Automatic selection of reference velocities for recursive depth migration


 Jared Greer
 1 years ago
 Views:
Transcription
1 Automatc selecton of mgraton veloctes Automatc selecton of reference veloctes for recursve depth mgraton Hugh D. Geger and Gary F. Margrave ABSTRACT Wave equaton depth mgraton methods such as phaseshft plus nterpolaton, extended spltstep Fourer, or Fourer fnte dfference plus nterpolaton requre a lmted set of reference veloctes for effcent wavefeld extrapolaton through laterally nhomogeneous velocty models. In basc mplementatons, reference veloctes are selected as ether a lnear or a geometrc progresson spannng the range of model veloctes. However, t s unlkely that the model veloctes are dstrbuted lnearly or geometrcally. If the reference veloctes can be dstrbuted statstcally to more closely approxmate the actual dstrbuton, the accuracy of the extrapolaton step can be mproved. In ths paper, we present a modfcaton to a prevously publshed algorthm for statstcal selecton of reference veloctes (Bagan et al. 1995). Key features of our automatc reference velocty selecton algorthm are 1) dvson of the velocty dstrbuton nto clusters 2) entropy based statstcal control to determne the mnmal number of reference veloctes requred wthn a cluster, 3) a novel greedy search that selects reference veloctes wthn each cluster at or near peaks n the probablty dstrbuton, and 4) calculaton of a sngle reference velocty f the velocty range wthn each cluster s less than a mnmum threshold. We show that our method s superor to Bagan et al. s method, whch ncludes only step (2) above, and  n place of step (3)  selecton of reference veloctes by pecewse constant nterpolaton of the probablty dstrbuton of the underlyng veloctes. Our automatc velocty selecton algorthm can be run usng a sngle parameter the approxmate desred velocty step expressed as a percentage although the maxmum step and mnmum threshold can be specfed f the defaults are not sutable. The automatc velocty selecton algorthm s mplemented as part of a prestack PSPI depth mgraton of the 2D Marmous model. The resultng mages are clearly superor to mages created usng a lnear or geometrcal dstrbuton of a smlar number of reference veloctes. The algorthm s sutable for 3D data, where the tradeoff between accuracy and effcency s more pronounced. INTRODUCTION Wave equaton depth mgraton methods such as phaseshft plus nterpolaton (Gazdag and Sguazzero, 1984), extended spltstep Fourer (Kessnger, 1992), or Fourer fnte dfference plus nterpolaton (Bond, 2002) requre a lmted set of reference veloctes for effcent wavefeld extrapolaton through laterally nhomogeneous velocty models. All of these authors suggests that a geometrc dstrbuton can produce a good set of reference veloctes. Kessnger (1992) mentons that, by emprcal testng, a percentage velocty ncrement of 15% provdes a good compromse between accuracy and effceny. Another standard method calculates a lnear dstrbuton of veloctes (e.g. Ferguson and Margraves, 2002), whch may have an advantage of ncreasng the accuracy of hgherangle wavefeld propagaton wth depth. CREWES Research Report Volume 16 (2004) 1
2 Geger and Margrave example velocty profles FIG. 1. The Marmous velocty model. Red lnes mark velocty profles used n ths study. Bagan et al. (1995) propose a statstcal method for optmal selecton of reference veloctes. The optmal choce of reference veloctes wll be a balance between accuracy and effcency. In ths study, we do not determne a quanttatve method for evaluatng optmalty. Instead, we compare the selected reference veloctes aganst the probablty dstrbuton of the veloctes over the range for the profle. Fgure 1 s a colour contour of the Marmous velocty model. The red lnes ndcate profles used n ths study. too few reference veloctes? ~3000 ms 1 (~230%) ~40 ms 1 (~ 2%) too many reference veloctes? ~320 ms 1 (~ 17%) ~70 ms 1 (~ 4%) ~70 ms 1 (~ 4%) ~80 ms 1 (~ 5%) FIG. 2. How should reference veloctes be chosen for wavenumberspace doman extrapolators such as PSPI? Emprcal testng (Kessgner, 1992) suggests that an ncrement of approxmately 15% provdes a reasonable compromse between accuracy and effcency. In selecton of the boundng veloctes creates too large an ncrement (230%), whereas n a careful selecton of veloctes that closely matches steps n the velocty profle may produce too many veloctes (steps of 2%, 4%, 4%, and 17%). 2 CREWES Research Report Volume 16 (2004)
3 Automatc selecton of mgraton veloctes Keepng Kessnger s emprcal percentage ncrement of 15% n mnd, we can easly determne when we mght have too few veloctes (Fgure 2. However, a good ft to a velocty profle, as shown n Fgure 2b, mght not satsfy Kessnger s emprcal ncrement. How then should we select veloctes to create a best ft to the underlyng probablty dsrbuton? In ths paper, we revew the method of Bagan, show that ther reference veloctes are not necessarly near the peaks n the probablty dstrbuton of the veloctes over a layer, and propose a new statstcal method that produces a more optmal dstrbuton of reference veloctes. We test our method aganst Bagan s method, and aganst the lnear and geometrc methods, usng velocty profles from the Marmous acoustc model (Versteed and Grau, 1991). LINEAR AND GEOMETRIC METHODS The lnear method s descrbed as follows: 1) choose an approxmate velocty spacng dv, 2) Calculate nv=round((v max v mn )/dv) and 3) determne references veloctes as equal ncrements of v step =(v max v mn )/nv. However, what s a good choce for dv? One opton s a value close to Kessnger s emprcal percentage. A queston remans, however: Wll the selected ncrement be optmal reasonable for both low and hgh veloctes? Fgure 4 llustrates the geometrc method appled to a Marmous velocty profle. too few reference veloctes? ~3000 ms 1 (~230%) ~40 ms 1 (~ 2%) too many reference veloctes? ~320 ms 1 (~ 17%) ~70 ms 1 (~ 4%) ~70 ms 1 (~ 4%) ~80 ms 1 (~ 5%) FIG. 2. How should reference veloctes be chosen for wavenumberspace doman extrapolators such as PSPI? Emprcal testng (Kessgner, 1992) suggests that an ncrement of approxmately 15% provdes a reasonable compromse between accuracy and effcency. In selecton of the boundng veloctes creates too large an ncrement (230%), whereas n a careful selecton of veloctes that closely matches steps n the velocty profle may produce too many veloctes (steps of 2%, 4%, 4%, and 17%). CREWES Research Report Volume 16 (2004) 3
4 Geger and Margrave The geometrc method s descrbed as follows: 1) choose an approprate percentage step v prcnt, 2) calculate v() = (1+v prcnt )*v(1). 3) The percentage can be adjusted by solvng a smple logarthmc equaton f reference veloctes are desred at both the mnmum and maxmum veloctes. As mentoned prevously, Kessgner (1992) recommends v prcnt =0.15. Fgure 4 llustrates the geometrc method appled to the deeper Marmous velocty profle. ~500 ms 1 (~10%) ~500 ms 1 (~20%) ~750 ms 1 (~15%) ~370 ms 1 (~15%) (detal for subsequent fgures) FIG. 3. Standard methods for selectng reference veloctes nclude a lnear nterpolaton between the mnmum and maxmum veloctes wthn a layer or cluster, and a geometrc nterpolaton based on a fxed percentage ncrement from the mnmum velocty. Emprcal testng (Kessgner, 1992) suggests that an ncrement of approxmately 15% provdes a reasonable compromse between accuracy and effcency. The green box n fgure shows the velocty profle used n Fgure 4. THE METHOD OF BAGAINI ET AL. (1995) The method of Bagan et al. (1995) can be descrbed as follows: 1) choose a prelmnary dv (geometrc?); 2) determne equally spaced bns over v mn :v max (e.g. Fgure 4a, where nb temp = 6)bn the veloctes to gve probablty densty P, where ΣP = 1, 4) determne theoptmal number of bns nb opt by statstcal entropy S=ΣP logp, where nb opt = round(exp(s)+0.5) (e.g. nb opt = 5 n Fgure 4); 5) calculate the cumulatve probablty dstrbuton Y, where Y = S P  each optmal bn wll hold 1/nB opt of the cumulatve probablty dstrbuton (e.g. 0.2 n Fgure 4; 6) start at v mn and lnearly nterpolate the poston of the reference veloctes from the temporary bn boundares (e.g. at 0.2, 0.4, 0.6, 0.8 n Fgure 4. 4 CREWES Research Report Volume 16 (2004)
5 Automatc selecton of mgraton veloctes FIG. 4. Bagan et al s (1995) method for selectng reference veloctes. the veloctes are bnned to create a dscrete probablty dstrbuton. An optmal number of reference veloctes nb opt s calculated usng a measure of statstcal entropy. the dscrete cumulatve probablty dstrbuton s dvded nto nb opt equal ncrements by lnearly nterpolatng from the bn boundares. Is ths method optmal? A lnear ncrement of the cumulatve probablty dstrbuton does not necessarly produce reference veloctes on or near the peaks n the probablty dstrbuton. In the worst case scenaro, none of the reference veloctes wll fall on peaks and the extrapolaton through that layer wll requre large nterpolatons. OUR NEW GREEDY PEAK SEARCH METHOD We propose a new method that specfcally searches for peaks n the probablty dstrbuton. We use Bagan s measure of statstcal entropy to determne an optmal number of reference veloctes. In all lkelhood, however, the number of peaks n the probablty dstrbuton wll not match the statstcally optmal number of number of reference veloctes. Our method uses a varety of technques to poston the reference veloctes closest to the peaks. In short, we collapse the closest peaks, startng wth the peaks of lowest probablty densty. A new reference velocty s determned as a weghted dstance between the two orgnal peaks, except at the ends where the values of the mnmum and maxmum veloctes are preserved as the boundng reference veloctes. CREWES Research Report Volume 16 (2004) 5
6 Geger and Margrave We also use a clusterng algorthm to dvde the velocty profle up nto clusters that mght be separated by a much larger percentage dfference than acceptable. Wthn each cluster, we can apply any of the above specfed methods. The general clusterng method s descrbed as follows: 1) sort the veloctes n the profle 2) select clusters where the percentage ncrement n sorted veloctes exceeds some maxmum value 3) each th cluster s now defned by a mnmum velocty. Startng wth the fst cluster (lowest velocty), determne M v a. If b. If M m % thresh m v and maxmum velocty v v 1+ v, then v m v M and ths cluster can safely be v avg m M v v extrapolated at the sngle velocty ( ) 2 = +. Set all veloctes wthn these bounds to the average velocty v n m, M avg xy v v = v, add ths use avg velocty to the velocty vector v = v, and ncrement k = k+ 1. M v M m c c 1+ c % max k, then the boundng veloctes for the cluster v m and are a vald step wthout any ntermedate veloctes M m % c. If c c > 1+ cmax there wll be at least three veloctes n the cluster (ncludng the boundng veloctes). Use the lnear, the geometrc, or the Bagan et al. (1995) measure of statstcal entropy to determne an optmal number of bns n the cluster. 4) Dependng on the method chosen n 3), calculate the reference veloctes wthn the cluster and cycle through all clusters determned n 2) In Fgure 5, we compare the selecton of reference veloctes wthn a cluster. The greedy peak search method shown n Fgures 5c and 5f does a better job of locatng the reference veloctes near the peaks n the probablty dstrbuton. MARMOUSI EXAMPLE We appled the varous technques to the select reference veloctes for PSPI mgraton of the Marmous data set. The results of the PSPI mgraton usng the clusterng algorthm wth the Bagan method are shown n Fgure 6. Fgure 6a s the bandlmted reflectvty calculated as usng gradents of the velocty and densty model. The modfed Bagan method obvously produces an excellent mage of Marmous (Fgure 6. Even the elusve target zone at depth (Fgure 6d) compares well wth the reflectvty (Fgure 6d). Ths research s ongong. More results wll be presented at the meetng 6 CREWES Research Report Volume 16 (2004)
7 Automatc selecton of mgraton veloctes FIG. 5. ac) Probablty dstrbuton of veloctes wthn a cluster from a selected layer of the Marmous (blue bars) and selected reference veloctes usng varous methods (red lnes). df) the velocty profle wth dstance (blue dotted lne), selected reference veloctes (red dotted lnes) and boundng veloctes (red lnes). Note that n and d) the reference veloctes by the statstcal entropy method of Bagan et al (1995) are not necessarly at the peaks n the dstrbuton. In and e), large gaps are lnearly nterpolated. In c) and f) the new greedy peak search method selects reference veloctes at the peaks n the probablty dstrbuton. The new method should produce more accurate wavefeld extrapolaton for the same computatonal cost, and hence better mages. CREWES Research Report Volume 16 (2004) 7
8 Geger and Margrave c) d) FIG. 6. Bandlmted reflectvty for Marmous acoustc model. Depth mage by PSPI mgraton wth crosscorrelaton magng condton usng modfed method of Bagan et al (1995), where reference veloctes are selected usng clusterng and statstcal entropy wthn clusters. c) and d) Zoom of full bandwdth reflectvty and PSPI mage at the target zone. The target s accurately maged, although the lmted bandwdth of the data results n a rngy appearance. 8 CREWES Research Report Volume 16 (2004)
9 CONCLUSIONS Automatc selecton of mgraton veloctes An optmal selecton of reference veloctes wthn a depth layer can maxmze the accuracy and effcency of wavenumber/spatal doman wavefeld extrapolators such as PSPI. A lnear or geometrc dstrbuton does not take nto account the underlyng dstrbuton of the veloctes. Hence, large nterpolatons between reference wavefelds may be requred, whch can result n reduced accuracy and a poor mage. The statstcal method of Bagan et al. (1995) dstrbutes the reference veloctes based on equal ntervals of the cumulatve probablty dstrbuton of the veloctes wthn a layer. On average, ths wll reduce the sze of the nterpolatons, but may stll produce a reference velocty dstrbuton that requres some large nterpolatons. We propose a modfcaton to the method of Bagan et al., whereby the veloctes wthn a layer are frst separated nto clusters dvded by large gaps n the dstrbuton, an optmal number of veloctes wthn a cluster s chosen based on Bagan et al. s method of statstcal entropy, a greedy search algorthm s used to select reference veloctes wthn each cluster as close as possble to the peaks n the probablty dstrbuton, and as weghted averages between smaller pars of peaks f there are more peaks than the optmal number of veloctes. A sngle reference velocty s selected for clusters or layers where the spread of veloctes s less than a specfed threshold. The new greedy peak search method was tested on the Marmous acoustc data set usng a PSPI waveequaton prestack shotrecord mgraton algorthm. The depth mages from the new peak search method are clearly more accurate than those produced by a geometrc dstrbuton. Surprsngly, a lnear dstrbuton s shown to produce reasonable mages n the shallow secton that are smlar to the new algorthm and much better than thosee produced usng a geometrc dstrbuton. At present, we do not have a good explanaton for ths result. In the shallow secton, the peak search method and the Bagan et al. method yeld smlar mages. The benefts of our new method are most pronounced n the deeper secton, where focusng and postonng are better than any of the methods used for comparson. REFERENCES Bagan, C., Bonom, E., Peron, E., 1995, Data parallel mplementaton of 3D PSPI: 65 nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Bond, B., 2002, Stable wdeangle Fourer fntedfference downward extrapolaton of 3D wavefelds: Geophyscs, 67, Ferguson R. and Margrave, G., 2002, Prestack depth mgraton by symmetrc nonstatonary phase shft:geophyscs, 67, Gazdag, J. and Sguazzero, P., 1984, Mgraton of sesmc data by phase shft plus nterpolaton: Geophyscs, 49, Kessnger, W., 1992, Extended spltstep Fourer mgraton: 62 nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Stoffa, P., Fokkema, J., de Luna Frere, R., and Kessnger, W., 1990, Spltstep Fourer mgraton: Geophyscs, 55, Versteeg, R., and Grau, G., Eds., 1991, The Marmous experence: Proc Eur. Assn. Expl. Geophys. Workshop. CREWES Research Report Volume 16 (2004) 9
y and the total sum of
Lnear regresson Testng for nonlnearty In analytcal chemstry, lnear regresson s commonly used n the constructon of calbraton functons requred for analytcal technques such as gas chromatography, atomc absorpton
More informationA Binarization Algorithm specialized on Document Images and Photos
A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a
More informationParallel matrixvector multiplication
Appendx A Parallel matrxvector multplcaton The reduced transton matrx of the threedmensonal cage model for gel electrophoress, descrbed n secton 3.2, becomes excessvely large for polymer lengths more
More informationS1 Note. Basis functions.
S1 Note. Bass functons. Contents Types of bass functons...1 The Fourer bass...2 Bsplne bass...3 Power and type I error rates wth dfferent numbers of bass functons...4 Table S1. Smulaton results of type
More informationContent Based Image Retrieval Using 2D Discrete Wavelet with Texture Feature with Different Classifiers
IOSR Journal of Electroncs and Communcaton Engneerng (IOSRJECE) eissn: 78834,p ISSN: 788735.Volume 9, Issue, Ver. IV (Mar  Apr. 04), PP 007 Content Based Image Retreval Usng D Dscrete Wavelet wth
More informationHigh resolution 3D Taup transform by matching pursuit Weiping Cao* and Warren S. Ross, Shearwater GeoServices
Hgh resoluton 3D Taup transform by matchng pursut Wepng Cao* and Warren S. Ross, Shearwater GeoServces Summary The 3D Taup transform s of vtal sgnfcance for processng sesmc data acqured wth modern wde
More informationThe Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique
//00 :0 AM Outlne and Readng The Greedy Method The Greedy Method Technque (secton.) Fractonal Knapsack Problem (secton..) Task Schedulng (secton..) Mnmum Spannng Trees (secton.) Change Money Problem Greedy
More informationSupport Vector Machines
/9/207 MIST.6060 Busness Intellgence and Data Mnng What are Support Vector Machnes? Support Vector Machnes Support Vector Machnes (SVMs) are supervsed learnng technques that analyze data and recognze patterns.
More informationAn EntropyBased Approach to Integrated Information Needs Assessment
Dstrbuton Statement A: Approved for publc release; dstrbuton s unlmted. An EntropyBased Approach to ntegrated nformaton Needs Assessment June 8, 2004 Wllam J. Farrell Lockheed Martn Advanced Technology
More informationAVO Modeling of Monochromatic Spherical Waves: Comparison to BandLimited Waves
AVO Modelng of Monochromatc Sphercal Waves: Comparson to BandLmted Waves Charles Ursenbach* Unversty of Calgary, Calgary, AB, Canada ursenbach@crewes.org and Arnm Haase Unversty of Calgary, Calgary, AB,
More informationLecture #15 Lecture Notes
Lecture #15 Lecture Notes The ocean water column s very much a 3D spatal entt and we need to represent that structure n an economcal way to deal wth t n calculatons. We wll dscuss one way to do so, emprcal
More informationI. INTRODUCTION J. Acoust. Soc. Am. 109 (6), June /2001/109(6)/2629/7/$ Acoustical Society of America 2629
Modelng elastc wave forward propagaton and reflecton usng the complex screen method XaoB Xe and RuShan Wu Insttute of Geophyscs and Planetary Physcs, Unversty of Calforna, Santa Cruz, Calforna 9564 Receved
More informationProgramming in Fortran 90 : 2017/2018
Programmng n Fortran 90 : 2017/2018 Programmng n Fortran 90 : 2017/2018 Exercse 1 : Evaluaton of functon dependng on nput Wrte a program who evaluate the functon f (x,y) for any two user specfed values
More informationA Fast ContentBased Multimedia Retrieval Technique Using Compressed Data
A Fast ContentBased Multmeda Retreval Technque Usng Compressed Data Borko Furht and Pornvt Saksobhavvat NSF Multmeda Laboratory Florda Atlantc Unversty, Boca Raton, Florda 3343 ABSTRACT In ths paper,
More informationSupport Vector Machines
Support Vector Machnes Decson surface s a hyperplane (lne n 2D) n feature space (smlar to the Perceptron) Arguably, the most mportant recent dscovery n machne learnng In a nutshell: map the data to a predetermned
More informationClassifier Selection Based on Data Complexity Measures *
Classfer Selecton Based on Data Complexty Measures * Edth HernándezReyes, J.A. CarrascoOchoa, and J.Fco. MartínezTrndad Natonal Insttute for Astrophyscs, Optcs and Electroncs, Lus Enrque Erro No.1 Sta.
More informationCourse Introduction. Algorithm 8/31/2017. COSC 320 Advanced Data Structures and Algorithms. COSC 320 Advanced Data Structures and Algorithms
Course Introducton Course Topcs Exams, abs, Proects A quc loo at a few algorthms 1 Advanced Data Structures and Algorthms Descrpton: We are gong to dscuss algorthm complexty analyss, algorthm desgn technques
More informationHermite Splines in Lie Groups as Products of Geodesics
Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the
More informationMathematics 256 a course in differential equations for engineering students
Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the
More informationUser Authentication Based On Behavioral Mouse Dynamics Biometrics
User Authentcaton Based On Behavoral Mouse Dynamcs Bometrcs CheeHyung Yoon Danel Donghyun Km Department of Computer Scence Department of Computer Scence Stanford Unversty Stanford Unversty Stanford, CA
More informationA MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS
Proceedngs of the Wnter Smulaton Conference M E Kuhl, N M Steger, F B Armstrong, and J A Jones, eds A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Mark W Brantley ChunHung
More informationNUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS
ARPN Journal of Engneerng and Appled Scences 006017 Asan Research Publshng Network (ARPN). All rghts reserved. NUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS Igor Grgoryev, Svetlana
More informationOutline. Type of Machine Learning. Examples of Application. Unsupervised Learning
Outlne Artfcal Intellgence and ts applcatons Lecture 8 Unsupervsed Learnng Professor Danel Yeung danyeung@eee.org Dr. Patrck Chan patrckchan@eee.org South Chna Unversty of Technology, Chna Introducton
More informationLearningBased TopN Selection Query Evaluation over Relational Databases
LearnngBased TopN Selecton Query Evaluaton over Relatonal Databases Lang Zhu *, Wey Meng ** * School of Mathematcs and Computer Scence, Hebe Unversty, Baodng, Hebe 071002, Chna, zhu@mal.hbu.edu.cn **
More informationWishing you all a Total Quality New Year!
Total Qualty Management and Sx Sgma Post Graduate Program 21415 Sesson 4 Vnay Kumar Kalakband Assstant Professor Operatons & Systems Area 1 Wshng you all a Total Qualty New Year! Hope you acheve Sx sgma
More informationActive Contours/Snakes
Actve Contours/Snakes Erkut Erdem Acknowledgement: The sldes are adapted from the sldes prepared by K. Grauman of Unversty of Texas at Austn Fttng: Edges vs. boundares Edges useful sgnal to ndcate occludng
More informationParallelism for Nested Loops with Nonuniform and Flow Dependences
Parallelsm for Nested Loops wth Nonunform and Flow Dependences SamJn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseodong, Cheonan, Chungnam, 33080, Korea. seong@cheonan.ac.kr
More informationTN348: Openlab Module  Colocalization
TN348: Openlab Module  Colocalzaton Topc The Colocalzaton module provdes the faclty to vsualze and quantfy colocalzaton between pars of mages. The Colocalzaton wndow contans a prevew of the two mages
More informationA Robust Method for Estimating the Fundamental Matrix
Proc. VIIth Dgtal Image Computng: Technques and Applcatons, Sun C., Talbot H., Ourseln S. and Adraansen T. (Eds.), 0 Dec. 003, Sydney A Robust Method for Estmatng the Fundamental Matrx C.L. Feng and Y.S.
More informationAPPLICATION OF A COMPUTATIONALLY EFFICIENT GEOSTATISTICAL APPROACH TO CHARACTERIZING VARIABLY SPACED WATERTABLE DATA
RFr"W/FZD JAN 2 4 1995 OST control # 1385 John J Q U ~ M Argonne Natonal Laboratory Argonne, L 60439 Tel: 7082525357, Fax: 7082523 611 APPLCATON OF A COMPUTATONALLY EFFCENT GEOSTATSTCAL APPROACH TO
More informationHierarchical clustering for gene expression data analysis
Herarchcal clusterng for gene expresson data analyss Gorgo Valentn emal: valentn@ds.unm.t Clusterng of Mcroarray Data. Clusterng of gene expresson profles (rows) => dscovery of coregulated and functonally
More information6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour
6.854 Advanced Algorthms Petar Maymounkov Problem Set 11 (November 23, 2005) Wth: Benjamn Rossman, Oren Wemann, and Pouya Kheradpour Problem 1. We reduce vertex cover to MAXSAT wth weghts, such that the
More informationCS 534: Computer Vision Model Fitting
CS 534: Computer Vson Model Fttng Sprng 004 Ahmed Elgammal Dept of Computer Scence CS 534 Model Fttng  1 Outlnes Model fttng s mportant Leastsquares fttng Maxmum lkelhood estmaton MAP estmaton Robust
More informationA Fast Visual Tracking Algorithm Based on Circle Pixels Matching
A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng
More informationThe Codesign Challenge
ECE 4530 Codesgn Challenge Fall 2007 Hardware/Software Codesgn The Codesgn Challenge Objectves In the codesgn challenge, your task s to accelerate a gven software reference mplementaton as fast as possble.
More informationEdge Detection in Noisy Images Using the Support Vector Machines
Edge Detecton n Nosy Images Usng the Support Vector Machnes Hlaro GómezMoreno, Saturnno MaldonadoBascón, Francsco LópezFerreras Sgnal Theory and Communcatons Department. Unversty of Alcalá Crta. MadrdBarcelona
More informationCompiler Design. Spring Register Allocation. Sample Exercises and Solutions. Prof. Pedro C. Diniz
Compler Desgn Sprng 2014 Regster Allocaton Sample Exercses and Solutons Prof. Pedro C. Dnz USC / Informaton Scences Insttute 4676 Admralty Way, Sute 1001 Marna del Rey, Calforna 90292 pedro@s.edu Regster
More informationREFRACTIVE INDEX SELECTION FOR POWDER MIXTURES
REFRACTIVE INDEX SELECTION FOR POWDER MIXTURES Laser dffracton s one of the most wdely used methods for partcle sze analyss of mcron and submcron sze powders and dspersons. It s quck and easy and provdes
More informationSome Advanced SPC Tools 1. Cumulative Sum Control (Cusum) Chart For the data shown in Table 91, the x chart can be generated.
Some Advanced SP Tools 1. umulatve Sum ontrol (usum) hart For the data shown n Table 91, the x chart can be generated. However, the shft taken place at sample #21 s not apparent. 92 For ths set samples,
More informationComputer Animation and Visualisation. Lecture 4. Rigging / Skinning
Computer Anmaton and Vsualsaton Lecture 4. Rggng / Sknnng Taku Komura Overvew Sknnng / Rggng Background knowledge Lnear Blendng How to decde weghts? Examplebased Method Anatomcal models Sknnng Assume
More informationQuality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation
Intellgent Informaton Management, 013, 5, 191195 Publshed Onlne November 013 (http://www.scrp.org/journal/m) http://dx.do.org/10.36/m.013.5601 Qualty Improvement Algorthm for Tetrahedral Mesh Based on
More informationR s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes
SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges
More informationUnsupervised Learning
Pattern Recognton Lecture 8 Outlne Introducton Unsupervsed Learnng Parametrc VS NonParametrc Approach Mxture of Denstes MaxmumLkelhood Estmates Clusterng Prof. Danel Yeung School of Computer Scence and
More information11. HARMS How To: CSV Import
and Rsk System 11. How To: CSV Import Preparng the spreadsheet for CSV Import Refer to the spreadsheet template to ad algnng spreadsheet columns wth Data Felds. The spreadsheet s shown n the Appendx, an
More informationHelsinki University Of Technology, Systems Analysis Laboratory Mat Independent research projects in applied mathematics (3 cr)
Helsnk Unversty Of Technology, Systems Analyss Laboratory Mat2.08 Independent research projects n appled mathematcs (3 cr) "! #$&% Antt Laukkanen 506 R ajlaukka@cc.hut.f 2 Introducton...3 2 Multattrbute
More informationTHE PULLPUSH ALGORITHM REVISITED
THE PULLPUSH ALGORITHM REVISITED Improvements, Computaton of Pont Denstes, and GPU Implementaton Martn Kraus Computer Graphcs & Vsualzaton Group, Technsche Unverstät München, Boltzmannstraße 3, 85748
More informationSkew Angle Estimation and Correction of Hand Written, Textual and Large areas of NonTextual Document Images: A Novel Approach
Angle Estmaton and Correcton of Hand Wrtten, Textual and Large areas of NonTextual Document Images: A Novel Approach D.R.Ramesh Babu Pyush M Kumat Mahesh D Dhannawat PES Insttute of Technology Research
More informationCornerBased Image Alignment using Pyramid Structure with Gradient Vector Similarity
Journal of Sgnal and Informaton Processng, 013, 4, 114119 do:10.436/jsp.013.43b00 Publshed Onlne August 013 (http://www.scrp.org/journal/jsp) CornerBased Image Algnment usng Pyramd Structure wth Gradent
More informationFitting: Deformable contours April 26 th, 2018
4/6/08 Fttng: Deformable contours Aprl 6 th, 08 Yong Jae Lee UC Davs Recap so far: Groupng and Fttng Goal: move from array of pxel values (or flter outputs) to a collecton of regons, objects, and shapes.
More informationSLAM Summer School 2006 Practical 2: SLAM using Monocular Vision
SLAM Summer School 2006 Practcal 2: SLAM usng Monocular Vson Javer Cvera, Unversty of Zaragoza Andrew J. Davson, Imperal College London J.M.M Montel, Unversty of Zaragoza. josemar@unzar.es, jcvera@unzar.es,
More informationAP PHYSICS B 2008 SCORING GUIDELINES
AP PHYSICS B 2008 SCORING GUIDELINES General Notes About 2008 AP Physcs Scorng Gudelnes 1. The solutons contan the most common method of solvng the freeresponse questons and the allocaton of ponts for
More informationSubspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;
Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features
More informationLobachevsky State University of Nizhni Novgorod. Polyhedron. Quick Start Guide
Lobachevsky State Unversty of Nzhn Novgorod Polyhedron Quck Start Gude Nzhn Novgorod 2016 Contents Specfcaton of Polyhedron software... 3 Theoretcal background... 4 1. Interface of Polyhedron... 6 1.1.
More informationMultiview 3D Position Estimation of Sports Players
Multvew 3D Poston Estmaton of Sports Players Robbe Vos and Wlle Brnk Appled Mathematcs Department of Mathematcal Scences Unversty of Stellenbosch, South Afrca Emal: vosrobbe@gmal.com Abstract The problem
More informationA Gradient Difference based Technique for Video Text Detection
A Gradent Dfference based Technque for Vdeo Text Detecton Palaahnakote Shvakumara, Trung Quy Phan and Chew Lm Tan School of Computng, Natonal Unversty of Sngapore {shva, phanquyt, tancl }@comp.nus.edu.sg
More informationImprovement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration
Improvement of Spatal Resoluton Usng BlockMatchng Based Moton Estmaton and Frame Integraton Danya Suga and Takayuk Hamamoto Graduate School of Engneerng, Tokyo Unversty of Scence, 631, Nuku, Katsuskaku,
More informationExplicit Formulas and Efficient Algorithm for Moment Computation of Coupled RC Trees with Lumped and Distributed Elements
Explct Formulas and Effcent Algorthm for Moment Computaton of Coupled RC Trees wth Lumped and Dstrbuted Elements Qngan Yu and Ernest S.Kuh Electroncs Research Lab. Unv. of Calforna at Berkeley Berkeley
More informationA Gradient Difference based Technique for Video Text Detection
2009 10th Internatonal Conference on Document Analyss and Recognton A Gradent Dfference based Technque for Vdeo Text Detecton Palaahnakote Shvakumara, Trung Quy Phan and Chew Lm Tan School of Computng,
More informationREFRACTION. a. To study the refraction of light from plane surfaces. b. To determine the index of refraction for Acrylic and Water.
Purpose Theory REFRACTION a. To study the refracton of lght from plane surfaces. b. To determne the ndex of refracton for Acrylc and Water. When a ray of lght passes from one medum nto another one of dfferent
More informationEcient Computation of the Most Probable Motion from Fuzzy. Moshe BenEzra Shmuel Peleg Michael Werman. The Hebrew University of Jerusalem
Ecent Computaton of the Most Probable Moton from Fuzzy Correspondences Moshe BenEzra Shmuel Peleg Mchael Werman Insttute of Computer Scence The Hebrew Unversty of Jerusalem 91904 Jerusalem, Israel Emal:
More informationSolutions to Programming Assignment Five Interpolation and Numerical Differentiation
College of Engneerng and Coputer Scence Mechancal Engneerng Departent Mechancal Engneerng 309 Nuercal Analyss of Engneerng Systes Sprng 04 Nuber: 537 Instructor: Larry Caretto Solutons to Prograng Assgnent
More informationBiostatistics 615/815
The EM Algorthm Bostatstcs 615/815 Lecture 17 Last Lecture: The Smplex Method General method for optmzaton Makes few assumptons about functon Crawls towards mnmum Some recommendatons Multple startng ponts
More informationHelp for TimeResolved Analysis TRI2 version 2.4 P Barber,
Help for TmeResolved Analyss TRI2 verson 2.4 P Barber, 22.01.10 Introducton Tmeresolved Analyss (TRA) becomes avalable under the processng menu once you have loaded and selected an mage that contans
More informationA mathematical programming approach to the analysis, design and scheduling of offshore oilfields
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and
More informationComparison of traveltime inversions on a limestone structure
Comparson of traveltme nversons on a lmestone structure Comparson of traveltme nversons on a lmestone structure Matthew D. Allen and Robert R. Stewart ABSRAC Four traveltme nverson technques were appled
More informationReducing Frame Rate for Object Tracking
Reducng Frame Rate for Object Trackng Pavel Korshunov 1 and We Tsang Oo 2 1 Natonal Unversty of Sngapore, Sngapore 11977, pavelkor@comp.nus.edu.sg 2 Natonal Unversty of Sngapore, Sngapore 11977, oowt@comp.nus.edu.sg
More informationMachine Learning: Algorithms and Applications
14/05/1 Machne Learnng: Algorthms and Applcatons Florano Zn Free Unversty of BozenBolzano Faculty of Computer Scence Academc Year 01101 Lecture 10: 14 May 01 Unsupervsed Learnng cont Sldes courtesy of
More informationLSTaSC Version 2.1. Willem Roux Livermore Software Technology Corporation, Livermore, CA, USA. Abstract
12 th Internatonal LSDYNA Users Conference Optmzaton(1) LSTaSC Verson 2.1 Wllem Roux Lvermore Software Technology Corporaton, Lvermore, CA, USA Abstract Ths paper gves an overvew of LSTaSC verson 2.1,
More informationA Modified Median Filter for the Removal of Impulse Noise Based on the Support Vector Machines
A Modfed Medan Flter for the Removal of Impulse Nose Based on the Support Vector Machnes H. GOMEZMORENO, S. MALDONADOBASCON, F. LOPEZFERRERAS, M. UTRILLA MANSO AND P. GILJIMENEZ Departamento de Teoría
More informationDesign of Structure Optimization with APDL
Desgn of Structure Optmzaton wth APDL Yanyun School of Cvl Engneerng and Archtecture, East Chna Jaotong Unversty Nanchang 330013 Chna Abstract In ths paper, the desgn process of structure optmzaton wth
More informationLecture 5: Multilayer Perceptrons
Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented
More informationLearning the Kernel Parameters in Kernel Minimum Distance Classifier
Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and ZhHua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department
More informationToday s Outline. Sorting: The Big Picture. Why Sort? Selection Sort: Idea. Insertion Sort: Idea. Sorting Chapter 7 in Weiss.
Today s Outlne Sortng Chapter 7 n Wess CSE 26 Data Structures Ruth Anderson Announcements Wrtten Homework #6 due Frday 2/26 at the begnnng of lecture Proect Code due Mon March 1 by 11pm Today s Topcs:
More informationMachine Learning. Topic 6: Clustering
Machne Learnng Topc 6: lusterng lusterng Groupng data nto (hopefully useful) sets. Thngs on the left Thngs on the rght Applcatons of lusterng Hypothess Generaton lusters mght suggest natural groups. Hypothess
More informationCircuit Analysis I (ENGR 2405) Chapter 3 Method of Analysis Nodal(KCL) and Mesh(KVL)
Crcut Analyss I (ENG 405) Chapter Method of Analyss Nodal(KCL) and Mesh(KVL) Nodal Analyss If nstead of focusng on the oltages of the crcut elements, one looks at the oltages at the nodes of the crcut,
More informationA NewtonType Method for Constrained LeastSquares DataFitting with EasytoControl Rational Curves
A NewtonType Method for Constraned LeastSquares DataFttng wth EasytoControl Ratonal Curves G. Cascola a, L. Roman b, a Department of Mathematcs, Unversty of Bologna, P.zza d Porta San Donato 5, 4017
More informationTESTING AND IMPROVING LOCAL ADAPTIVE IMPORTANCE SAMPLING IN LJF LOCALJT IN MULTIPLY SECTIONED BAYESIAN NETWORKS
TESTING AND IMPROVING LOCAL ADAPTIVE IMPORTANCE SAMPLING IN LJF LOCALJT IN MULTIPLY SECTIONED BAYESIAN NETWORKS Dan Wu 1 and Sona Bhatt 2 1 School of Computer Scence Unversty of Wndsor, Wndsor, Ontaro
More informationDesign of a Real Time FPGAbased Three Dimensional Positioning Algorithm
Desgn of a Real Tme FPGAbased Three Dmensonal Postonng Algorthm Nathan G. JohnsonWllams, Student Member IEEE, Robert S. Myaoka, Member IEEE, Xaol L, Student Member IEEE, Tom K. Lewellen, Fellow IEEE,
More informationTopology Design using LSTaSC Version 2 and LSDYNA
Topology Desgn usng LSTaSC Verson 2 and LSDYNA Wllem Roux Lvermore Software Technology Corporaton, Lvermore, CA, USA Abstract Ths paper gves an overvew of LSTaSC verson 2, a topology optmzaton tool
More informationSorting Review. Sorting. Comparison Sorting. CSE 680 Prof. Roger Crawfis. Assumptions
Sortng Revew Introducton to Algorthms Qucksort CSE 680 Prof. Roger Crawfs Inserton Sort T(n) = Θ(n 2 ) Inplace Merge Sort T(n) = Θ(n lg(n)) Not nplace Selecton Sort (from homework) T(n) = Θ(n 2 ) Inplace
More informationDesign and Analysis of Algorithms
Desgn and Analyss of Algorthms Heaps and Heapsort Reference: CLRS Chapter 6 Topcs: Heaps Heapsort Prorty queue Huo Hongwe Recap and overvew The story so far... Inserton sort runnng tme of Θ(n 2 ); sorts
More informationProblem Set 3 Solutions
Introducton to Algorthms October 4, 2002 Massachusetts Insttute of Technology 6046J/18410J Professors Erk Demane and Shaf Goldwasser Handout 14 Problem Set 3 Solutons (Exercses were not to be turned n,
More informationArray transposition in CUDA shared memory
Array transposton n CUDA shared memory Mke Gles February 19, 2014 Abstract Ths short note s nspred by some code wrtten by Jeremy Appleyard for the transposton of data through shared memory. I had some
More informationAnnouncements. Supervised Learning
Announcements See Chapter 5 of Duda, Hart, and Stork. Tutoral by Burge lnked to on web page. Supervsed Learnng Classfcaton wth labeled eamples. Images vectors n hghd space. Supervsed Learnng Labeled eamples
More informationIncremental Learning with Support Vector Machines and Fuzzy Set Theory
The 25th Workshop on Combnatoral Mathematcs and Computaton Theory Incremental Learnng wth Support Vector Machnes and Fuzzy Set Theory YuMng Chuang 1 and ChaHwa Ln 2* 1 Department of Computer Scence and
More informationHierarchical agglomerative. Cluster Analysis. Christine Siedle Clustering 1
Herarchcal agglomeratve Cluster Analyss Chrstne Sedle 1932004 Clusterng 1 Classfcaton Basc (unconscous & conscous) human strategy to reduce complexty Always based Cluster analyss to fnd or confrm types
More informationOptimal Scheduling of Capture Times in a Multiple Capture Imaging System
Optmal Schedulng of Capture Tmes n a Multple Capture Imagng System Tng Chen and Abbas El Gamal Informaton Systems Laboratory Department of Electrcal Engneerng Stanford Unversty Stanford, Calforna 9435,
More informationNAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics
Introducton G10 NAG Fortran Lbrary Chapter Introducton G10 Smoothng n Statstcs Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Smoothng Methods... 2 2.2 Smoothng Splnes and Regresson
More informationCHAPTER 10: ALGORITHM DESIGN TECHNIQUES
CHAPTER 10: ALGORITHM DESIGN TECHNIQUES So far, we have been concerned wth the effcent mplementaton of algorthms. We have seen that when an algorthm s gven, the actual data structures need not be specfed.
More informationOutline. SelfOrganizing Maps (SOM) US Hebbian Learning, Cntd. The learning rule is Hebbian like:
SelfOrganzng Maps (SOM) Turgay İBRİKÇİ, PhD. Outlne Introducton Structures of SOM SOM Archtecture Neghborhoods SOM Algorthm Examples Summary 1 2 Unsupervsed Hebban Learnng US Hebban Learnng, Cntd 3 A
More informationParameter estimation for incomplete bivariate longitudinal data in clinical trials
Parameter estmaton for ncomplete bvarate longtudnal data n clncal trals Naum M. Khutoryansky Novo Nordsk Pharmaceutcals, Inc., Prnceton, NJ ABSTRACT Bvarate models are useful when analyzng longtudnal data
More informationSelftuning Histograms: Building Histograms Without Looking at Data
Selftunng Hstograms: Buldng Hstograms Wthout Lookng at Data Ashraf Aboulnaga Computer Scences Department Unversty of Wsconsn  Madson ashraf@cs.wsc.edu Surajt Chaudhur Mcrosoft Research surajtc@mcrosoft.com
More informationParallel Numerics. 1 Preconditioning & Iterative Solvers (From 2016)
Technsche Unverstät München WSe 6/7 Insttut für Informatk Prof. Dr. Thomas Huckle Dpl.Math. Benjamn Uekermann Parallel Numercs Exercse : Prevous Exam Questons Precondtonng & Iteratve Solvers (From 6)
More information= 0) is the 2D Fourier transform of the field (1),, z = 0). The phase ) is defined in the dispersion relation as where
GEOPHYSICS, VOL. 61, NO. 5 (SEPTEMBEROCTOBER 1996); P. 1412 1416, 4 FIGS. Short Note Prestack migration by splitstep DSR. Alexander Mihai Popovici* INTRODUCTION The doublesquareroot (DSR) prestack
More informationHighBoost Mesh Filtering for 3D Shape Enhancement
HghBoost Mesh Flterng for 3D Shape Enhancement Hrokazu Yagou Λ Alexander Belyaev y Damng We z Λ y z ; ; Shape Modelng Laboratory, Unversty of Azu, AzuWakamatsu 9658580 Japan y Computer Graphcs Group,
More informationMachine Learning. Support Vector Machines. (contains material adapted from talks by Constantin F. Aliferis & Ioannis Tsamardinos, and Martin Law)
Machne Learnng Support Vector Machnes (contans materal adapted from talks by Constantn F. Alfers & Ioanns Tsamardnos, and Martn Law) Bryan Pardo, Machne Learnng: EECS 349 Fall 2014 Support Vector Machnes
More informationCSCI 104 Sorting Algorithms. Mark Redekopp David Kempe
CSCI 104 Sortng Algorthms Mark Redekopp Davd Kempe Algorthm Effcency SORTING 2 Sortng If we have an unordered lst, sequental search becomes our only choce If we wll perform a lot of searches t may be benefcal
More informationOPTIMAL VIDEO SUMMARY GENERATION AND ENCODING. (ICIP Draft v0.2, )
OPTIMAL VIDEO SUMMARY GENERATION AND ENCODING + Zhu L, * Aggelos atsaggelos and + Bhavan Gandh (ICIP Draft v.2, 223) + Multmeda Communcaton Research Lab, Motorola Labs, Schaumburg * Department of Electrcal
More informationDesign for Reliability: Case Studies in Manufacturing Process Synthesis
Desgn for Relablty: Case Studes n Manufacturng Process Synthess Y. Lawrence Yao*, and Chao Lu Department of Mechancal Engneerng, Columba Unversty, Mudd Bldg., MC 473, New York, NY 7, USA * Correspondng
More informationAssignment # 2. Farrukh Jabeen Algorithms 510 Assignment #2 Due Date: June 15, 2009.
Farrukh Jabeen Algorthms 51 Assgnment #2 Due Date: June 15, 29. Assgnment # 2 Chapter 3 Dscrete Fourer Transforms Implement the FFT for the DFT. Descrbed n sectons 3.1 and 3.2. Delverables: 1. Concse descrpton
More information