效性VARP (Variance ponent estimation) 方差元素估计Variability 变异性Variable 变量Variance 方差Variation 变异Varimax orthogonal rotation 方差最大正交旋转Volume of distribution 容积W test W检验Weibull distribution 威布尔分布Weight 权数Weighted Chi-square test 加权卡方检验/Cochran检验Weighted linear regression method 加权直线回归Weighted mean 加权平均数Weighted mean square 加权平均方差Weighted sum of square 加权平方和Weighting coefficient 权重系数Weighting method 加权法W-estimation W 估计量W-estimation of location 位置W估计量Width 宽度Wilcoxon paired test 威斯康星配对法/配对符号秩和检验Wild point 野点/狂点Wild value 野值/狂值Winsorized mean 缩尾均值Withdraw 失访Youden's index 尤登指数Z test Z检验Zero correlation 零相关Z-transformation Z变换。
Geophys.J.Int.(2007)170,1089–1094doi:10.1111/j.1365-246X.2006.03505.xG J I S e i s m o l o g yFA S T T R A C K PA P E RAbsolute S -velocity estimation from receiver functionsL.Svenningsen and B.H.JacobsenDepartment of Earth Sciences,University of Aarhus,Høegh-Guldbergs Gade 2,8000Aarhus C,Denmark.E-mails:lasse.svenningsen@geo.au.dk (LS);bo@geo.au.dk (BHJ)Accepted 2007May 23.Received 2007May 18;in original form 2006December 22S U M M A R YWe present a novel method to recover absolute S velocities from receiver functions.For a homogeneous half-space the S velocity can be calculated from the horizontal slow-ness and the angle of surface particle motion for an incident P wave.Generally,the calcu-lated S velocity is an apparent half-space value which depends on model inhomogeneity and P -waveform.We therefore,suggest to calculate such apparent half-space S velocities from low-pass filtered (smoothed)receiver functions using a suite of filter-parameters,T .The use of receiver functions neutralize the influence of the P -waveform,and the successive low-pass filterings emphasize the variation of S velocity with depth.We apply this V S ,app .(T )technique to teleseismic data from three stations:FUR,BFO and SUM,situated on thick sediments,bedrock and the Greenland ice cap,respectively.The ob-served V S ,app .(T )curves indicate the absolute S velocities from the near surface to the uppermost mantle beneath each station,clearly revealing the different geological environments.Applica-tion of linearized,iterative inversion quantify these observations into V S (z )models,practically independent of the S -velocity starting model.The obtained models show high consistency with independent geoscientific results.These cases provide also a general validation of the V S ,app .(T )method.We propose the computation of V S ,app .(T )curves for individual three-component broad-band stations,both for direct indication of the S velocities and for inverse modelling.Key words:absolute velocity,apparent incidence angle,free surface,receiver function,S velocity.1I N T R O D U C T I O NIn applied receiver function analysis it is often stated that receiver functions are not sensitive to the absolute levels of the S veloc-ity (e.g.Ammon et al.1990;Kind et al.1995;Schlindwein 2006;Tomlinson et al.2006).In the present paper,we show that this is not entirely correct.We present a simple transform which clearly emphasizes the absolute S -velocity information present in receiver functions.The effect of the free surface on an incoming teleseismic P wave plays a key role in this method.A plane P wave incident on a free surface is reflected as a P wave and a converted SV wave.The particle motion (or polariza-tion)observed by a three-component seismograph on this surface is the superposition of the incoming and the two outgoing waves.As a result the apparent incidence angle (i P )defined by the surface particle motion is different from the true P wave incidence angle (i P ).The relation between true and apparent incidence angles was early quantified in Wiechert (1907,eq.128)(see also e.g.Nuttli &Whitmore 1961)from which follows sin(12i P)V S =sin(i P )V P=p ,(1)where V P and V S are compressional and shear velocities of thehalf-space and p the horizontal slowness (ray parameter)of the P wave.Eq.(1)can be rearranged toV S =sin 12i Pp ,(2)which defines the half-space S velocity as a function of the observed apparent incidence angle and slowness of a P wave.No assumptions are made concerning V P or V P /V S .Bostock &Rondenay (1999)derived an equivalent but less simple expression (their eq.A6)from the free-surface transfer matrix of Kennett (1991).For general velocity distributions,the S velocity estimate using eq.(2)is an apparent half-space S velocity,V S ,app .,which depends on the S -and P -velocity structure of the subsurface,the incoming P -waveform and the event slowness and backazimuth.We propose to neutralize the influence of the P -waveform on V S ,app .by estimating i P from (Z ,R )receiver functions instead of raw (Z ,R )data.Further we suggest to estimate i P as a func-tion of a low-pass (smoothing)filter-parameter,T ,resulting in V S ,app .(T )curves that emphasize the absolute S velocity variation with depth.C2007The Authors1089Journal compilation C2007RAS1090L.Svenningsen and B.H.Jacobsen051015t [s]051015t [s]051015t [s]051015t [s]Figure 1.The synthetic (Z ,R )receiver functions for the layer-over-half-space model in Fig.2(a),low-pass filtered (smoothed)using four different filter-parameters,T .The values of T and the resulting V S ,app .(T )estimate are written on each plot and the amplitudes of R RF and Z RF at t =0are marked with red dots.2V S ,app .(T )E S T I M AT I O N T E C H N I Q U E The use of (Z ,R )receiver functions in the estimation of i P yields some advantages relative to estimation of i P from raw records of (Z ,R )particle motion.Receiver function estimation is the decon-volution of the Z component from the R component (R RF )and Z deconvolved from itself (Z RF )performed in either frequency do-main (e.g.Ammon 1991)or time domain (e.g.Petersen et al.1993).Deconvolution neutralizes the incoming P waves,which dominate Z ,so that Z RF is an approximate zero-phase spike with arrival instant at exactly t =0.Therefore,i P can be estimated asi P =arctan R RF (t =0)Z RF (t =0) .(3)To estimate i P as a function of the low-pass filter-parameter T ,the (Z ,R )receiver functions are smoothed in time domain with a squared-cosine shape of width T according toh (t )= cos 2 πt 2Tfor |t |<T 0for |t |≥T .(4)Only the amplitudes of the filtered (Z RF ,R RF )at t =0are relevant(eq.3).Therefore,i P (T )can be computed ef ficiently asi P (T )≡arctan T −T R RF (τ)cos 2 πτ2Td τ T −T Z RF (τ)cos 2 πτ2T d τ .(5)Note that,larger T implies more smoothing so that more and more multiples in fluence the values of the filtered receiver functions at t =0(see Fig.1).Combination of eqs (5)and (2)yields the V S ,app .(T )estimateV S ,app .(T )≡sin 12i P (T ) p.(6)3S Y N T H E T I C V S ,app .(T )R E S P O N S E C U RV E SGiven the estimation procedure of Section 2the V S ,app .(T )response of simple models can be studied.The synthetic (Z ,R )data used are calculated with a propagator matrix approach (e.g.Kennett 1983).This approach includes all multiples,which is important for the syn-thetic V S ,app .(T )estimates to obtain the correct asymptotic behaviour for large T .Poisson –Birch assumptions,which relate V P and ρ(density)to V S (see caption of Fig.2)are made for the V S models used in this section,and the slowness is set to p =6.0s deg −1.3.1Layer-over-half-space 3.1.1Examples for four T valuesFig.1illustrates the synthetic (Z RF ,R RF )estimate for a layer-over-half-space model (Fig.2a)filtered using four values of the filter-parameter T :0.5,2,8and 32s.For each T the resulting V S ,app .(T )value is given.V S ,app .(T =0.5s)equals the S velocity of the upper layer,V S ,1and V S ,app .(T =2s)lies between the S velocity of the upper layer and that of the half-space,V S ,1and V S ,2,respectively.V S ,app .(T =8s)is higher than both V S ,1and V S ,2;V S ,app .(T =32s)is quite close to V S ,2.These differences in estimated V S ,app .(T )are caused by converted arrivals (primary and multiples)present on R RF after P at t =0;successively,more of these arrivals interfere with P at t =0as T is increased.3.1.2The basic V S ,app .(T )curveThe black curve in Fig.2(b)illustrates the V S ,app .(T )response of the model in Fig.2(a)calculated from the synthetic receiver functions using eqs (5)and (6)for a suite of logarithmically distributed T values.The four results of Fig.1for the same model are marked by small circles.Notice the position of the marker at T =8s on the part of the V S ,app .(T )curve that ‘overshoots ’even V S ,2.We observe the following fundamental properties of the basic layer-over-half-space V S ,app .(T )response curve in Fig.2(b):(i)V S ,app .(T )=V S ,1for T <t Ps ,where t Ps is the delay-time of the P -to-S converted phase (Ps )from the layer boundary.Only the direct P contributes to R RF (t =0).(ii)V S ,app .(T )>V S ,1for T >t Ps ,because Ps and possibly several of the multiples interfere with P at R RF (t =0).(iii)V S ,app .(T )>V S ,2for T ∼7t Ps ,where predominantly the strong positive phases Ps and PpPs interfere with P at R RF (t =0).(iv)V S ,app .(T )→V S ,2for large T ,because the positive (Ps and PpPs )and the negative (PpSs and PsSs )main converted phases as well as progressively more of the higher order multiples interfere with P at R RF (t =0).The asymptotic convergence to V S ,2for large T (property iv)can be understood physically by considering the limit where the wave-length relative to the thickness of the upper layer goes to in finity.In this limit only the parameters of the half-space can play a role.For T above ca .20times t Ps ,V S ,app .(T )is generally converged to within 2per cent of V S ,2.However,estimates for such large T are not needed to constrain the asymptotic V S value by inversion (see Section 5).3.2V S ,app .(T )for multiple layersFig.2(c)shows a crust-like model with a sediment layer and crys-talline crust on a mantle half-space.The V S ,app .(T )response of this model is shown in Fig.2(d)as the black curve.Qualitatively,each boundary below the free surface produces a V S ,app .(T )response like the basic one for a layer-over-half-spaceC2007The Authors,GJI ,170,1089–1094Journal compilation C2007RASAbsolute V S from receiver functions1091V S (z) [km/s]z [k m ]0.11 10100V S,app.(T) [km/s]T [s ]0.11 2 1030 100V S (z) [km/s]z [k m ]0.11 10100V S,app.(T) [km/s]T [s ]Figure 2.(a)Illustrates the V S model used to calculate the low-pass filtered receiver functions of Fig.1and the black V S ,app .(T )curve in (b).The four VS ,app .(T )estimates of Fig.1are marked with small circles.T =t Ps for the interface,at 1.2s,is marked as the point where the V S ,app .(T )curve bends away from V S ,1.Notice that the V S ,app .(T )curve overshoots V S ,2with a maximum at 8.5s or ca .7t Ps .(c)illustrates a crust-like model with 2km of sediments,28km of crystalline crust and a mantle half-space.(d)illustrates the V S ,app .(T )response of this model,with t Ps for the two interfaces marked at 0.5and 4.4s,respectively.At these values of T the basic response curves as in (b)would bend away from the S velocity of the layer above the interface.However,the V S ,app.(T )curvedoes not fully converge to V S ,2before bending off towards V S ,3at T =4.4s,t Ps for the lower interface.Poisson –Birch assumptions,V P /V S =√3and ρ=320V P +770,are made for both the model in (a)and (c).The slowness for the black V S ,app .(T )curves equals p =6.0s deg −1,but for comparison also VS ,app .(T )curves for the extreme slowness values p =4.4and 7.6s deg−1are included as red curves.(Fig.2b).In general,the response of multilayered models is well ap-proximated as the superposition of such layer-over-half-space part-responses.For each boundary the part-response is shifted along the logarithmic T -axis by multiplication with a factor related to the total t Ps for that boundary and scaled in the V S ,app .axis to match the velocity contrast.Thus interfaces result in kinks where T equal the interface t Ps and bumps where T ∼7t Ps in an observed V S ,app .(T )curve.These scaling properties make it natural to plot V S ,app .(T )curves on logarithmic T axes and the models on logarithmic z axes.3.3Averaging V S ,app .(T )for different slownessesThe slownesses (p )of the observed teleseismic events used in this article (Section 4)are accurately estimated using the global refer-ence model IASP91(Kennett &Engdahl 1991)and vary from 4.4to 7.6s deg −1.The in fluence of this variation in p on the synthetic V S ,app .(T )response curves of Figs 2(b)and (d)is exempli fied in these figures as the red curves which represent the V S ,app .(T )responses for the two extreme values of p .For both Figs 2(b)and (d)the average of the red curves coincides within drawing accuracy with the black V S ,app .(T )curve which is calculated for p =6.0s deg −1,the average slowness of the two extremes.In general it is a good approxima-tion to model the average V S ,app .(T )for several events of different slowness by V S ,app .(T )computed for the average slowness,that is,1N N i =1V S ,app .(T ,p i )∼=V S ,app . T ,1N N i =1p i.(7)This does not apply to direct or inverse modelling of receiver func-tions,where only narrow bins of slowness are typically averaged.4A P P L I C AT I O N T O O B S E RV E D D ATA The synthetic examples of Section 3clearly illustrate that V S ,app .(T )provides useful information about the absolute S -velocity levels be-neath a single station.To test performance of the method on observed data we estimate V S ,app .(T )curves for three different broad-band stations:F ¨u rstenfeldbruck (FUR),Black Forest Observatory (BFO)and Summit (SUM).These stations represent three very differentgeologic settings which are well understood and previously studiedin detail using a variety of different geophysical methods.Hence the scope of this section is mainly a validation of the V S ,app .(T )method.4.1Station settingsFUR is situated just north of the Alps on relatively thick deposits of Molasse overlain by moraine.BFO is on bedrock in the mountains east of the Rhine Graben.Both stations are part of the German Regional Seismic Network (GRSN).SUM is installed centrally on the thick Greenland ice sheet by the GLATIS project (Dahl-Jensen et al.2003)and is now a semi-permanent GEOFON station renamed to SUMG.4.2Observed V S ,app .(T )Teleseismic events between 50◦and 100◦were used.Figs 3(a)–(c)illustrate the V S ,app .(T )estimates calculated using eqs (5)and (6)from the (Z RF ,R RF )estimates of these events.Both ambient noise and deconvolution noise cause a very conspicuous scatter.To subdue outliers,only estimates within the 68per cent fraction closest to the median (black curve)at each T are plotted as light grey dots.For Gaussian errors this 68per cent fraction equals one standard deviation and the median equals the mean.For non-Gaussian errors the median is a more robust estimate,although the difference is minimal in most cases.4.2.1FUR (109events)The V S ,app .(T )equals ca .1.0km s −1for the lowest T values and increases gradually to 4km s −1at T ≈4s where the curve forms a bump.A second bump at T ≈25s reaches ca .4.7km s −1.The initial and gradually increasing velocity level of V S ,app .(T )indicates soft sediments compacting with depth.The first bump indicates overshoot from a sharp transition to the basement of higher S velocity and the second bump indicates overshoot from Moho thus revealing the crust –mantle transition.C2007The Authors,GJI ,170,1089–1094Journal compilation C2007RAS1092L.Svenningsen and B.H.Jacobsen1 10T [s ]V S,app.(T) [km/s]VS,app.(T) [km/s]VS,app.(T) [km/s]V S(z) [km/s]z [k m ]V S(z) [km/s]V S(z) [km/s]Figure 3.(a)–(c)show V S ,app .(T )estimates for the three stations.For each T the light grey dots mark the 68per cent fraction of the estimates closest to median,shown as the black curve.The red curve is the response of the final inversion model.(d)–(f)illustrate the results of the inversion for each station.The V S (z )starting models are shown as green curves and the final best –fitting models as red curves.A constant S velocity of 2km s −1was chosen as starting model.In (e)two additional blue curves illustrate inversion results for BFO using constant V P /V S ratios of 1.6and 1.9,respectively.4.2.2BFO (85events)For BFO the V S ,app .(T )curve starts at 2.8km s −1and increases smoothly to a moderate bump at V S ,app .(T )≈3.5km s −1for T in the range of 1–3s.Hereafter V S ,app .(T )increases more steeply and forms a second bump at V S ,app .(T )≈5km s −1for T ≈23s.The high initial level of this V S ,app .(T )curve indicates crystalline rocks at the surface.The first bump is overshoot from an increase of the S velocity in the uppermost crust and the second bump is overshoot due to Moho.4.2.3SUM (27events)The V S ,app .(T )curve for SUM is almost constant at 1.7–1.8km s −1for T <ca .0.9s.For higher T values the curve forms a sharp bump at T ≈5.8s reaching 4.4km s −1.A second and barely resolved maximum is indicated for T >30s,reaching ca .5km s −1.The constant part of the V S ,app .(T )curve at 1.7–1.8km s −1clearly reveals the thick ice sheet with an S velocity of glacial ice (Benjumea &Teixido 2001).After the constant part the V S ,app .(T )curve in-creases steeply,thus revealing a t Ps of ca .0.9s for the ice-basement transition which equals T at this bend.The first bump is overshoot due to the ice-basement transition,and the second bump is overshoot related to Moho.5M O D E L L I N G O F V S (z )F R O M V S ,app .(T )We apply standard linearized iterative inversion to quantify simple and yet geologically signi ficant models of the S velocity as a function of depth V S (z ).An observed median V S ,app .(T )curve is modelled by a mode-rate number of horizontal homogeneous layers over a half-space,with suf ficient layers to explain the main features of the observed V S ,app .(T )curve (see Section 4.2).The inversion is performed us-ing weighted linearized least-squares iteration (e.g.Menke 1989,eq.9.11)m i +1=m i + G T C −1obs G +C −1mod −1G T C −1obs [d obs −g (m i )]+C −1mod (m 0−m i ) ,(8)where the vector d obs is the observed V S ,app .(T )median and the vec-tor m 0is the prior model of S velocities and interface positions.m iis the model vector before the iteration step and m i +1is the updated model after the iteration.Relative weighting of data is implemented through C obs which is approximated as a diagonal matrix with ele-ments de fined from the 68per cent fraction centred at the median(see Fig.3a –c).C mod is a diagonal matrix with the uncertainties of m 0which implement possible a priori constraints on interval S velocities and interfaces.The interface positions are parametrized in delay time of the Ps phase,t Ps (e.g.Zhu &Kanamori 2000,eq.2) t Ps = zV −2S −p 2−V −2P −p 2(9)and at each iteration the depth vector,z ,is updated using the opti-mized t Ps and V S parameters in m i .The forward mapping,g ,represents computation of synthetic wave fields which are deconvolved to form synthetic (Z ,R )receiver functions,convolved with the observed average Z RF taken as the basic wavelet and finally inserted in eqs (5)and (6).G is the matrix of partial derivatives computed simply from differences between responses with perturbations of individual parameters.During the iterations G changes slightly.Note that our inversion is performed without any a priori con-straints on V S ,that is,the corresponding diagonal elements of C mod are in finite.To exemplify utilization of the high frequency phase arrivals in the receiver function,as for example,Ps from Moho,we have included one pick of a clear Ps phase for each station (see Fig.4).Such constraints on t Ps for an interface are easily imple-mented with the parametrization used as one non-in finite diagonal element in C mod .01234t [s]01234t [s]01234t [s]Figure 4.Observed mean R RF with picked Ps phases marked by vertical red lines with error bars attached to show the uncertainty estimate.For FUR and BFO the Moho Ps is picked and for SUM the pick is Ps from the base of the ice.Note the different amplitudes at t =0for the stations,which directly indicate the absolute V S level of the near surface:very low at FUR,intermediate at SUM and high at BFO (cf .Section 4.1).C2007The Authors,GJI ,170,1089–1094Journal compilation C2007RASAbsolute V S from receiver functions10935.1Inversion resultsFigs3(d)–(f)illustrate the results of the inversion.In thefirst iteration the interface t Ps delay times arefixed and only V S is optimized.In the following iterations both t Ps and V S are optimized.Thefinal models and their responses(red curves in Fig.3)are practically independent of the S-velocity starting model.To illustrate this we let the inversion start at a constant S velocity of2km s−1(green curves).However,starting at4km s−1yields practically the same final models within two to four iterations.This result is in contrast to important previous studies of receiver function inversion where S velocities were constrained by the starting model(Ammon et al. 1990;Kind et al.1995).The latter study also used tight constraints on the parameters of the mantle half-space.The V P/V S values were assumed to be1.8for sediments and the mantle,1.73for the crystalline crust and2.2for ice.The effect of these choices on the inferred V S(z),which is analysed in Section6, is rather small.The results of the linearized inversion quantify the significant geological features expected from direct inspection of the three ob-served V S,app.(T)median curves(Section4.2).For FUR the inversion required three interfaces in addition to Moho to reproduce the main features of the observed median V S,app.(T)curve.For BFO only two additional interfaces were needed,whereas for SUM the observed V S,app.(T)median curve was wellfitted with only an ice layer,a crystalline crust and a mantle half-space.In general,our inversion results agree well with models obtained by other studies in the vicinity of FUR,BFO and SUM.For FUR Kind et al.(1995)obtained a gradual increase of V S starting at around1km s−1for the near surface increasing to above3km s−1 at3km depth.Our inversion result(Fig.3d)has two layers with S velocities corresponding to sediments,0.7and1.8km s−1,respec-tively.Below the interface at2.1km depth V S increases to above 3km s−1.This result agrees well with the ca.2.5km of sediments published in Tr¨u mpy&Dal Piaz(1992)and in Hurtig et al.(1992) for the position of FUR.For the crystalline crust below FUR Kind et al.(1995)obtained an almost constant and quite high V S of ca.3.8km s−1and a Moho depth of32km.Our results indicate a crust with an interface at6.1 km,a Moho depth of30km and S velocities of3.0and3.6km s−1, respectively,for the upper and lower crustal layer.The resulting average V S of the crystalline crust is3.5km s−1and the ave-rage of the entire crust is3.4km s−1.This is consistent with a crustal average V S of3.4–3.6km s−1obtained for the region of FUR and BFO using dispersion of Rayleigh waves(Pasyanos& Walter2002,Fig.9d).The Moho depth obtained for FUR is also consistent with the30–32km in the Moho depth map of Ziegler& D´e zes(2005).The Moho depth obtained for BFO is24km(Fig.3e)which com-pares very well to the22–24km found by Kind et al.(1995)and in the map of Ziegler&D´e zes(2005).Our inversion result yields crustal interfaces at0.7and7.6km which agrees well with inter-faces at1km and ca.7km obtained by(Kind et al.1995)who has an additional interface at14km which is not needed to ex-plain the V S,app.(T)data.The S velocity of the thin surface layer (2.2km s−1)matches well with that of Kind et al.(1995).For the crustal layers our velocities of3.2and3.6km s−1are slightly (0.1–0.2km s−1)higher than those of Kind et al.(1995).Still the crustal average V S of3.5km s−1we obtain is consistent with the surface wave inversion results of Pasyanos&Walter (2002).For FUR and BFO we obtain relatively well-constrained upper-mantle S velocities of4.5–4.6km s−1without applying any a priori S velocity information.These values are slightly higher but agree well with the uppermost mantle S velocity of4.47km s−1in the global reference model IASP91(Kennett&Engdahl1991).Our result is also consistent with uppermost mantle S velocities in southern Germany of4.3–4.6km s−1obtained by Pasyanos&Walter(2002) and4.4–4.5km s−1at40km depth obtained by Friederich(1998). The inversion result for SUM(Fig.3f)yields an ice thickness of 3.1km with an S velocity of1.7km s−1,which is within the range expected for glacial ice(Benjumea&Teixido2001).The obtained ice thickness is very consistent with the3053m obtained in the GISP2ice core drilling near SUM(Gow et al.1997).The depth of Moho for SUM obtained by Dahl-Jensen et al.(2003)is ca.50km compared to our inversion result of53km.The V S obtained for the crystalline crust is3.8km s−1,which is quite well constrained by the high overshoot at T equal to5–6s.This result is also consistent with a high average crustal V P of6.7km s−1obtained by combined land-sea seismic refraction experiments west of SUM in the Scoresby sund region(Mandler&Jokat1998)where also large crustal thicknesses (up to48km)were obtained.For a V P/V S ratio in the range1.7–1.8a V S of3.7–3.9km s−1corresponds to the average V P of that study.From inversion of surface wave dispersion curves Darbyshire et al.(2004)obtained a relatively high S velocity(up to ca. 5km s−1)in the uppermost mantle(50–100km depth)beneath central Greenland.This unusually high result is consistent with our result of4.9km s−1obtained for SUM although our mantle velocity for SUM is not very well constrained due to the larger scatter of V S,app.(T)at T values greater than ca.10s(see Fig.3c).6E R R O R S O U RC E S A N DA P P L I C AT I O N P E R S P E C T I V E SThe earthquake distances used(Section4.2)yield minimum time delays between the phases P and PP of ca.115s,posing an upper limit to the values of T.For T below this limit the PcP phase still might interfere.However,this phase is much weaker than P and typically disregarded in standard receiver function estimation which forms the basis of the V S,app.(T)method.The assumptions of V P/V S ratios in model layers influence the inversion of the V S,app.(T)curves.This error source may be as-sessed from Fig.3(e)where the data from BFO were also inverted using a constant V P/V S ratio equal to1.6and1.9(blue curves). Mainly the depths are influenced by the choice of V P/V S whereas the difference in the V S levels are very small.Thus,even for such very large variations in V P/V S the S-velocity structure of the crust–mantle is by no means masked.We also note that the RMS residual for the response of thefinal models obtained using1.6and1.9are18 and25per cent higher than the residual obtained using the preferred V P/V S ratios,although visually theirfit were still reasonable.This indicates that to some degree information on V P/V S can also be constrained using V S,app.(T).However,inverting for both V S,depths and V P/V S would render the inversion much more non-linear and prone to non-uniqueness.In V S,app.(T)estimation the best accuracy is expected for broad-band stations with many high-quality events.By experience,events below magnitude ca.6.5are often influenced by long periodic noise (tens to hundreds of seconds)due to their lower signal strength.The level of this noise is quite site dependent and is a main contributor to the large scatter at high T values.However,with many events available the V S,app.(T)median is a very robust estimate.C 2007The Authors,GJI,170,1089–1094 Journal compilation C 2007RAS1094L.Svenningsen and B.H.JacobsenFor temporary stations,the availability of events with broad frequency-information may pose a limitation.With high frequencies available,as for local earthquakes,the near-surface S-velocity strat-ification may be resolved in detail so that the V S,app.(T)method may also be an important supplement to site-effect modelling in earth-quake hazard studies.7C O N C L U S I O NWe have presented a novel and simple method to emphasize the information on absolute S velocities present in receiver functions. The method is based on estimation of P-wave angles of surface particle motion from low-passfiltered(Z,R)receiver functions at t=0.These estimates and the P-wave slowness are combined in an expression for the free-surface effect to produce estimates of appar-ent half-space S velocity as a function of the low-pass(smoothing)filter-parameter,T.For synthetic data our results show that the V S,app.(T)method recovers the absolute levels of the S velocity from the near-surface to the uppermost mantle beneath a single three-component broad-band station.The V S,app.(T)method was validated by application to observed data from three different broad-band stations with well studied geological settings.Significant crustal features beneath each of the stations stand out in the observed V S,app.(T)curves,with the absolute level of the S velocities clearly emphasized.The V S(z)models for the crust and uppermost mantle obtained using linearized inversion quantify the features indicated by visual inspection of the V S,app.(T) curves.Our inversion results,which were obtained without prior con-straints on V S,are in good agreement with independent results ob-tained using other methods.These methods include drilling,seismic reflection/refraction,Rayleigh wave dispersion analysis and clas-sical receiver function modelling/inversion using narrow a priori velocity constraints.Thus,we conclude that when a broad frequency-band is preserved in(Z,R)receiver functions,it is,indeed,possible to derive the absolute values of S velocity from the near surface to the uppermost mantle without relying on prior velocity values or supplementary data like surface wave-dispersion.Thesefindings contrast previous influential studies of receiver function inversion where S velocities were constrained by starting models and a priori mantle parameters. 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