Lecture04 Georeferencing
Others are based on ordering
E.g. street addresses in most parts of the world order houses along streets
Others are only nominal
Placenames do not involve ordering or measuring
Metric references
Essential to the making of maps and the display of mapped information in GIS Provide the potential for infinitely fine spatial resolution (provided we have sufficiently accurate measuring devices) From measurements of two or three locations it is possible to compute distances
Linear Referencing
A system for georeferencing positions on a road, street, rail, or river network Is closely related to street address but uses an explicit measurement of distance rather then the much less reliable surrogate of street address number Combines the name of the link with an offset distance along the link from a fixed point, most often an intersection
Lecture 4: Georeferencing
Thanks to Joana Barros: Birkbeck College, London
Georeferencing
„To georeference‟ the act of assigning locations to atoms of information Is essential in GIS, since all information must be linked to the Earth‟s surface The method of georeferencing must be: Unique, linking information to exactly one location Shared, so different users understand the
Georeferencing systems
Placenames Postal addresses and postal codes Linear referencing systems Cadastres Latitude and longitude Projections and coordinate systems The Global Positioning System
meaning of a georeference
Persistent through time, so today‟s
georeferences are still meaningful tomorrow
Uniqueness
A georeference may be unique only within a defined domain, not globally
Users of Linear Referencing
Transportation authorities To keep track of pavement quality, signs, traffic conditions on roads Police To record the locations of accidents
Principal meridians: Geographers lines
Township and Range
Latitude and Longitude
The most comprehensive and powerful method of georeferencing
Provides potential for very fine spatial resolution Allows distance to be computed between pairs of locations Supports other forms of spatial analysis
Georeferences as Measurements
Some georeferences are metric
They define location using measures of distance from fixed places
E.g. distance from the Equator or from the Greenwich Meridian
Useful for mapping
Postcodes in Canada
Forward Sortation Areas (FSA)
The first three characters of the six-character postcode form the FSA
Central part of the Toronto metropolitan region
There are many instances of Springfield in the U.S., but only one in any state The meaning of a reference to London may depend on context, since there are smaller Londons in several parts of the world
Cadastral Maps
Defined as the map of land ownership in an area, maintained for the purposes of taxing land, or of creating a public record of ownership
Gould/Tobler‟s experiment (See CSISS Classics)
Where do postal addresses fail as georeferences?
In rural areas
Urban-style addresses have been extended recently to many rural areas
Placenames
The earliest form of georeferencing
And the most commonly used in everyday activities
Many names of geographic features are universally recognized
Others may be understood only by locals
Names work at many different scales
From continents to small villages and neighborhoods
Names may pass out of use in time
Defined in many countries
E.g. ZIP codes in the US
Hierarchically structured
The first few characters define large areas Subsequent characters designate smaller areas Coarser spatial resolution than postal address
Problem Cases
Locations in rural areas may be a long way from an intersection or other suitable zero point Pairs of streets may intersect more than once Measurements of distance along streets may be inaccurate, depending on the measuring device, e.g. a car odometer
Uses a well-defined and fixed reference frame
Based on the Earth‟s rotation and center of mass, and the Greenwich Meridian
For natural features
Lakes, mountains, and rivers cannot ses
When numbering on streets is not sequential
E.g. in Japan
Postcodes as Georeferences
ZIP Code Boundaries in the US
ZIP code boundaries are a convenient way to summarize data in the US. The dots on the left have been summarized as a density per square mile on the right
Chap4 构造特征
计算机辅助工业设计系列课程——Pro/Engineer Wildfire应用教程
三.关于其它圆角方式（yuanjiao.PRT） 1)Edge Chain eg4:长方体 2)Surf-Surf eg5: 3)Edge-Surf （先选曲面再选曲线） eg6: 4)多个圆角交汇于一点，圆角区域过渡的问题
孔的肩部深度 钻孔深度（尖部深度） 沉头 埋头
计算机辅助工业设计系列课程——Pro/Engineer Wildfire应用教程
§4-3 圆角特征
二. 各类圆角的创建
创建恒定倒圆角
可以添加或去除“设置” 可以添加或去除“参照” 要定义半径，可拖动半径图柄至所需距离
创建可变倒圆角
在半径的图柄之上，右键单击鼠标，然后从快捷菜单中选取 “添加半径”，在快捷菜单中选取“删除”(Delete)，可删 除半径 半径值的位置设置 使用快捷菜单中的“成为可变”(Make Variable)，可将 现有“恒定”倒圆角转换为“可变”倒圆角
§4-2 打孔特征(Hole)
计算机辅助工业设计系列课程——Pro/Engineer Wildfire应用教程
§4-2 打孔特征
三. Sketched Hole 1. 步骤： 1) 孔的类型为“草绘”（而不是“简单”）再点草绘图标 进入草绘。 2) 建立孔的旋转剖面 3) 选择孔要放置的位置 4) 指定孔中心轴的位置 Eg5:-1-P112-5-8
计算机辅助工业设计系列课程——Pro/Engineer Wildfire应用教程
Chap 4
主要内容
第一节 概述
构造特征
第二节 打孔特征(Hole) 第三节 圆角特征(Round)
Lec4_Introduction_to_Quantum_Mechanics
Semiconductor physics II
Introduction to Quantum Mechanics
1
What is Quantum Mechanics
Classical theoretical physics -- Newton's laws of motion. -- The motion of large objects, such as planets and satellites. Quantum mechanics -- the behaviors of electrons and high-frequency electromagnetic waves. Wave mechanics: The formulation of quantum mechanics to describe behavior and characteristics of these electrons. -- Schrodinger wave equation
5
Maximum kinetic energy
Tmax
Quanta －thermal radiation emitted from a heated surface in discrete packets of energy －Postulated by Planck in 1900 The energy of these quanta
13
Using the technique of separation of variables
Ψ ( x, t ) = ψ ( x )φ (t )
a function of the position
2
Principles of Quantum Mechanics
Lecture_4
autcln summary file
• One-way post-fit residual statistics – Only in postfit autcln summary – Gives RMS in mm
• by station and each satellite for a station • Normal values are 3-10 mm • >10 mm is not good
Nov-4-02 GAMIT/GLOBK Tutorial 4 5
Analyzing a solution: bias parameters
• Number of biases fixed – Fixed bias have no sigmas in Q-file – 608 B1L1 SMYC-TBLE 4- 2 0.0000000000 10.0000 \ – 609*B1L1 SMYC-TBLE 4- 5 0.0000000000 2.3133 \ 0.0367 -2.31330402 – The * means not fixed and sigma is given • Adjustments – parameters should not change much
Nov-4-02 GAMIT/GLOBK Tutorial 4 7
autcln output
• autcln.out.Z – full output – automatically compressed – use uncompress or use zcat to view – Lists actions taken by autcln • autcln.prefit.sum • autcln.post.sum – Summaries – Look at these
lecture 4
i 1 j 1 r k
O
ij
E ij E ij
2
Contingency tables: Chi-square test
• Testing procedure (5 steps) • 1) Hypothesis • H0: the distribution criteria are statistically independent • 2) Sample distribution • Chi-square distribution • Degrees of freedom: (k-1)(r-1)
Single linear regression: correlation
Single linear regression: relation between b and r
Regression coefficient b presents the character of the relation, but tells nothing about the strength
Ecellij Prowi Pcolumn totaln j
Men Income (* € 1000,-) low 20 middle 20 - 40 High > 40 Total Oij 25 30 35 90 Eij 27 33 30 90 Women Oij Eij 20 18 25 22 15 20 60 60 Total 45 55 50 150
Contingency tables: example
Sex Women abs. % 20 33 25 42 15 25 60 100
Income (* €1000,-) low ( 20) middle (20-40) high (> 40) Total abs. 25 30 35 90
Lecture4
•Solve line by line with TDMA •Use SOR to overrelax
DO ITERATIONS = 1 , MANY DO J = 1 , NY CALCULATE COEFFICIENTS FOR I = 1 , NX USE TDMA TO SOLVE FOR Tcalci,j, i=1,NX USE SOR: NEXT J CALCULATE RESIDUAL ERROR NEXT ITERATIONS
Ti +1, j + Ti −1, j + Ti , j +1 + Ti , j −1 − 4Ti , j +
∆x 2 ∂ 4T ∆y 2 ∂ 4T error = + 4 12 ∂x 12 ∂y 4
Co D.M. Christopher
Computational Methods in Heat Transfer, D.M. Christopher
Finite Differencing (uniform grid)
∂ ∂T ∂ ∂T & = 0dx dy ∫∫ ∂x (λ ∂x ) + ∂y (λ ∂y ) + Q
•Diagonal (not tridiagonal) •Symmetric (usually) •Sparse (many zeros)
Computational Methods in Heat Transfer, D.M. Christopher
Solution Methodology
• Direct solver
λ
4
-20
4
ai ≥ ∑ an
(n ≠ i)
读有限元Fortran程序笔记范文
读有限元程序笔记1.ALLOCATABLE::COORD(:,:),PROPS(:,:,:) !声明两个可变大小的数组，COORD(:,:)是二维数组，PROPS(:,:,:)是三维数组。
2.Fortran程序行首为C代表改行为注释，不会被编译3.全局变量（common），不同的程序之间，也就是在不同的函数之间或者是主程序跟函数之间，除了可以通过传递参数的方法来共享内存，还可以通过“全局变量”来让不同程序中声明出来的变量使用相同的内存位置。
4.Dimensional维的，viscoplastic塑性的，elastic有弹力的，finite有限的，element元素，program程序。
5.THREE DIMENSIONAL ELASTIC-VISCOPLASTIC FINITE ELEMENT PROGRAM三维弹塑性有限元程序6.Module可以用来封装程序模块，通常是用来把程序中，具备相关功能的函数及变量封装在一起。
程序在开始定义了一个module模块，在模块中定义了MXKKK=，MXGSJ=1000，MXGSJ=1000三个常量（PARAMETER表示常量），并且每个常量都赋了值。
在module模块中定义了NELEM,NPOIN,NPROP,MXDFN,NSTEP,IDEVP,IDDP,LTYPE以及NFIX1,NPL,NVL,NSL,NHL,NTL,IDCVG,NTOTV,NKK以及DTIME,TOLER,SCALE,DSCALE这些全局变量（common表示全局变量），定义了ICM(3,8),CGAUS(2),VSHAP(8,8),DERIV(3,8,8)以及POSGP(3),COPG(3),EJ(3,3),EJACI(3,3),R(8,8)这些维数与大小都确定的全局数组变量，定义了COORD(:,:),PROPS(:,:,:)以及STRSG(:,:,:),DJ(:,:),CARTD(:,:,:,:)以及TRANJ(:,:,:,:),DJRMX(:,:,:)以及DREMX(:,:,:),DJEMX(:,:,:,:)以及CREMX(:,:,:),CJEMX(:,:,:,:)以及MELEM(:,:),MPROP(:),ISSOR(:,:),NNDEX(:)以及MPFIX(:,:),MPSJ(:),MMATP(:),MPIV(:)以及TSTIF(:)以及ADISP(:),TDISP(:),ALOAD(:)以及PSNBR(:,:,:),PSNBJ(:,:)以及PSTNR(:,:,:),PSTNJ(:,:)以及STRSP(:,:),STRSJ(:,:)这些维数确定但是大小不确定的可变大小的数组，ALLOCATABLE表示可变大小的数组变量。
FLUENT官方培训教材完整版幻灯片
100%
简化模型
在保证计算精度的前提下，合理 简化模型以降低计算量。
80%
设定边界条件
根据实际问题，设定模型的边界 条件，如入口、出口、壁面等。
网格划分策略及技巧
选择合适的网格类型
根据模型特点选择合适的网格 类型，如结构化网格、非结构 化网格等。
求解策略
采用有限体积法进行数值求解，结合适当的 湍流模型和热传导方程进行迭代计算。
结果分析
展示温度场、热流量和努塞尔数等关键结果 ，评估热设计方案的合理性。
07
总结回顾与拓展学习资源推荐
本次培训内容总结回顾
FLUENT软件基础操作
介绍了FLUENT软件界面、基本功能 、操作流程等。
前处理与网格划分
演示技巧
分享动画演示的实用技巧，如选择合适的帧率、添加背景音乐和解 说等。
输出格式
支持多种动画输出格式，如AVI、MP4等，方便在不同场合进行演 示和分享。
数据提取、导出及报告编写
数据提取
从计算结果中提取关键数据，如某点的速度、压力值等。
数据导出
将提取的数据导出为Excel、CSV等格式，便于进一步分析 和处理。
求解策略
采用有限体积法进行数值求解 ，结合湍流模型捕捉流动细节 ，提高计算精度。
结果分析
展示管道内的速度场、压力场 和流量分布等关键结果，评估
管道设计的合理性。
案例三：多相流混合过程模拟
问题描述
多相流体（如气液、气 固等）在混合过程中的 相互作用和流动特性。
建模方法
在FLUENT中建立多相 流模型，定义各相的物 理属性和相互作用机制
lecture04
functions: f1, f2 represented by function nodes
dependencies represented by edges
5 7
LDPC Code
x · HT=0
0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1
© ftw. 2004
9
Bad News
The tree assumption for random LDPC codes is only fulfilled if the block length goes to infinity. For finite length codes, the graph usually contains closed loops (cycles). These cycles cause correlations between the messages and the assumption of independent observations is not fulfilled. Conclusion: The Sum-Product algorithm is suboptimal.
1 2 3 4 5 C 6 7 D 8 9 E 10 A
georeferencing
一．影像校准
所有图件扫描后都必须经过扫描纠正，对扫描后的栅格图进行检查，以确保矢量化工作顺利进行。
对影像的校准有很多方法,下面介绍一种常用方法。
1．打开ArcMap，增加Georeferncing工具条。
2．把需要进行纠正的影像增加到ArcMap中，会发现Georeferncing工具条中的工具被激活。
3．在校正中我们需要知道一些特殊点的坐标。
通过读图，我们知道坐标的点就是公里网格的交点，我们可以从图中均匀的取几个点。
一般在实际中，这些点应该能够均匀分布。
4．首先将Georeferncing工具条的Georeferncing菜单下Auto Adjust不选择。
5．在Georeferncing工具条上，点击Add Control Point按钮。
6．使用该工具在扫描图上精确到找一个控制点点击，然后鼠标右击输入该点实际的坐标位置，如下图所示：
7．用相同的方法，在影像上增加多个控制点，输入它们的实际坐标。
8．增加所有控制点后，在Georeferencing菜单下，点击Update Display。
9．更新后，就变成真实的坐标。
10．在Georeferencing菜单下，点击Rectify，将校准后的影像另存。
后面我们的数字化工作是对这个校准后的影像进行操作的。
英文文章
ORIGINAL PAPERLower Carboniferous post-orogenic granites in central-eastern Sierra de Velasco,Sierras Pampeanas,Argentina:U–Pb monazite geochronology,geochemistry and Sr–Nd isotopesPablo Grosse ÆFrank So¨llner ÆMiguel A.Ba ´ez ÆAlejandro J.Toselli ÆJuana N.Rossi ÆJesus D.de la RosaReceived:1October 2007/Accepted:19December 2007/Published online:22January 2008ÓSpringer-Verlag 2008Abstract The central-eastern part of the Sierra de Velasco (Sierras Pampeanas,NW Argentina)is formed by the large Huaco (40930km)and Sanagasta (25915km)granite massifs and the small La Chinchilla stock (292km).The larger granites intrude into Ordovician metagranitoids and crosscut Devonian (?)mylonitic shear zones,whereas the small stock sharply intrudes into the Huaco granite.The two voluminous granites are biotitic-muscovitic and biotitic porphyritic syeno-to monzogranites.They contain small and rounded tonalitic and quartz-dioritic mafic micro-granular enclaves.The small stock is an equigranular,zinnwaldite-and fluorite-bearing monzogranite.The stud-ied granites are silica-rich (SiO 2[70%),potassium-rich (K 2O [4%),ferroan,alkali-calcic to slightly calk-alkalic,and moderately to weakly peraluminous (A/CNK:1.06–1.18Huaco granite, 1.01–1.09Sanagasta granite, 1.05–1.06La Chinchilla stock).They have moderate to strong enrichments in several LIL (Li,Rb,Cs)and HFS (Nb,Ta,Y,Th,U)elements,and low Sr,Ba and Eu contents.U–Pb monazite age determinations indicate Lower Carboniferous crystallization ages:350–358Ma for the Huaco granite,352.7±1.4Ma for the Sanagasta granite and 344.5±1.4Ma for the La Chinchilla stock.The larger granites have similar e Nd values between -2.1and -4.3,whereas the younger stock has higher e Nd of -0.6to -1.4,roughly comparable to the values obtained for the Carboniferous San Blas granite (-1.4to -1.7),located in the north of the sierra.The Huaco and Sanagasta granites have a mainly crustal source,but with some participation of a more primitive,possibly mantle-derived,component.The main crustal component can be attributed to Ordovician peralu-minous metagranitoids.The La Chinchilla stock derives from a more primitive source,suggesting an increase with time in the participation of the primitive component during magma genesis.The studied granites were generated during a post-orogenic period in a within-plate setting,possibly as a response to the collapse of the previous Famatinian oro-gen,extension of the crust and mantle upwelling.They are part of the group of Middle Devonian–Lower Carboniferous granites of the Sierras Pampeanas.The distribution and U–Pb ages of these granites suggests a northward arc-par-allel migration of this mainly post-orogenic magmatism with time.Keywords Carboniferous post-orogenic granites ÁU–Pb monazite geochronology ÁGeochemistry ÁSr–Nd isotopes ÁSierra de Velasco ÁSierras Pampeanas ÁArgentinaP.Grosse (&)Instituto Superior de Correlacio´n Geolo ´gica (CONICET)and Fundacio´n Miguel Lillo,Miguel Lillo 251,4000San Miguel de Tucuma´n,Argentina e-mail:pablogrosse@F.So¨llner Department fu¨r Geo-und Umweltwissenschaften,Ludwig-Maximilians-Universita¨t,Luisenstrasse 37,80333Munich,GermanyM.A.Ba´ez ÁA.J.Toselli ÁJ.N.Rossi Instituto Superior de Correlacio´n Geolo ´gica (CONICET)and Facultad de Ciencias Naturales,Universidad Nacional de Tucuma´n,Miguel Lillo 205,4000San Miguel de Tucuma´n,Argentina J.D.de la RosaDepartamento de Geologı´a,Universidad de Huelva,Campus Universitario El Carmen,21071Huelva,SpainInt J Earth Sci (Geol Rundsch)(2009)98:1001–1025DOI 10.1007/s00531-007-0297-5IntroductionThe Sierras Pampeanas geological province of north-western Argentina contains abundant granitoid massifs generated during the Famatinian orogenic cycle(for details see Rapela et al.2001a;Miller and So¨llner2005).Most of these Famatinian granitoids are related to the main sub-duction phase of this cycle(e.g.Pankhurst et al.2000; Rapela et al.2001a;Miller and So¨llner2005)and have Early-Middle Ordovician ages(e.g.Pankhurst et al.1998, 2000;So¨llner et al.2001;Ho¨ckenreiner et al.2003) (Fig.1a).These granitoids are distributed along two sub-parallel,NNW–SSE trending belts:a main calc-alkaline I-type belt towards the southwest,and an inner peralumi-nous and S-type belt towards the northeast(Fig.1a).Additionally,numerous younger granites of Middle Devonian to Lower Carboniferous age are also present in the Sierras Pampeanas(e.g.Brogioni1987,1993;Rapela et al.1991;Grissom et al.1998;Llambı´as et al.1998; Saavedra et al.1998;Siegesmund et al.2004;Dahlquist et al.2006)(Fig.1a).The genesis of these granites is not well constrained,and they have been alternatively con-sidered as products of a crustal reheating process during a final phase of the Famatinian cycle,(e.g.Grissom et al. 1998;Llambı´as et al.1998;Ho¨ckenreiner et al.2003; Miller and So¨llner2005)or part of a separate cycle called Achalian(e.g.Sims et al.1998;Rapela et al.2001a; Siegesmund et al.2004;Lo´pez de Luchi et al.2007).The Sierra de Velasco is located in the central region of the Sierras Pampeanas(Fig.1a)and consists almost entirely of rocks of granitoid composition,making it the largest granitic massif of this geological province.The Sierra de Velasco granitoids have generally been regarded as part of the Famatinian inner peraluminous S-type belt (e.g.Rapela et al.1990;Toselli et al.1996,2000;Pank-hurst et al.2000),with the exception of the southern portion of the sierra which seems to correspond to the main calc-alkaline I-type belt(Bellos et al.2002;Bellos2005) (Fig.1a,b).However,field studies carried out in the northern(Ba´ez et al.2002;Ba´ez and Basei2005)and central(Grosse and Sardi2005;Grosse et al.2005)parts of the sierra indicate the presence of younger undeformed granites(Fig.1b),possibly belonging to the late-Famatin-ian,or Achalian,granite group.Recent U–Pb age determinations have confirmed that the northern unde-formed granites are of Lower Carboniferous age(Ba´ez et al.2004;Dahlquist et al.2006).The central undeformed granites have yet to be dated.The goal of this study is to determine the absolute ages and the geochemistry of the undeformed granites located in the central part of the Sierra de Velasco.To this end,we have carried out U–Pb dating on monazite and whole-rock elemental and Sr–Nd isotopic geochemical analyses.The obtained data are used to place constraints on the possible magma sources and geotectonic setting of these granites, and to discuss regional implications.Geological setting:the Sierra de VelascoThe Sierra de Velasco is dominated by rocks of granitoid composition.Low grade metamorphic rocks are only present as small outcrops along the easternflank of the sierra(Fig.1b,c).These phyllites and mica schists have been correlated with the La Ce´bila Formation,located in the Sierra de Ambato(Gonza´lez Bonorino1951;Espizua and Caminos1979).Recent discovery of marine fossils in this formation constrains its age to the Lower Ordovician (Verdecchia et al.2007),in agreement with detrital zircon geochronology(Rapela et al.2007).The granitoid units of the Sierra de Velasco have been reviewed and described by Toselli et al.(2000,2005)and Ba´ez et al.(2005).Two groups can be distinguished (Fig.1b):older deformed granitoids(here referred to as metagranitoids)and younger undeformed granites.The metagranitoids are the most abundant rocks.They are weakly to strongly foliated,depending on the degree of deformation.The main variety consists of strongly pera-luminous porphyritic two-mica-,garnet-,sillimanite-and kyanite-bearing meta-monzogranites(Rossi et al.2000, 2005).Subordinate varieties include strongly peraluminous porphyritic biotite–cordierite meta-monzogranites and moderately peraluminous coarse-to medium-grained bio-tite meta-granodiorites and meta-tonalites.In the southern part of the sierra,the main lithologies are metaluminous to weakly peraluminous biotite-hornblende meta-granodior-ites and meta-tonalites(Bellos2005)(Fig.1b).Two U–Pb SHRIMP determinations indicate Lower Ordovician ages for the metagranitoids(481±3Ma,Pankhurst et al.2000; 481±2Ma,Rapela et al.2001b).All of the metagranitoids are cut by several NNW–SSE trending mylonitic shear zones(Fig.1b).No age determi-nations exist of these shear zones in the Sierra de Velasco. However,similar mylonitic shear zones in other areas of the Sierras Pampeanas have been dated,with ages varying between the Upper Ordovician and the Upper Devonian (Northrup et al.1998;Rapela et al.1998;Sims et al.1998; Lo´pez et al.2000;Ho¨ckenreiner et al.2003).The precise Sm–Nd age of402±2Ma(Ho¨ckenreiner et al.2003) obtained on syntectonically grown garnet from mylonites of the Sierra de Copacabana(Fig.1a),which can be traced directly into the Sierra de Velasco(Lo´pez and Toselli 1993;So¨llner et al.2003),can be considered the best age estimate of mylonitization in this range.The undeformed granites crop out in the northern and central-eastern parts of the sierra(Fig.1b).Toselli et al.(2006)have grouped these granites in the Aimogasta batholith.The northern San Blas and Asha granites intrude the older metagranitoids and cross-cut the mylonitic shearzones (Ba´ez et al.2002;Ba ´ez and Basei 2005).They are moderately to weakly peraluminous porphyritic two-mica monzogranites.Existing U–Pb ages are 334±5Ma(conventional U–Pb method on zircon,Ba ´ez et al.2004)and 340±3Ma (U–Pb SHRIMP on zircon,Dahlquistet al.2006)for the San Blas granite,and 344±1Ma(conventional U–Pb method on monazite,Ba´ez et al.2004)for the Asha granite.In restricted areas,the granitic rocks are unconformably overlain by continental sandstones and conglomerates of the Paganzo Group (Salfity and Gorustovich 1984),ofFig.1a General geological map of the Sierras Pampeanas of NW Argentina with the main lithologies;sierras considered in the text are named.b General geology of the Sierra deVelasco;c Geological map of the central part of the Sierra de Velasco showing the Huaco,Sanagasta and La Chinchilla granites,with locations of dated samples;Bt biotite,Ms muscovite,Crd cordierite,Mzgr monzogranite,Ton tonalite,Grd granodioriteUpper Carboniferous to Permian age,deposited during regional uplift of the Sierras Pampeanas.Unconsolidated Tertiary-recent sediments,related to Andean tectonics, locallyfill basins and formfluvial terraces and cones. The Huaco,Sanagasta and La Chinchilla granitesThe central-eastern region of the Sierra de Velasco is formed mainly by two large granitic massifs,the Huaco granite(HG)and the Sanagasta granite(SG)(Fig.1c) (Grosse and Sardi2005).These granites consist of adjacent, sub-elipsoidal bodies with dimensions of approximately 40930km for the HG and25915km for the SG. Additionally,a small stock of around292km,named La Chinchilla stock(LCS),has been recognized in the central area of the HG(Fig.1c)(Grosse et al.2005).The HG and the SG intrude into the older metagranitoids and mylonites and are not deformed.The contacts are sharp and the granites truncate both the structures of the metag-ranitoids and the mylonitic shear zones,and contain enclaves of both of these host rocks.Thesefield relation-ships indicate that the granites are younger than both the crystallization of the metagranitoids and their deformation. The contact between the HG and the SG is irregular and transitional,suggesting that the two granites have similar ages and consist of two coeval magmatic pulses.The transitional area between the two granites is of*100–200m;in Fig.1c the contact between the granites was drawn along this transitional zone.The LCS clearly intrudes into the HG and is thus younger.The contacts are sharp and straight,and aplitic dykes from the LCS com-monly cut through the HG.Both the HG and the SG are rather homogeneous por-phyritic syeno-to monzogranites.They are characterized by abundant K-feldspar megacrysts up to12cm long (generally between2and5cm)set in a medium-to coarse-grained groundmass of quartz,plagioclase,K-feldspar, micas and accessory minerals.The megacrysts are usually oriented,defining a primary magmatic foliation.The HG consists in grayish-white K-feldspar megacrysts (30–36vol.%)and a groundmass of anhedral quartz(25–39%),subhedral plagioclase laths(An10–23)(18–31%), interstitial perthitic K-feldspar(2–14%),dark brown to straw-colored biotite(4–10%)and muscovite(2–6%). Accessory minerals include apatite(up to0.5%),zircon, monazite and ilmenite,all of which are generally associ-ated with,or included in,biotite.The SG contains pink K-feldspar megacrysts(33–37%) that are occasionally mantled by plagioclase generating a Rapakivi-like texture.The groundmass consists in anhedral quartz(23–34%),subhedral plagioclase laths(An18–24) (17–33%),interstitial perthitic K-feldspar(2–17%),and dark brown to straw-colored biotite(3–10%).Muscovite is absent or very scarce(0–2%).Accessory minerals are commonly found included in biotite.Apatite is less abundant than in the HG,whereas zircon,monazite and especially the opaque minerals(both ilmenite and magne-tite)are more frequent.In addition,titanite and allanite are sometimes present.Both the HG and the SG commonly contain small and rounded mafic microgranular enclaves.These generally have ovoid shapes,elongated parallel to the magmaticflow direction.The enclaves arefine-to veryfine-grained equigranular tonalites and quartz-diorites.They contain abundant biotite(15–50%)forming small,subhedral crys-tals.Opaque minerals and acicular apatite are common. The enclaves usually contain much larger xenocrysts of quartz,feldspar or biotite,and have chilled margins,sug-gesting partial assimilation and homogenization with the enclosing granites.Pegmatites and aplites are very common in these gran-ites,specially in the HG.The larger pegmatites are zoned and belong to the rare-element class,beryl type,beryl-columbite-phosphate sub-type with a hybrid LCT-NYF affiliation(Galliski1993;Sardi2005;Sardi and Grosse 2005).The HG also contains a small outcrop of an orbic-ular granite(Quartino and Villar Fabre1962;Grosse et al. 2006b).The LCS is a medium-grained,equigranular to slightly porphyritic,monzogranite.It shows a weak textural zona-tion determined by a progressive increase in grain size towards the center of the stock,where a slight porphyritic texture is present(up to10%of K-feldspar megacrysts). Mineralogically,the LCS consists of quartz(37–42%), plagioclase(almost pure albite,An1–2)(25–33%),K-feld-spar(19–34%),discolored,very pale brown to pale red-brown biotite(4–9%),anhedral and irregularly shaped fluorite(up to1%)and small quantities of zircon,monazite, opaque minerals and very scarce apatite.Beryl is occa-sionally present as euhedral prismatic crystals.Microprobe analyses(Grosse et al.2006a)indicate that the biotites of the HG and the SG have compositions ranging from Fe-biotites to siderophyllites(according to the classification diagram of Tischendorf et al.1997)and have high Fe/(Fe+Mg)ratios(0.76–0.82),typical of evolved granites.In the discrimination diagram of Nachit et al.(1985),they plot in the calc-alkalinefield.Biotites from de LCS have very high Fe/(Fe+Mg)ratios(0.94–0.97)and are Li-rich.They classify mainly as zinnwaldites and also as protolithionites in the classification diagram of Tischendorf et al.(1997).Zircons of the HG and the SG have similar morpholo-gies.They correspond mainly to the S17–19and S22–23 types of Pupin(1980),which are characteristic of calc-alkaline series granites.On the other hand,the zirconsof the LCS are different,with morphologies mostly of the P5-type of Pupin(1980),of primitive alkaline affiliation. The San Blas granite,in the north of the sierra(Fig.1b), has the same zircon typology as the LCS.No previous U–Pb age determinations exist of the HG and the SG,while the LCS has not been previously dated by any method.K–Ar and Rb–Sr geochronological studies have been carried out on granites of the Sierra de Velasco, which in some cases correspond to the HG or SG(see compilation in Linares and Gonza´lez1990).The ages in these studies are very variable,spanning from the Ordo-vician to the Permian,probably due to the inherent problems of the methods used(low closure temperature,Ar loss,etc.).Analytical methodsU–Pb geochronologyU–Pb geochronology was carried out at the Department of Earth-and Environmental Sciences,Ludwig-Maximilians-Universita¨t,Munich,Germany.Heavy mineral concen-trates,mainly zircons and monazites,were obtained using standard crushing,magnetic separation,and heavy-liquid techniques.For each analyzed sample around50monazite crystals were handpicked.Chosen crystals were yellow, translucent,anhedral to subhedral and lacked inclusions and fractures.We chose to analyze monazites because this mineral generally does not contain inherited cores and does not suffer radiogenic Pb loss at low temperatures,both common problems in zircons(see Parrish1990for discussion).Additionally,the closing temperature of monazite,although slightly lower than that of zircon(for details see Romer and Ro¨tzler2001),is sufficiently high to maintain the system unperturbed by low-temperature post-crystallization events.The monazite fractions were cleaned with purified6N HCl,H2O and acetone,and then deposited in Teflon inserts together with a mixed205Pb–233U spike.Subsequently, samples were dissolved in autoclaves,heated at180°C,for 5days using48%HF and subsequently6N HCl.The U and Pb of the samples were separated using small50l l ion exchange columns with Dowex raisin AG198100–200 mesh.The isotopic ratios of Pb and U were determined with a thermal ionization mass spectrometer(TIMS) Finnigan MAT261/262.Pb isotopes were measured in static mode and U isotopes in dynamic mode.Standards (NBS982Pb and U500)were used for measurement con-trol.U–Pb data was treated using the PBDAT1.24(Ludwig 1994)and ISOPLOT/Ex2.49x(Ludwig2001)programs. Errors quoted are at the2r confidence level.The correc-tions for initial non-radiogenic Pb was obtained following the model of Stacey and Kramers(1975).The U decay constants proposed by the IUGS(Steiger and Ja¨ger1977) were used for the age calculations.Mass fractionation was corrected using0.13±0.06%/a.m.u.for Pb and0.05±0.04%per a.m.u for U.Together with the samples,a procedural blank was analyzed to determine the level of contamination.For Pb blank corrections a mean value of 0.2ng and an isotopic composition of208Pb/204Pb=38.14; 207Pb/204Pb=15.63;206Pb/204Pb=18.15was used.Long term measured standards gave values of:NBS982(Pb): 208Pb/206Pb=0.99474±0.00013(0.013%,2rm,n=94); U500(U):238U/235U=1.00312±0.00027(=0.027%, 2r m,n=14).Whole-rock major and trace element geochemistry Whole-rock geochemistry was determined at the universi-ties of Oviedo(major elements)and Huelva(trace elements),Spain.Major elements were analyzed by X-ray fluorescence(XRF)with a Phillips PW2404system using glass beads.The typical precision of this method is better than±1.5%relative.Trace elements were analyzed by inductively coupled plasma mass spectrometry(ICP-MS) with an HP-4500system.Samples were dissolved using a mixture of HF+HNO3(8:3),a second dissolution in HNO3after evaporation andfinal dissolution in HCl.The precision and accuracy for most elements is between5and 10%relative(5–7%for Rb,Sr,Nd and Sm)and was controlled by repeated analyses of international rock stan-dards SARM-1(granite)and SARM-4(norite).Details on the method can be found in de la Rosa et al.(2001).Sr and Nd isotope geochemistrySr and Nd isotope analyses were carried out at the Department of Earth-and Environmental Sciences, Ludwig-Maximilians-Universita¨t,Munich,Germany.The analyzed powders were the same as those used for major and trace element analyses.For the determination of con-centrations and for comparison with the ICP-MS data,a mixed Sm–Nd spike was added to12samples.For the remaining samples,and for all Rb–Sr calculations,the concentrations obtained by ICP-MS were used.Samples(approximately0.1g each)were dissolved on a hot plate(140°C)during36h using a mixture of5ml of HF48%+HNO3(5:1).Sr and REE were separated using ion exchange columns with Dowex AG50W raisin.Nd and Sm were then separated from the total REE fractions using smaller ion exchange columns with bis(2-ethyl-hexyl)phosphoric acid(HDEHP)and Teflon powder.Theisotopic ratios of Sr,Nd and Sm were determined with a thermal ionization mass spectrometer (TIMS)Finnigan MAT 261/262.Standards were used for measurement control (NBS987,AMES Nd and AMES Sm).All errors used are at the 95%(2r )confidence level.Mass fraction-ation was corrected normalizing the isotopic ratios to 88Sr/86Sr =8.3752094for Sr,146Nd/144Nd =0.7219for Nd,and 148Sm/152Sm =0.4204548for Sm.CHUR con-stants used for e Nd calculation were 143Nd/144Nd =0.512638(Goldstein et al.1984)and 147Sm/144Nd =0.1967(Peucat et al.1988).One-step model ages were calculated following Goldstein et al.(1984)(with 143Nd/144Nd (DM)=0.51315and 147Sm/144Nd (DM)=0.217)and two-step model ages were calculated following Liew and Hofmann (1988)(with 143Nd/144Nd (DM)=0.513151,147Sm/144Nd (DM)=0.219and 147Sm/144Nd (CC)=0.12).During the period of analyses,the measured standards gave the following average values:NBS987(Sr):87Sr/86Sr =0.710230±0.000013(0.0018%,2r m ,n =8);AMES (Nd):143Nd/144Nd =0.512131±0.000007(0.0013%,2r m ,n =10);AMES (Sm):149Sm/147Sm =0.91262±0.00016(0.018%,2r m ,n =3).U–Pb monazite geochronologyMonazite fractions of six samples were analyzed,three of which correspond to the Sanagasta granite (SG),two to the Huaco granite (HG),and one to the La Chinchilla stock (LCS).Locations of the analyzed samples are shown in Fig.1c.Table 1shows the analytical results.In the U–Pb concordia diagram (Fig.2),two of the six analyzed samples are concordant whereas the other four are discordant,three of which plot above the concordia (phe-nomenon called ‘‘reverse discordance’’)and one below.Reverse discordance in monazite has been observed by many authors and seems to be a common phenomenon in this mineral (Parrish et al.1990,and references therein).Scha¨rer (1984)suggests that reverse discordances are owed to an excess in 206Pb due to the decay of 230Th,an inter-mediate product in the decay chain of 238U to 206Pb,incorporated in significant amounts in the crystal during crystallization of monazite,because this mineral is a carrier of Th.This might be valid for sample 7703Mo,which is slightly reverse discordant (Fig.2).However,samples 7365Mo,7381Mo and 7369Mo are strongly reverse and normally discordant,respectively (Fig.2).These samples probably suffered loss of U (7365Mo,7381Mo)and radiogenic Pb (7369Mo).The two samples of the HG are strongly reverse discor-dant,probably due to loss of U (U contents:6,135and 10,129ppm)(Fig.2).207Pb/206Pb ages of both samples are equivalent within limits of errors at 350±5andT a b l e 1U –P b m o n a z i t e d a t a o f t h e t h r e e s t u d i e d g r a n i t e s o f c e n t r a l -e a s t e r n S i e r r a d e V e l a s c oS a m p l eW e i g h t (g )U (p p m )T h (p p m )P b (p p m )206P b /204P b m e a s u r e dC a l c u l a t e d a t o m i c r a t i o sC a l c u l a t e d a g e s (i n M a )206P b /238U2r (%)207P b /235U2r(%)207P b /206P b2r (%)206P b /238U2r207P b /235U2r207P b /206P b2rH u a c o g r a n i t e7365M o0.0001521016983552159071340.068090.210.502170.250.053490.12424.60.9413.21.0349.75.37381M o 0.000138613546863146943430.113740.210.841770.240.053680.11694.41.5620.11.5357.54.9S a n a g a s t a g r a n i t e7369M o0.00011030483830554140230800.005920.210.043480.280.053300.1738.00.143.20.1341.57.87379M o0.000093331166434104940230.056270.210.414820.260.053470.15352.90.7352.30.9348.76.77703M o0.00015022266190997831150.056310.210.411960.330.053060.24353.20.7350.31.2331.311.0L a C h i n c h i l l a s t o c k7740M o 0.00012226816011092719720.054910.210.402970.330.053230.24344.60.7343.81.1338.610.9R a d i o g e n i c P b c o r r e c t e d f o r b l a n k a n d f o r i n i t i a l P b (f o l l o w i n g t h e m o d e l o f S t a c e y a n d K r a m e r s 1975).U c o r r e c t e d f o r b l a n k .A g e s c a l c u l a t e d u s i n g t h e P B D A T 1.24p r o g r a m (L u d w i g 1994)a n d t h e d e c a y c o n s t a n t s r e c o m m e n d e d b y t h e I U G S (S t e i g e r a n d J a¨g e r 1977)358±5Ma.These ages are interpreted as the best estimatefor crystallization of the HG.Recently,So¨llner et al.(2007)have carried out LA-ICP-MS U–Pb age determinations on zircons of sample 7365of the HG,obtaining a main crystallization age of 354±4Ma,thus confirming the monazite 207Pb/206Pb ages.In addition,many of these zir-cons have non-detrital inherited cores with Ordovician ages,suggesting significant participation of Ordovician metag-ranitoids in the formation of the HG (So¨llner et al.2007).Only one of the three samples of the SG (sample 7379Mo)gives a concordant age of 352.7±1.4Ma (degree of discordance =1.5%,Fig.2).Sample 7703Mo is slightly reverse discordant at 350.3±1.2Ma (207Pb/235U age),whereas sample 7369Mo is strongly discordant at 38.0±0.1Ma (206Pb/238U age;207Pb/206Pb age =342±8Ma)(Fig.2),suggesting loss of radiogenic Pb,possibly related to the very high measured U content (30,483ppm)and the presence of dim and/or fractured crystals.All three data points,including the origin,fit a regression line with an upper intercept of 340±26Ma (MSWD =3.8).The concordant age of 352.7±1.4Ma of sample 7379Mo is interpreted as the most precise and adequate age of crystallization of the SG.Sample 7740Mo of the LCS is concordant at 344.5±1.4Ma (degree of discordance =1.2%,Fig.2),which is interpreted as dating the time of crystallization of the LCS.GeochemistryMajor and trace elementsTable 2shows 31whole-rock major and trace element chemical analyses of the studied granites;13analysescorrespond to the HG,10to the SG,4to the LCS and 4to mafic microgranular enclaves of the HG and the SG (see also Grosse et al.2007).For comparison,the average composition of the border and central facies of the San Blas granite are also shown (calculated from 13analyses of Ba´ez 2006).The HG and the SG are characterized by a high and restricted SiO 2range of 69.7–74.7%(wt%).With slightly lower average SiO 2,the SG has somewhat higher Fe 2O 3tot ,MgO,TiO 2and CaO concentrations than the HG,although both granites are poor in these oxides.They are,on the other hand,rich in alkalis (generally [8%),specially in K 2O (generally [5%).Both granites are peraluminous;the HG is mainly moderately peraluminous (Alumina Satura-tion Index,A/CNK,= 1.06–1.18),whereas the SG is weakly peraluminous (A/CNK =1.01–1.09).In major element variation diagrams (Fig.3),both granites show similar,poorly defined correlations.Fe 2O 3tot ,MgO and TiO 2decrease with increasing SiO 2suggesting fractionation of mafic phases,mainly biotite.Al 2O 3,CaO and P 2O 5also decrease,suggesting fractionation of pla-gioclase and apatite,respectively,whereas Na 2O and K 2O do not correlate well with SiO 2.The HG and the SG can be distinguished well in an A/CNK versus SiO 2diagram (Fig.4a)and in the A–B diagram of Debon and Le Fort (1983)(Fig.4b),due to the different variations in peraluminosity:it decreases with differentia-tion in the HG,while it increases with differentiation in the SG.These opposite tendencies can be explained by frac-tionation of muscovite in the HG (which will strongly decrease the peraluminosity of the remaining melt due to its high peraluminosity)and the absence of this mineral in the SG (where the increase in peraluminosity is due mainly to the fractionation of plagioclase,whose A/CNK =1).Fig.2U–Pb Concordiadiagram of monazites from the three studied granites of central-eastern Sierra de Velasco.Two samples correspond to the Huaco granite (HG:7365Mo and 7381Mo),three to theSanagasta granite (SG:7369Mo,7379Mo and 7703Mo)and one to the La Chinchilla stock (LCS:7740Mo).See text for further explanations.Plotted errorellipses and quoted errors are at the 2r confidence level。