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GPGN 461/561 Lab Fall 2011 - Center for Wave Phenomena

1. Figure 6 8 The light cone for a point scatterer at x z By classical geometry a vertical slice through the cone in x t the z 0 plane where we record our data is a hyperbola depth section but could be a time section A useful diagram for understanding the diffraction stack is the light cone diagram in Figure 6 8 A light cone is the representation of the surface where solutions of the wave equation live The scatterer is located at the point x z Time increases downward A horizontal slice through the cone reveals the circular wavefronts that are the circles drawn in Hagedoorn s method A vertical slice through the cone in x t reveals the hyperbola that is the characteristic shape of a diffraction in a constant wavespeed medium 6 4 Migration as a mathematical mapping Another diagram that reveals migration as a type of data transformation or mapping may be seen in Figure 6 9 Here we see that the impulse response of the migration operator is a circular curve in constant wavespeed media The diffraction in x t may be thought of as the impulse response of the modeling operation that made the data from a point at r z Migration by diffraction stack therefore consists of selecting a point x z modeling the diffraction curve in x t and then summing through the data over this curve Note that this must be done for every output point to make the image Figure 6 9 represents more than migration Goi
2. suttoz lt junk su t 0 0 15 2 v 1500 2000 3000 gt junki su suxwigb lt junk su title test pattern amp suxwigb lt junki su title depth section amp The program suztot has been provided to apply depth to time conversion as the inverse of sutotz Because we know the values of the velocity that were used we must 95 trace number trace number a 10 20 30 b 10 20 30 0 0 gt 0 05 1004 by h f by l 0 104 hj 2 nn nmm 5 o E r amp 200 0 154 h hi gt 0 20 300 0 254 test pattern depth section c trace number 10 20 30 LL 0 time s EAR FO e d OE Raps T mA di Meus time section reconstructed Figure 5 2 a Test pattern b Test pattern corrected from time to depth c Test pattern corrected back from depth to time section Note that the curvature seen depth section indicates a non piecewise constant v t Note that the reconstructed time section has waveforms that are distorted by repeated sinc interpolation The sinc interpolation applied in the depth to time calculation has not had an anti alias filter applied 56 b
3. int gelev Receiver group elevation from sea level all elevations above the Vertical datum are positive and below are negative int selev Surface elevation at source int sdepth Source depth below surface a positive number 45 int gdel Datum elevation at receiver group int sdel Datum elevation at source int swdep Water depth at source int gwdep Water depth at receiver group short scalel Scalar to be applied to the previous 7 entries to give the real value Scalar 1 10 100 1000 10000 If positive scalar is used as a multiplier if negative scalar is used as a divisor short scalco Scalar to be applied to the next 4 entries to give the real value Scalar 1 10 100 1000 10000 If positive scalar is used as a multiplier if negative scalar is used as a divisor int sx Source coordinate X int sy Source coordinate Y int gx Group coordinate X int gy Group coordinate Y short counit Coordinate units for previous 4 entries and for the 7 entries before scalel Length meters or feet Seconds of arc Decimal degrees Degrees minutes seconds DMS e UNBE Il In case 2 the X values are longitude and the Y values are latitude a positive value designates the number of seconds east of Greenwich or north of the equator 46 In case 4 to encode DDDMMSS counit DDD 10 4
4. suplane suxwigb amp this symbol the ampersand indicates that the program is being run in background the pipe symbol The commandline itself is the interactive prompt that the shell program is providing so that you can supply input The proper input for a commandline is an executable file which may be a compiled program or a Unix shell script T he command prompt is saying Type program name here Try running this command with and without the ampersand amp If you run suplane suxwigb The plot comes up but you have to kill the plot window before you can get your com mandline back whereas suplane suxwigb amp allows you to have the plot on the screen and have the commandline To make the plot better we may add some axis labeling suplane suxwigb title suplane test pattern labeli time s label2 trace number amp Here the command is broken across a line So it will fit this page of this book On your screen it would be typed as one long line 19 time s trace number 10 20 30 0 05 0 10 0 15 0 20 0 25 suplane test pattern Figure 2 1 The suplane test pattern 20 to see a test pattern consisting of three intersecting lines in the form of seismic traces The data consist of seismic traces with only single values that are nonzero This is variable area display in which each place where the trace is positive valued is shaded black See Figure 2 1 Equivalently you
5. plot as wiggle traces Equivalently we may do suplane gt junk su make suplane data write to a file suspecfx lt junk su gt junk su find the amplitude spectrum write to a file suxwigb junki su amp view the output as wiggle traces This does exactly the same thing in terms of final output as the previous example with the exception that here two files have been created See Figure 2 2 22 2 2 1 Questions for discussion e What is the Fourier transform of a function e What is an amplitude spectrum e Why do the plots of the amplitude spectrum in Figure 2 2 appear as they do 2 3 Unix Quick Reference Cards The two figures Fig 2 3 and Fig 2 4 are a Quick Reference cards for some Unix commands 23 LLO sqndsym npocpunipur amay ayyy 0 JOSMOIG MOA 398 QIM ODIAA DHOAA ou uo aps STY ssoooe o 8661 1sna ny sI Se euondo OU 10 sox o qeueA opou 1o3nduioo Joquunu oureuo jueuiuodiAuo K1o0joouip x ssaid pue Aay oyuoo umop p ou X V 1ejuduied siy ui pasn suoneinasqqy pied oouado Joi1 spueuiuioo xu SJOIAYAS ADOIONHOAL NOILVINHOAJNI I ALISYAAINA 8086 Z L09 SOLIOJOOIIP ulojs s jou 19u 930 POYUT o1e SALIOJOAIIP s1osn ATUO SWOIYD uo po e1sur IEMS I SN ATUO Uto NOA WOO ojur POSSO ar NOA J IBA9MOH ESIDA DOTA pue eqo ur posso or noA UdYM UA SAY SUIOIYD NOK epdurexo 10j ssoooe ULI no jeu sueoui urojs s o r POWYS siu Jojurz3 eopl n N Lep eers
6. 20 40 60 80 0 xe c O Q 35 c H dx ey jns ctl 2 Synthetic Seismogram Figure 6 4 The dashed line is the interpreted reflector taken to be the envelope of the circles Mathematically this method of migration may be thought of as the reconstruction of the reflector by defining the tangent vectors of the reflector What then are the circles we have drawn The answer can by found by looking at Figure 6 5 For our 2D constant wavespeed example all solutions of the wave equation which is to say all wavefronts can be found by passing a horizontal plane through the cone in Figure 6 5 Both physical causal solutions the positive t cone and the nonphysical anti causal solutions the negative t cone are depicted We use the causal cone for modeling and the anti causal or reverse time cone for migration To see what a given circle means in Hagadoorn s method we may look at the reverse time cone in Figure 6 6 We may think of the curve on the t 0 plane as the locus of all possible positions from which the reflection originated or we may think of this as the wavefront of the backward propagated wave If we were to apply the Hagedoorn method on the computer we might consider creating for each seismic trace a panel of seismic traces replicating our original seismic arrivals but on a semicircular pattern Spraying out our seismic data for each trace along the respective Hagedoorn circle would yield one new panel of trace
7. medium For scalar waves which is to say waves that do not experience mode conversion the angle of incidence equals the angle of reflection For elastic waves the angle of reflection is a function of the angle of incidence and of the velocities and densities of the media on either side of the reflector The scattered wave therefore carries information about both the orientation of the reflector and its location Thus an image formed from such data is a solution to an inverse problem wherein the wavespeed of the medium and the location and orientation 53 x x Figure 5 1 Cartoon showing the simple shifting of time to depth The spatial coordinates x do not change in the transformation only the time scale t is stretched to the depth scale z Note that vertical relief looks greater in a depth section as compared with a time section of the reflector are the unknown variables being solved for 5 2 Inverse scattering imaging as time to depth conversion In geophysics there are three common types of inverse scattering imaging techniques that may be encountered These are sonar ground penetrating radar GPR and reflection seismic In each case a species of wave is introduced into the subsurface This wave is reflected off of structures within the Earth and travels back up to the surface of the Earth where it is recorded In the raw form the coordinates of the data consist of the spatial coordinates of the record
8. sh that is found on all other Unix and Unix like systems The common working shell environment that a user is usually set up to login in under may be csh the C shell tcsh the T shell which is a non proprietary version of csh ksh the Korn shell which is proprietary zsh which is an open source version of Korn shell or bash which is an open source version of the Bourne shell The user has access to an application called terminal in the graphical user environ ment that when launched usually by double clicking invokes a window called a terminal window The word terminal harks back to an earlier day when a physical device called a terminal consisting of a screen and keyboard but no mouse constituted the users interface to the computer It is at the prompt on the terminal window that the user has access to a commandline where Unix commands are typed Most commands on Unix like systems are not built in commands in the shell but are actually programs that are run under the users working shell environment The shell commandline prompt is asking the user to input the name of an executable program 1 5 The working environment In the Unix world all filenames program names shells and directory names as well as passwords are case sensitive in their input so please be careful in running the examples that follow If the user types cd lt change directory with no argument n takes the user to his her home don t
9. 6 Zero offset aka poststack migration The first reflection seismic experiment as applied to the petroleum exploration was con ducted by physicist John Clarence Karcher in Oklahoma in 1921 Oklahoma was the center of the US oil industry at that time It is clear from reading documents from that era that the expectations of reflection seismic methods were that the results should be similar to sonar That is the expectation was that the signal would travel straight down into the subsurface reflect off of a few structures and then travel straight back up to be recorded There was no expectation of off vertical reflections We of course know that this is not the case By the 1930s many geophysicists were well aware of the geometrical issues at the heart of proper seismic interpretation With the formation of the Society of Exploration Geophysicists in 1930 followed by the first issue of the Society s journal Geophysics the proper usage of seismic data for geologic interpretation became known to the geophysical community In Figure 6 1 we see the classical bowtie feature seen over a syncline To the early interpreter of seismic data this diagram would not have constituted an image of the subsurface but rather a source of geometrical data such as dip pertaining the subsurface reflector Another notion that became apparent is that parts of the data on the seismic traces is displaced from its correct position by the properties of wav
10. MM 10 2 SS with scalco 1 To encode DDDMMSS ss counit DDD 10 6 MM 10 4 SS 1072 with scalco 100 short short short short short short short wevel Weathering velocity swevel Subweathering velocity sut Uphole time at source in milliseconds gut Uphole time at receiver group in milliseconds sstat Source static correction in milliseconds gstat Group static correction in milliseconds tstat Total static applied in milliseconds Zero if no static has been applied short laga Lag time A time in ms between end of 240 byte trace identification header and time break positive if time break occurs after end of header time break is defined as the initiation pulse which maybe recorded on an auxiliary trace or as otherwise specified by the recording system short lagb lag time B time in ms between the time break and the initiation time of the energy source may be positive or negative short delrt delay recording time time in ms between initiation time of energy source and time when recording of data samples begins for deep water work if recording does not start at zero time short muts mute time start 47 short mute mute time end unsigned short ns number of samples in this trace unsigned short dt sample interval in micro seconds Short gain gain typ
11. contain extending downward The root directory is called pronounced slash While there exist graphical browsers on most Unix like operating systems it is more efficient for users working on the commandline of a terminal windows to use a few simple commands to view and navigate the contents of the directory structure These commands pwd print working directory ls list contents and cd change directory Locating yourself on the system If you type cd pwd 1s 10 Vi Quick Reference http www sfu ca yzhang linux MOVEMENT lines ends at lt CR gt sentence ends at puncuation space section ends at lt EOF gt By Character Marking Position on Screen h 4 1 e OE add mp mark current position as p a z p move to mark position p move to first non whitespace on line w mark p Miscellaneous Movement j fm forward to character m Fm backward to character m By Line tm forward to character before m nG tolinen Tm backward to character after m 0 first last position on line w move to next word stops at puncuation or first non whitespace char on line WwW move to next word skips punctuation first character on next prev line b move to previous word stops at punctuation B move to previous word skips punctuation By Screen e end of word puncuation not part of word F B scroll foward back one full screen E end of word punctuation part of word D U
12. cp cwpscratch Datal radar su cp cwpscratch Data1 seismic su AAA A A This is a literal dot which means the current directory 1s should show the file sonar su For the rest of this document when you are directed to make Temp directories it will be assumed that you are putting these in your personal scratch directory 3 1 Viewing an SU data file Wiggle traces and Image plots Though we are assuming that the examples sonar su seismic su and radar su are finished products our mode of presentation of these datasets may change the way we view them entirely Proper presentation can enhance features we want to see suppress parts of the data that we are less interested in accentuate signal and suppress noise Improper presentation on the other hand can take turn the best images into something that is totally useless 3 1 1 Wiggle traces A common mode of presentation of seismic data is the wiggle trace Such a represen tation consists of representing the oscillations of the data as a graph of amplitude as a function of time with successive traces plotted side by side Amplitudes of one polarity usually positive are shaded black where as negative amplitudes are not shaded Note that such presentation introduces a bias in the way we view the data accentuating the positive amplitudes Furthermore wiggle traces may make dipping structures appear fatter than they actually are owing to the fact that a trace is a
13. data shows surange lt junk su 32 traces tracl 1 32 1 32 tracr 1 32 1 32 offset 400 ns 64 dt 4000 whereas the depth converted data has a greater number of samples surange lt junk1 su 32 traces tracl 1 32 1 32 tracr 1 32 1 32 trid 30 offset 400 ns 126 K ns has increased dt 4000 di 3 000000 and finally the depth to time converted data surange lt junk2 su 32 traces tracl 1 32 1 32 tracr 1 32 1 32 offset 400 ns 63 lt ns is now 63 dt 4000 shows ns 63 rather than the original ns 64 samples 58 5 4 1 How time depth and depth time conversion works The way that this works is simple Each sample of the data is a function of time We have velocities to use for each time value If the velocity is constant then the process of time to depth conversion is more of a relabeling process than a calculation However for situations where the velocity varies as we go to later times in the data we have to deal with the fact that the sample spacing of the time to depth shifted data changes as the velocity changes Indeed constant or piecewise constant profiles rarely accurately represent wavespeed variation in the real earth The depth is calculated for each sample but because we want the output to be uniformly sampled we have to interpolate the missing depth values This interpolation may be done many ways but in this program it is done by fitting a sinc function
14. every color plot you encounter requires a colorscale for you to be able to know what the values mean Furthermore some colors ranges are brighter than others By moving the bright color to a different part of the amplitude range you can totally change the image This is a source of richness of display but it is also a potential source of trouble if the proper balance of color is not chosen 3 4 Normalization Median balancing A common data amplitude balancing is to balance the colorscale on the median values in the data The median is the middle value meaning that half the values are larger than the median value and half the data are less than the median value Type these commands to see that in SU sunormalize mode med lt sonar su suximage legend 1 sunormalize mode med lt sonar su suximage legend 1 perc 99 We will find perc 99 to be useful Note that you may zoom in on regions of the plot you find interesting 3l 400 200 99 and legend 1 Figure 3 3 Image of sonar su data with perc 32 EJ ximage EJ ximage O ximage E ximage JEJE 0 5 Figure 3 4 Comparison of the default hsv0 hsv2 and hsv7 colormaps Rendering these plots in grayscales emphasizes the location of the bright spot in the colorbar 33 400 200 99 and legend 1 Figure 3 5 Image of sonar su data with perc 34 200 400 0 05 0 25 Figure 3 6 Image of sonar su data with median normalization and per
15. if I would be willing to help teach the Seismic Processing Lab This was the year following Ken Larner s retirement Terry was teaching the lecture but decided that the students should have a practical problem to work on The choice was between data shot in the Geophysics Field Camp the previous summer or the Viking Graben dataset which Terry had brought with him from his time at Carnegie Mellon University We chose the latter and decided that the students should produce as their final project a poster presentation similar to those seen at the SEG annual meeting Terry seemed to think that we could just hand the students the SU User s Manual and the data and let them have at it I felt that more needed to be done to instruct students in the subject of seismic processing while simultaneously introducing them to the Unix operating system shell language programming and of course Seismic Unx In the years that have elapsed my understanding of the subject of seismic processing has continued to grow and in each successive semester I have gathered more examples and figured out how to apply more types of processing techniques to the data My vision of the material is that we are replicating the seismic processors base ex perience such as a professional would have obtained in the petroleum industry in the late 1970s The idea is not to train students in a particular routine of processing but to teach them how to think like geophysicists Be
16. is now embedded in the x z t cube A seismic arrival to be migrated at the coordinates 7 is placed at the apex of the cone The circle that we draw on the seismogram for that point is the set of points obtained by the intersection of the cone witi eh AMG SA ss arai e Sec adu as se didis NN anes RO SCA de respon Hagedoorn s method of graphical migration applied to the diffraction from a point scatterer Only a few of the Hagedoorn circles are drawn here but the reader should be aware that any Hagedoorn circle through a diffraction event will intersect the apex of the diffraction hyperbola The light cone for a point scatterer at z z By classical geometry a vertical slice through the cone in x t the z 0 plane where we record our datal isa hyperbolss gt ose i te ee ig eh eor Bes Cartoon showing the relationship between types of migration a shows a point in 7 b the impulse response of the migration operation in x z c shows a diffraction d the diffraction stack as the output point Wali coe qi doutes ese qe que ue aces de bee pour ae ite n RYE des 70 71 Preface I started writing these notes in 2005 to aid in the teaching of a seismic processing lab that is part of the courses Seismic Processing GPGN561 and Advanced Seismic Methods GPGN452 later GPGN461 in the Department of Geophysics Colorado School of Mines Golden CO In October of 2005 Geophysics Department chairman Terry Young asked me
17. number i e CDP CMP CRP int cdpt trace number within the ensemble each ensemble starts with trace number one short trid trace identification code 1 Other O Unknown Seismic data Dead Dummy Time break Uphole Sweep Timing Water break Near field gun signature OMAN ODOT PWN KE Il urs e Il Far field gun signature 11 Seismic pressure sensor 12 Multicomponent seismic sensor Vertical component 13 Multicomponent seismic sensor Cross line component 43 14 Multicomponent seismic sensor in line component 15 Rotated multicomponent seismic sensor Vertical component 16 Rotated multicomponent seismic sensor Transverse component 17 Rotated multicomponent seismic sensor Radial component 18 Vibrator reaction mass 19 Vibrator baseplate 20 Vibrator estimated ground force 21 Vibrator reference 22 Time velocity pairs 23 N optional use maximum N 32 767 Following are CWP id flags 109 autocorrelation 110 Fourier transformed no packing xr 0 xi Ol xr N 1 xi N 1 111 Fourier transformed unpacked Nyquist xr 0 xi 0 xr N 2 xi N 2 112 Fourier transformed packed Nyquist even N xr 0 xr N 2 xr i1 xi i1 xr N 2 1 xi N 2 1 note the exceptional second entry odd N xr 0 xr N 1 2 xr 1 xi 1 l xr N 1 2 1 xi N 1 2 71 x31 N15 72 note the exceptional second amp la
18. scroll forward back half a screen s next previous sentence E Y show one more line at bottom top J next previous section L go to the bottom of the screen ht next previous paragraph Zd position line with cursor at top goto matching parenthesis Z position line with cursor at middle Z position line with cursor at EDITING TEXT Entering Text Searching and Replacing a append after cursor lw search forward for w A or a append at end of line w search backward for w i insert before cursor Iw n search forward for w and move down n lines Io i insert at beginning of line n repeat search forward o open line below cursor N repeat search backward o open line above cursor cm change text m is movement s oldiInew replace next occurence of old with new Cut Copy Paste Working w Buffers dm delete m is movement dd delete line D or d delete to end of line x delete char under cursor X delete char before cursor ym yank to buffer m is movement yy or Y yank to buffer current line p paste from buffer after cursor P paste from buffer before cursor bdd cut line into named buffer b a z bp paste from named buffer b s oldinew g replace all occurences on the line x ys old new g replace all ocurrences from line x to y s old new g replace all occurrences in file slold new gc same as above with confirmation Miscellaneous n gt m _ indent n lines m is movement n m un indent left n lines m
19. step models seen in cartoon well log diagrams does not accurately depict the complexity of actual well logs The simplest approximation to a real well log is a piecewise continuous curve with piecewise linear being the simplest curve That is we assume a functional form of v t mt b for velocity as a function of time For the example of t 0 0 15 2 v 1500 2000 3000 in the region from t 0 0 to t 15 the velocity profile would be given by vi f 500 15 t 1500 and in the region from t 15 to t 2 the velocity profile is given by v2 t 1000 05 t 2000 Calculating the values of the depths Z1 Z2 Z3 we see trivially that Z1 0 and that integrating the two equations above yields Z2 131 25 and Z3 193 75 respectively 59 5 5 Sonar and Radar bad header values and incomplete information Most likely depth conversion for sonar and radar requires simply knowing the speed of sound in water and the speed of light respectively This sounds simple and if we had all of the information in a neat and consistent form it would be The first complication comes from the fact that SU is a seismic package When non seismic data are used in a seismic package often the time sampling interval must be scaled to store the data The reason for this is to save storage space in the header the creators of the SEG Y data format chose the time sampling interval dt not to be a floating point number but rather as an unsigned s
20. u qof punossyovg puadsng s2204d Ju244n2 puadsng u ssa204d 2aotuaM SIDIS SNIDIS ss2204d JUL u qol m3 sqof Jo 181 Mie spuooos u 40f da2 g dmo u2242 2umsa2y SuiJJo42s u2242 dog sassa2o4d Jdnssaquy uondrrsoq yxo uo5 3j u25 3q 29pupuruoo u dois x ZI u6 MA sd u25 TPL sqof u deo s x b mo x S B x YD pueuiruio JO1 U0D ss92o0Jd 42jiduio2 qposnq amp If o od 42pidiuO2 UD4O 4 SIL O LO 840442 40f APOD J YII PEU 42piduioo J d If o 99 uondtibosoaq pueuiuio Jejiduio fJo pua mdmo fier Sfo Suiuui8aq mdmo f peau saou2ua fip 2p sisrT Y If Mp ud yomu mpy souy smdmo Sf ud dais J alf adowad ajajaq fuu g sp f opf 2umuoy af if Aw sagaid auy u omu f mdg Sf u mds fuos pvouaquudiy fuos cf on pf apf dop g If do Sof om aapdwuod gf Lf duis Jo apou uoysajosd adunyy Jf apou powyo f onu cf f samuomouo amp f df if eo 12242 q su2Juo0o0 api ISTT f aow apf fo squaquod 4S1 f wo Junoo ADYD Y D40A UIT f OM AONPA 1X21 Hj po 4OJipa u2242sqjnf sovurq soeuio 40npo uaa42sqmf 1A If ta uondrrnsoq pueuiuio uone ndiueyy al 4 Pion suuo Aof amp ajua qpnuput XINN mui fo uoipoifijou juDisu 42 04 JDU puag jouluuat BUDS dos J O1 uoissas JDUIULIA aADS 4ajuud aui 01 f opf mdmo uondr sq ue aumu AUDU WEU us q aUIDUasn reu uolssas xo HJ duos f 421uud q id pueuiuio djep 7 uone2iunuiuio nding U pupuiuioo Juadad juqng uj spu
21. user may copy stuff into a scratch area on one day and then work on a different computer on a different day thinking that their stuff has been removed The availability and use of scratch directories is important because each user has a quota that limits the amount of space that he or she may use in his her home directory On systems where a scratch directory is provided that also has write permission the user may create his her personal work area via cd scratch mkdir yourusername lt here yourusername is the your user name on the system Unless otherwise stated this text will assume that you are conducting further operations in your personal scratch work area 1 10 Shell environment variables and path The working shell is a program that has a configuration that gives the user access to executable files on the system Recall that echoing the value of the SHELL variable echo SHELL returns the value of the users working shell environment tells you what shell program is your working shell environment There are other envi ronmental variables other than SHELL Again note that if this command returns one of the values bin sh bin ksh bin bash bin zsh then you are working in the SH family and need to follow instructions for working with that type of environment If on the other hand the echo SHELL command returns one of the values 14 bin csh bin tcsh then you are working in the CSH family and
22. usr local bin usr sbin set path path CWPROOT bin Save the file and log out and log back in You will need to log out completely from the system not just from particular terminal windows When you log back in and pull up a terminal window typing echo CWPROOT will yield usr local cwp 16 and echo PATH will yield lib u yourusername bin usr bin X11 usr local bin bin usr bin usr local bin usr sbin usr local cwp bin 1 12 2 The SH family The process is similar for the SH family of shells The file of interest has a name of the form profile bashrc and the bash profile The bash profile is read once by the shell but the bashrc file is read everytime a window is opened or a shell is invoked Thus what is set here influences the users complete environment The default form of this file may show a path line similar to PATH PATH HOME bin usr local bin which should be edited to read export CWPROOT usr local cwp PATH PATH HOME bin usr local bin CWPROOT bin The important part of the path is to add the CWPROOT bin on the end of the PATH line no matter what it says The user then logs out and logs back in for the changes to take effect In each case the PATH and CWPROOT variables are necessary to be set for the users working shell environment to find the executables of Seismic Unix 1 13 Unix help mechanism Unix man pages Every program on a Unix or Uni
23. with up to 3 planes suplane optional parameters gt stdout Optional Parameters npl 3 number of planes nt 64 number of time samples 39 ntr 32 number of traces taper 0 no end of plane taper 1 taper planes to zero at the end offset 400 offset dt 0 004 time sample interval in seconds plane 1 dipi 0 dip of plane 1 ms trace leni 3 ntr 4 HORIZONTAL extent of plane traces cti nt 2 time sample for center pivot cxi ntr 2 trace for center pivot plane 2 dip2 4 dip of plane 42 ms trace len2 3 ntr 4 HORIZONTAL extent of plane traces ct2 nb 2 time sample for center pivot cx2 ntr 2 trace for center pivot More As with the Unix man pages typing the space bar shows the rest of the help page Each of these programs has a relatively large number of possible argument set tings The programs suxwigb and suximage both call programs named respectively xwigb and ximage Type ximage xwigb All of the setting for xwigb and ximage apply to suxwigb and suximage That is a lot of settings Correspondingly there are plotting programs that write out PostScript graphics out put for plotting supsimage psimage supswigb pswigb supswigp pswigp The SU versions of these programs call the respective programs that do not have the su prefix AAA AHH 4 2 Finding the names of programs with suname SU is big package containing several hundred program
24. you 52 Chapter 5 Lab Activity 4 Migration Imaging as depth conversion Geophysical imaging often called migration in the seismic context is an example of a general topic called inverse scattering imaging Simply stated inverse scattering imaging is the process of making pictures with echos We have all encountered examples of this in our daily lives Our eyes operate by making images of the world around us from scattered light Medical ultrasound uses the echos of high frequency sound waves to image structures within the human body Ultrasound is also used in an industrial setting for nondestructive testing NDT Seismic prospectors look for oil using the echos of seismic waves Earthquake seismologists determine the internal structure of the deep earth with echos of waves from earthquakes Near surface investigators use the echos of ground penetrating radar waves to image objects in the shallow subsurface 5 1 Imaging as the solution to an inverse problem Acoustic and elastic waves echo off of jumps in the wavespeed and or the density of the medium In the case of electromagnetic scattering the signal is coming from a volume of material or a layer rather than a boundary between layers which has a differing conductivity from the surrounding material In each case the propagating wave impinges on the boundary at some angle and is reflected from the boundary at an angle determined by the law of reflection for the
25. 000 100 surange lt radar su 501 traces trac 1 501 1 501 tracr 1 501 1 501 trid 1 ns 463 dt 800 hour 11 minute 3 33 3 33 Sec 0 59 41 7 surange lt seismc su 801 traces tracl 1200 2000 1200 2000 tracr 67441 115081 67441 115081 fldr 594 991 594 991 tracf 18 2 2 ep 700 1100 700 1100 cdp 1200 2000 1200 2000 cdpt 1 8 2 72 trid 1 nhs 57 60 60 60 gelev 10 selev 6 scalel 1 scalco 1 Sx 18212 28212 18212 28212 gx 15000 25000 15000 25000 counit 3 mute 48 ns 601 dt 4000 In each case where four numbers appear these are the minimum and maximum values in the header followed by the first and last values in the data panel You may use sukey word to determine the meaning of any of the header field key words seen here via 51 sukeyword key where key is the specific keyword For example sukeyword tracl returns int tracl Trace sequence number within line numbers continue to increase if the same line continues across multiple SEG Y files The first field int tells us that this is defined as type integer in the header The short description is the SEG s definition for this field This can be a big deal Ofttimes users will want to define decimal values for the header fields Please note that the keyword names we use here are not an industry standard but are peculiar to SU These are an invention of Einar K
26. 4070496 268 4070228 1 dev none 4075032 4988 4070044 1 dev shm none 4075032 124 4074908 1 var run none 4075032 O 4075032 0 var lock none 4075032 O 4075032 0 lib init rw isengard mines edu usr local cwp 20314752 6037440 13228736 32 usr local cwp isengard mines edu usr local sedpak54 20314752 6037440 13228736 32 usr local sedpak54 isengard mines edu u 206424768 50614912 145324096 26 u isengard mines edu data cwpscratch 30963712 9732128 19658720 34 cwpscratch isengard mines edu data 103212320 19418464 78550976 20 data 12 isengard mines edu scratch 396341312 199520 376008736 1 scratch the hardware devices on the far left column Those whose names begin with dev are hardware devices on the specific computer The items that begin with a machine name in this case isengard mines edu exist physically on another machine named isengard but are remotely mounted as to appear to be on this machine The second column from the left shows the total space on the device the third column shows the amount of space used while the fourth shows the amount available the fifth column shows the usage as a percentage of space used Finally the far right column shows the directory where these devices are mounted In Unix devices are mounted in such a way that they appear to be files or directories Under Unix like operating systems the user sees only a directory tree and not individual hardware devices If
27. Geophysical Image Processing with Seismic Unix GPGN 461 561 Lab Fall 2011 Instructor John Stockwell Research Associate Center for Wave Phenomena copyright John W Stockwell Jr 2009 2010 2011 all rights reserved License You may download this document for educational purposes and personal use only but not for republication September 1 2011 Contents 1 Seismic Processing Lab Preliminary issues LI Motivation for thelabi ut Lour qae E e due yv ao Re 1 2 Unix and Unix like operating systems 1 2 1 Steep learning curve ce uo ood nec de m as ho Rs rn de ge ac ut on 143 AsO BCI Tie n ze ie c5 nci erg he ore ea ara un s au c CR i e at A Wines ae ui aep oe aom qtu qr us enhn n 1 5 The working environment 11053 4 4x 9a 4 4 4 46 Vos E RR AE Bs OR 1 6 Setting the working environment lor Choice Of edi price 4 348 ee Ale ee b DR RUE EEA EUR Rr E 1 8 The Unix directory structure Var en gode en giten ca Sede 1 9 Scratch and Data directories a a a 1 10 Shell environment variables and path ln 1 10 1 The path or PATH ne as mU cw 1 10 2 The CWPROOT variable aoaaa Be ek Baek 4s 1 11 Shell configuration files 2l 1 12 Setting up the working environment oaoa a a lll t121 The C SB amba a i tee By a eS ERU CES ee PS ld2o ro TheSH family i aea qose Be E BD e E gt een Sw 1 13 Unix help mechanism Unix man pages aoaaa lll Lab Activity 1 Gett
28. What are the trace header fields sukeyword If you type sukeyword o you will obtain a listing of the file segy h which defines the SU trace header format The term segy is derived from SEG Y a popular data exchange standard established by the Society of Exploration Geophysicists SEG in 1975 and later revised in 2005 The SU trace header is largely the same as that defined for the SEG Y format The first 240 bytes of each seismic trace in a SEG Y dataset consist of this trace header The data are always uniformly sampled in time so the data portion of the trace consisting of amplitude values only follows immediately after the trace header While it may be tempting to think of a seismic section as an array of traces in the computer these traces simply follow one after the other The part of the listing from sukeyword that is relevant at this point is skipping typedef struct segy trace identification header int tracl Trace sequence number within line 42 numbers continue to increase if the same line continues across multiple SEG Y files int tracr Trace sequence number within SEG Y file each file starts with trace sequence one int fldr Original field record number int tracf Trace number within original field record int ep energy source point number Used when more than one record occurs at the same effective surface location int cdp Ensemble
29. abel2 Distance m perform finite difference acoustic modeling to generate data for a single shot in the sufdmod2 lt velfile nz n1 dz d1 nx n2 dx d2 verbose 1 xs xs zs zs hsz hsz vsx vsx hsfile hsfile vsfile vsfile ssfile ssfile verbose verbose tmax tmax abs 1 1 1 1 mt mt suxmovie clip 1 0 title Acoustic Finite Differencing windowtitle Movie labeli 1abeli label2 label2 ni n1 di d1 f1 f1 n2 n2 d2 d2 f2 f2 loop 1 sleep 20000 geometry 800x400 amp exit 0 You may run the demo by typing XSyncline The result shows the wavespeed profile for the model This is similar to the simple model that will be discussed later in the these notes A movie showing snapshots of the wavefield will begin Watch the wavefront of the energy from the shot expand You may stop and restart the movie by pressing the far right mouse button Of interest are the frames at which the first reflections begin As the movie progresses you will see 66 the reflected field progress as the reflection point propagates along the reflector surface Indeed from viewing this movie we can see why an integral over the reflector surface called the Kirchhoff modeling formula is a way of modeling the reflected field Note that you only see wavefronts there is nothing like a ray to be seen A ray is the trajectory taken by a point on a wavefront Second notice that the bowtie forms as the caustic in the
30. able Because a course in seismic processing is of broad interest and may draw students with varied backgrounds and varied familiarity with computing systems we begin with the basics The reader familiar with these topics may skip to the next chapter 1 3 Logging in As with most computer systems there is a prompt usually containing the word login or the word username that indicates the place where the user logs in The user is then prompted for a password Once on the system the user either has a windowed user interface as the default or initiates such an interface with a command such as startx in Linux 1 4 What is a Shell Some of the difficult and confusing aspects of Unix and Unix like operating systems are encountered at the very beginning of using the system The first of these is the notion of a shell Unix is an hierarchical operating system that runs a program called the kernel that is is the heart of the operating system Everything else consists of programs that are run by the kernel and which give the user access to the kernel and thus to the hardware of the machine The program that allows the user interfaces with the computer is called the working shell The basic level of shell on all Unix systems is called sh the Bourne shell Under Linux based systems this shell is actually an open source rewritten version called bash the Bourne again shell but it has an alias that makes it appear to be the same as the
31. age plot If we view An alternative is an image plot suximage lt sonar su amp This should look better We usually use image plots for datasets of more than 50 traces We use wiggle traces for smaller datasets 3 2 Greyscale There are only 256 shades of gray available in this plot If a single point in the dataset makes a large spike then it is possible that most of the 256 shades are used up by that one amplitude Therefore scaling amplitudes is often necessary The simplest processing of the data is to amplitude truncate clip the data The term clip refers to old time strip chart records which when amplitudes were too large appeared if someone had taken scissors and clipped of the tops of the sinusoids of the oscillations Try suximage lt sonar su perc 99 amp suximage lt sonar su perc 99 legend 1 The perc 99 passes only those items of the 99th percentile and below in amplitude You may need to look up percentile on the Internet In other words it clips amplitude truncates the data to remove the top 1 per cent of amplitudes Try different values of perc to see what this does 28 200 400 0 05 0 10 0 15 0 20 0 25 Figure 3 1 Image of sonar su data no perc Only the largest amplitudes are visible 29 200 400 0 05 0 10 0 15 Figure 3 2 Image of sonar su data with perc 99 Clipping the top 1 percentile of amplitudes brings up the lower amplitu
32. an easy program to use for this e Prepare a report of your results The report should consist of Your plots a short paragraph describing what you saw Think of it as a figure caption a listing of the actual commandlines that you ran to get the plots Not more than 3 pages total Make sure that your name the due date and the assignment number are at the top of the first page e Save your report in the form of a PDF file and email to john dix mines edu 36 68357 9 0 30397 999 0 68000 median no median Figure 3 7 Comparison of seismic su median normalized with the same data with no median normalization Amplitudes are clipped to 3 0 in each case Note that there are features visible on the plot without median normalization that cannot be seen on the median normalized data 37 3 6 Concluding Remarks There are many ways of presenting data Two of the most important questions that a scientist can ask when seeing a plot are What is the meaning of the colorscale or grayscale of a plot and What normalization or balancing has been applied to the data before the plot The answers to these questions may be as important as the answer to the question What processing has been applied to these data 3 6 1 What do the numbers mean The scale divisions seen on the plots in this chapter that have been obtained by running suximage with legend 1 show numerical values values
33. c 99 35 Note that if you put both the median normalized and simple perc 99 files on the screen side by side there are differences but these may not be striking differences The program suximage has a feature that the user may change colormaps by pressing the h key or the r key Try this and you will see that the selection of the colormap can make a considerable difference in the appearance of the image Even with the same data the colormap For example in Figure 3 7 we see the result of applying the commands suximage lt seismic su wbox 250 hbox 600 cmap hsv4 clip 3 title no median amp compared with sunormalize mode median lt seismic su suximage wbox 250 hbox 600 cmap hsv4 clip 3 title no median amp Note that the line is broken to fit on the page When you type this the pipe follows immediately after the seismic su Here the 3 5 Homework problem 1 Due Thursday 1 Sept 2011 Repeat display gaining experiments of the previous section with radar su and seis mic su to see what median balancing and setting perc does to these data e Capture representative plots with axes properly labeled You can use the Linux screen capture feature or find another way to capture plots into a file such as by using supsimage to make PostScript plots Feel free to use different values of perc and different colormaps than were used in the previous examples The OpenOffice Word wordprocessing program is
34. cause seismic processing techniques are not exclusively used on petroleum industry data the notion of geophysical image processing rather than simply seismic processing is conveyed Chapter 1 Seismic Processing Lab Preliminary issues 1 1 Motivation for the lab In the lecture portion of the course GPGN452 561 now GPGN461 561 Advanced Seis mic Methods Seismic Processing the student is given a word picture and chalkboard introduction of the process of seismic data acquisition and the application of a myriad of processing steps for converting raw seismic data into a scientifically useful picture of the earth s subsurface This lab is designed to provide students with a practical hands on experience in the reality of applying seismic processing techniques to synthetic and real data The course however is not a training course in seismic processing as one might get in an industrial setting Rather than training a student to use a particular collection of software tools we believe that it is better that the student cultivate a broader understanding of the subject of seismic processing We seek also to help students develop some practical skills that will serve them in a general way even if they do not go into the field of oil and gas exploration and development Consequently we make use of freely available open source software the Seismic Unix package running on small scale hardware Linux based PCs Students are also en
35. cour aged to install the SU software on their own personal Linux or Mac PCs so that they may work and play with the data and with the codes at their leisure Given the limited scale of our available hardware and time our goal is modest to introduce students to seismic data processing through a 2D single component processing application The intended range of experience is approximately that which a seismic processor of the late 1970s would have experienced on a vastly slower more expensive and more difficult to use processing platform 1 2 Unix and Unix like operating systems The Unix operating system as well as any other Unix like operating system which includes the various forms of Linux UBUNTU Free BSD Unix and Mac OS X is commonly used in the exploration seismic community Consequently learning aspects this operating system is time well spent Many users may have grown up with a point and click environment where a given program is run via a graphical user interface GUI featuring menus and assorted windows Certainly there are such software applications in the world of commercial seismic processing but none of these are inexpensive and none give the user access to the source code of the application There is also an expert user level of work where such GUI driven tools do not exist however and programs are run from the commandline of a terminal window or are executed as part of a processing sequence in shell scrip
36. de amplitudes of the plot 30 3 9 Legend making grayscale values scientifically meaningful To be scientifically useful which is to say quantitative we need to be able to translate shades of gray into numerical values This is done via a gray scale or legend A legend is a scale or other device that allows us to see the meanings of the graphical convention used on a plot Try suximage lt sonar su legend 1 amp This will show a grayscale bar There are a number of colorscales available Place the mouse cursor on the plot and press h you will see that further pressings of h will re plot the data in a different colorscale Now press r a few times The h scales are scales in hue and the r scales are in red green blue rgb Note that the brightest part of each scale is chosen to emphasize a different amplitude With colormapping some parts of the plot may be emphasized at the expense of other parts The issue of colormaps often is one of selecting the location of the bright part of the colorbar versus darker colors Even perfectly processed data may be rendered uninterpretable by a poor selection of colormapping This effect may be seen in Figure 3 4 Repeat the previous this time clipping by percentile suximage lt sonar su legend 1 perc 99 amp The ease at which colorscales are defined and the fact that there are no real standards on colorscales mean that effectively
37. e of field instruments code 1 fixed 2 binary 3 floating point 4 N optional use short igc instrument gain constant short igi instrument early or initial gain short corr correlated 1 no 2 yes short sfs sweep frequency at start short sfe sweep frequency at end short slen sweep length in ms short styp sweep type code 1 linear 2 cos squared 3 other short stas sweep trace length at start in ms short stae sweep trace length at end in ms short tatyp taper type 1 linear 2 cos 2 3 other short afilf alias filter frequency if used short afils alias filter slope short nofilf notch filter frequency if used 48 short short short short short short short nofils notch filter slope lcf low cut frequency if used hcf high cut frequency if used lcs low cut slope hcs high cut slope year year data recorded day day of year short hour hour of day 24 hour clock short minute minute of hour short sec second of minute short timbas time basis code 1 local 2 GMT 3 other short trwf trace weighting factor defined as 1 2 N volts for the least significant bit short grnors geophone group number of roll switch position one short grnofr geophone group number of trace one withi
38. e propagation Assuming that all reflections are normal incidence for this zero offset geometry it is clear that parts of the bowtie originate from higher positions on the sides of the syncline Thus the notion of migrating those arrivals to their correct location became an important idea for interpretation Because the seismic data were analog rather than digital such corrections would naturally be applied graphically While graphical migration techniques had been applied since the 1930s the first notable technical paper describing this technique was published by J G Mendel Hage doorn in 1954 This paper is important because Hagedoorn s description of the migration process inspired early digital computer implementations of migration 63 Depth m Time in Seconds 20 40 60 TT n sell 0 1000 2000 3000 2 Synthetic Seismogram v 2000 m s p const v 3000 m s p const Simple Single Reflector Model Figure 6 1 a Synthetic Zero offset data b Simple earth model 64 4000 6 1 Migration as reverse time propagation One way of looking at migration is as a reverse time propagation The idea may be visualized by running the output from a forward modeling demo in reverse time Do the following noting that you need to replace yourusername with your actual username on the system so that the items are copied to your personal scratch area cp cwpscratch Datai syncline
39. eld dt Make sure that you give a justification explaining why your choice of the appropriate power of 10 scaling factor is likely the correct one Remember that the depth scale on you output data should make sense 5 8 Concluding Remarks When receiving software either that is given to us or that which we purchase it is important to try to figure out what assumptions are built into the software One way to do that is to try the software out on test patterns When receiving data it is important to know everything that you can possibly know about the data such as the spacing of the traces the time sampling interval any pro cessing that has been applied When explaining seismic imaging to non geophysicists it is tempting to say that seis mic imaging is sort of like sonar However sonar is a rough surface scattering imaging whereas seismic is a specular or mirror reflection scattering imaging In rough surface scattering the image may indeed be formed by straight down and straight back re flections In seismic this is rarely the case We must take offset between the source and receiver into account In seismic there are also rough surface contributions These are the diffractions we look for on stacked data In the early days of seismic well into the 1930s there were practitioners of the seismic method who thought that seismic was like sonar and expected that seismic datasets should be data images 62 Chapter
40. eopI n N 1 AW ojuo p noA ay K10joarmp ojurzq SIY 0 10320JIp OAS STU WOY O T AOU 0 pojueA 20A uuor J o durexo 10 SAY UM Syu oroqui S IJEU Jo SAJ doo SAY IAOU 03 spueuruioo xru AreurpJo ou N ULI NOA PAS ojur pe33o jem sys yYFnoy UdAd so rj OJUTZ JOY oos YS SAY JOY SISH ous UAM MON ojuiz3AIqqeaf n N po u9juo p no ous junoooe OJUIZA Joy uo e 798 0 sjue pue PAS uo junoooe JOY ojur posSo st Wqqey eorssof JI o durexo 104 aumuasn JO oureurosn umo Jno oynnsqns pue oAoqe aes no se jsnf uonezipojideo ou osn no ains og JdS 2aumuaasnimju po Jojuizg aumu42snmyN po 9391g 2umu42snyn N po Jourz aumwua2snnyN po Aleqoo aumpusasnjayN po ouo 2umuasnim Ny po TWIA SAS IIO AUB WOI A1OJALIP urojs S AUP 0 198 0 DSN 0j spueuiuioo OY AIL IH SIAO ou Jo Aue uo soft INO 0 398 ueo NOA our Passo are NOA s1ognduioo osou JO YOTYM ILU ON Sjunoooe MLY NOA uorqA UO sjsou XUN BUSS dU 10 peureu sorojoerrp ur 5 srp euo uo K 21 ose S H INOA jeu SULU jeu SAN PAF AH JIOMION OY uo paS ale JS SMAV LS pue ojurzz PAS UZ 3 eq0 WYJ s1ognduioo xun Teu SLIN A uo poses s l s li SIN uum BuppoAM ty References Ivers 24 UNIX Quick Reference card p1 From the Un Figure 2 3 JSHASL ue q poeu osou 1dooxo pueururoo uoeo JO puo dU W NAA LAA SSAA JAYS uodf nx3 u qof puno48240f 2umsay u qof punossyong aunsay puno482pq ut pupunuoo uny
41. ero offset reflection seismograms recorded over the undulating reflector model in Figure 6 1b The wave speed in the upper medium is assumed to be 2000 m s and the data are drawn in such a way that 1 0 s two way time is equivalent to 1000 m of distance Thus the time scale translates into a depth scale that is compatible with the horizontal scale If we draw a circle centered at time t 0 of a given seismic trace and passing through a given seismic arrival we have sketched all possible reflection points from which the seismic arrival could have originated These circles are the same as the incident field seen in the seismic movie If we recall seismic migration finds the place where the incident field interacts with the reflected field the reflector surface When similar circles are drawn for every arrival on every trace the result is a collection of circles whose envelope delineates the reflector See Fig 6 3 for an idea of what this should look like 67 0 Time in S conds Synthetic Seismogram Figure 6 2 The Hagedoorn method applied to the arrivals on a single seismic trace Trace 20 40 60 8 Figure 6 3 Hagedoorn s method applied to the simple data of Fig 6 1 Here circles each centered at time t 0 on a specific trace pass through the maximum amplitudes on each arrival on each trace The circle represents the locus of possible reflection points in z z where the signal in time could have originated 68 Trace
42. etting 60 According to a personal communication by Dr Tono the geologic setting of the sonar data is thus The deposits and images were produced at the Saint Anthony Falls Lab of the University of Minnesota Here experimental stratigraphy is produced under precisely controlled conditions of subsidence base level and sediment supply By superimposing optical images of the sectioned deposits on seismic images we can directly observe the ability of seismic profiling to distinguish different geological features The experimental basin is 5 m by 5 m 25 m2 and 0 61 m deep Sediment and water were mixed in a funnel and fed into the basin at one corner This produced an approximately radially symmetrical fluvial system which aver aged 2 50 m from source to shoreline The edges of the basin were artificially roughened in order to direct the channels away from the walls The ocean level was maintained through a variable discharge siphon located in the op posite corner of the basin Though we imposed a gradual base level rise in order to simulate subsidence the shoreline maintained a constant position through the experiment Dr Tono goes on to describe the experimental layout The outgoing pulse is generated with a Prototype JRS DPR300 Pulser Receiver which drives a 900 volt square pulse into the transducer It is set to a pulse receive frequency of 100 Hz with an input gain of 30 dB in echo mode The high pass filter i
43. guage many configurations of the shell environment are possible To find the configuration files for your operating system type ls a show directory listing of all y 8 files and sub directories pwd lt print working directory then the user will see a number of files whose names begin with a dot 15 1 12 Setting up the working environment One of the most difficult and confusing aspects of working on Unix like systems is en countered right at the beginning This is the problem of setting up user s personal environment There are two sets of instructions given here One for the CSH family of shells and the other for the SH family 1 12 1 The CSH family Each of the shell types returned by SHELL has a different configuration file For the csh family tcsh csh the configuration files are cshre and login To configure the shell edit the file cshrc Also the path variable is lower case You will likely find a line beginning with set path with entries something like set path lib bin usr bin X11 usr local bin bin usr bin usr local bin usr sbin Suppose that the Seismic Unix package is installed in the directory usr local cwp on your system Then we would add one line above to set the CWPROOT environment variable And one line below to define the user s path setenv CWPROOT usr local cwp set path lib bin usr bin X11 usr local bin bin usr bin
44. hort integer On a 32 bit machine the size of the largest value that an unsigned short can take on is 65535 Thus scaling is necessary Usually these scale factors are multiples of 10 Try doing depth conversion on the sonar and radar data using values you know for the speed of sound suttoz v SPEED_OF_SOUND_IN_WATER lt sonar su suximage perc 99 amp and the speed of light suttoz v SPEED_OF_LIGHT lt radar su suximage perc 99 amp respectively The speed of light is 2 998 x 105m s The speed of sound in water is 1500m s Likely the correct values to use in each case will be off by some multiple of 10 owing to the fact that the natural frequencies available for radar and sonar are not in the same band as those used for seismic data If we type sukeyword dt unsigned short dt sample interval in micro seconds we see that the time sampling interval dt is expressed in microseconds Seismic fre quencies range from a few Hz to maybe 200 hz but likely are not up into the kilohertz range unless some special survey is being conducted Sonar frequencies likely range ten s of kilohertz to hundreds of kilohertz Radar operates in the megahertz range So it is common for the user to fake the units on the time sampling interval so as to fit the requirements of a seismic code 5 6 The sonar data The sonar su file is one of the profiles collected by Dr Henrique Tono of Duke Univer sity in a special laboratory s
45. ic method The technique started out as an aid in interpretation becoming later an imaging technology Today seismic migration is viewed by many as the solution to an inverse problem wherein recorded seismic data are used as input to solve for the reflectivity of the reflectors as well as other important material parameters that characterize lithology 73
46. ing position and traveltime which may be represented as the ordered triple of numbers Data xzi x t It is implied that some form of processing is needed to convert data collected in the input coordinates of space and time Data r x3 t into an image in the output coordinates that are purely spatial DepthImage yi yo ya or are new spatial coordinates and a migrated time coordinate TimeImage y1 ys T When the output is in space and migrated time we call the process time migration and the output a time section When the output is in purely spatial coordinates we call the process depth migration and the output a depth section Each type of section is found useful in exploration seismic 54 Thus for our migration as depth conversion we will consider the final step of pro cessing as a process that converts the data from Data yi yo 7 to data in DepthImage y1 yo ya in purely spatial coordinates The simplest cases of such processing occur when the output spatial coordinates on the recording surface are such that y z and yg z2 Then the remaining problem is to trade time for depth Often the symbol z is used to represent depth with z increasing positively as we go deeper into the earth Clearly special circumstances are needed for this simple case to exist Effectively such an imaging problem is one dimensional This type of problem may result from the construction of synthetic well logs from migra
47. ing started with Unix and SU 2 1 Pipe redirect in lt redirect out gt and run in background amp 2 2 Stringing commands together uoc ox ER B eges 2 2 1 Questions for discussion 1o wea ud e gom Seded 2 3 Unix Quick Reference Cards 4k S Rs ar KEIRA Aes Re hed Lab Activity 2 viewing data 3 0 1 Data image examples x2 eos RR BAI 3 1 Viewing an SU data file Wiggle traces and Image plots 3 1 1 Wiggle traces TERCER ECRIRE a Gul Imag plots o d acte e d det ah oh te ee EL ae UR as eu Bee Greyscale mkr aap tras oer ee a e eee A ACR SNE amp epee ies a 3 3 Legend making grayscale values scientifically meaningful 3 4 Normalization Median balancing ll man cO d0du020 05 1 i 1o0 0c Bee ee Pe ee NIN DD D Ot Ot OTH C2 19 21 22 23 23 3 5 Homework problem 1 Due Thursday 1 Sept 2011 3 6 Concluding Remarks 4 4 2x4 Gb Beg bgt Seas oo tenuta oben acne 3 6 1 What do the numbers mean 2 0004 Help features in Seismic Unix AN CMe selidoto eL aec e tet BE noL ene ptt A EO start La cod mt 4 2 Finding the names of programs with suname 4 3 Lab Activity 3 Exploring the trace header structure 4 3 1 What are the trace header fields sukeyword 4 4 Concluding Remarks x eo dy qued eeu XC Be EEE arp ip Lab Activity 4 Migration Imaging as depth conversion 5 1 Imaging as the solution to an inverse prob
48. is movement repeat last command U undo changes on current line u undo last command J join end of line with next line at lt cr gt uf insert text from external file f G show status Figure 1 1 A quick reference for the vi editor 11 You will see that your current working directory location which is your called your home directory You should see something like pwd home yourusername where yourusername is your username on the system Other users likely have their home directories in home or something similar depending on how your system administrator has set things up The command Is will show you the contents of your home directory which may consist of files or other subdirectories The codes for Seismic Unix are installed in some system directory path We will assume that all of the CWP SU Seismic Unix codes are located in usr local cwp This denotes a directory cwp which is the sub directory of a directory called local which is in turn a directory of the directory usr that itself is a sub directory of slash It is worth wile for the user to spend some time learning the layout of his or her directories There is a command called df which shows the hardware devices that constitute the available storage on the users machine A typical output from typing df Filesystem 1K blocks Used Available Use Mounted on dev sda1 295101892 45219392 234892216 17 none
49. jartannson the author of the original suite of programs call SY that later became the basis of the SU package 4 4 Concluding Remarks Every data processing package has help features and internal documentation None of these are usually perfect and all are usually aimed at people who already understand the package Look for the help features and demos of a package When receiving a dataset the most important questions that a scientist can ask about a dataset that he or she receives are What is the format of the data Are the data uniformly sampled For seismic data Have the headers been set and What are ranges of the the header values Do the header values make sense Note also that data coming in from the field frequently requires that the headers be set in the data Transferring header information from seismic observers logs into seismic trace headers is called setting geometry Setting geometry can be one of the biggest headaches in preparing data for processing Vendors may remap the SEG Y header fields both in terms of the meaning of the header field and with respect to the data type Obtaining a header map of data when you obtain seismic data can prevent confusion and save you a lot of work When receiving data on tape remember that tape reading is more of an art than a science It is best to ask for data in a format you can use rather than allow someone else to dictate that format to
50. kage and may be too much information for everyday usage What is more common is that we might want a bit more information than a selfdoc but not a complete listing This is where the sudoc feature is useful Typing sudoc NAME yields the sudoc entry of the program NAME For example we might be interested in seeing information about suplane sudoc suplane and comparing that with the selfdoc for the same program suplane 41 As the number of SU programs you come in contact increases you will find it useful to continually be referring to the listing from suname The sudoc feature is an alternative to Unix man pages The database of sudocs is captured from the actual selfdocs in the source code automatically via a shell script so these do not go out of step with the actual code the way a separately written man page might 4 3 Lab Activity 3 Exploring the trace header structure You may have noticed that the plotting programs seem to know a lot about the data you have been viewing Yet you have never been asked to give the number of samples per trace or the number of traces For example suximage lt sonar su perc 99 amp shows a plot without being told the dimensions of the data But how did the program know the number of traces and the number of samples per trace in the data The program knows because this and all other SU programs read information from a header that is present on each seismic trace 4 3 1
51. lem 5 2 Inverse scattering imaging as time to depth conversion 5 3 Time to depth with suttoz depth to time with suztot 5 4 Time to depth conversion of a test pattern l l 5 4 1 How time depth and depth time conversion works 5 5 Sonar and Radar bad header values and incomplete information S Ehe SOMA dataz aiir be qon ue Aci dee e e e eser Sees Qnod 5 7 Homework Problem 2 Time to depth conversion of the sonar su and the radar su data Due Thursday 8 Sept 2011 Ln 5 8 Concluding Remarks 6 520 4 oo E ek ee ek eee E be d Zero offset aka poststack migration 6 1 Migration as reverse time propagation llle 6 2 Lab Activity 5 Hagedoorn s graphical migration 6 3 Migration as a Diffraction stack ses 41 xe Ser xo NUS VU es 6 4 Migration as a mathematical mapping 6 5 Concluding Remarks ERRORS S OT E CO CET Boe T LLL TTE List of Figures 1 1 2 1 2 2 2 3 2 4 3 1 3 2 3 3 3 4 3 5 3 6 3 7 5 1 5 2 A quick reference for the vi editor 0000000 0a The suplane test pattern llle a The suplane test pattern b the Fourier transform time to frequency of the suplane test pattern via suspecfx UNIX Quick Reference card pl From the University References UNIX Quick Reference card p2 Lai ma ae asp dee a EA Image of sonar su data no perc Only the la
52. n original field record short grnlof geophone group number of last trace within original field record short short gaps gap size total number of groups dropped otrav overtravel taper code 1 down or behind 2 up or ahead 49 cwp local assignments float di sample spacing for non seismic data float f1 first sample location for non seismic data float d2 sample spacing between traces float 2 first trace location float ungpow negative of power used for dynamic range compression float unscale reciprocal of scaling factor to normalize range int ntr number of traces short mark mark selected traces short shortpad alignment padding short unass 14 unassigned NOTE last entry causes a break in the word alignment if we REALLY want to maintain 240 bytes the following entry should be an odd number of short UINT2 OR do the insertion above the mark keyword entry float data SU_NFLTS segy Not all of these header fields get used all of the time Some headers are more important than others The most relevant fields to normal SU usage are the header fields tracl tracr dt cdp offset sx gx sy gy and delrt To see the header field ranges on sonar su radar su and seismic su type surange lt sonar su 50 584 traces tracl cdp muts ns dt 1 584 1 584 1 584 1 584 75 3
53. need to follow the alternate series of in structions given In the modern world of Linux it is quite common for the default shell to be something called binbash an open source version of binsh 1 10 1 The path or PATH Another important variable is the path or PATH The value path variable tells the location that the working shell looks for executable files in Usually executables are stored in a sub directory bin of some directory Because there may be many software packages installed on a system there may be many such locations To find out what paths you can access which is to say which executables your shell can see type echo path Or echo PATH G6 The result will be a listing separated by colons of paths or by spaces to executable programs 1 10 2 The CWPROOT variable The variable PATH is important but SHELL and PATH are not the only possible envi ronment variable Often programmers will use an environment variable to give a users shell access to some attribute or information regarding a specific piece of software This is done because sometimes software packages are of restricted interest For SU the path CWPROOT is necessary for running the SU suite of programs We need to set this environment variable and to put the suite of Seismic Unix programs on the users path 1 11 Shell configuration files Because the users shell has as an attribute a natural programming lan
54. ng from a to b is Hagedoorn s migration method Going from c to d is the diffraction stack migration method If however we reverse directions mapping from from b to a or from d to c then we are modeling or doing data based de migration which is the inverse of migration The idea then is that modeling is the forward process and migration is the inverse operation f2 a b Sx z c x d x t z x z Figure 6 9 Cartoon showing the relationship between types of migration a shows a point in 7 b the impulse response of the migration operation in x z c shows a diffraction d the diffraction stack as the output point x z 6 5 Concluding Remarks The notion of the value and motivation of using seismic data has changed through the history of seismic methods Originally seismic data were used to find estimates of depth of perhaps a single important horizon As the technique developed the depth to and dip of a specific target reflector was found Most notably was Frank Rieber s dip finder The dip finder was a recording system that was effectively an analog computer that delivered an estimate of depth and dip for stronger reflectors These data were then used for drawing geologic cross sections In fact Frank Rieber s dip finder was doing something similar to a variety of migration called map migration As the petroleum and natural gas industry evolved so did the importance of the seism
55. ory via mkdir scratch yourusername Here yourusername is the actual username that you are designated as on this system Please feel free to ask for help as you need it The scratch directory may reside physically on the computer where you are sitting or it may be remotely mounted In computer environements where the directory is locally on the a given computer you will have to keep working on the same system If you change computers you will have to transfer the items from your personal scratch area to that new machine In labs where the directory is remotely mounted you may work on any machine that has the directory mounted Remember scratch directories are not backed up If you want to save materials permanently it is a good idea to make use of a USB storage device 3 0 1 Data image examples 06 Three small datasets are provided These are labeled sonar su radar su and seis mic su and are located in the directory cwpscratch Data1 We will pretend that these data examples are data images which is to say these are examples that require no further processing Do the following cd scratch yourusername this takes you to scratch yourusername 26 This represents the prompt at the beginning of the commandline Do not type the when entering commands mkdir Tempi this creates the directory Tempi cd Tempi change working directory to Temp1 cp cwpscratch Datal sonar su
56. ows the user to write programs called shell scripts Thus Unix like systems have scripting languages as their basic interface environment This endows Unix like operating systems with vastly more flexibility and power than other operating systems you may have encountered With more flexibility and power there comes more complexity It is possible to perform many configuration changes and personalizations to your working environment which can enhance your user experience For these notes we concentrate only on enough of these to allow you to work effectively on the examples in the text 1 7 Choice of editor To edit files on a Unix like system the user must adopt an editor The traditional Unix editor is vi or one of its non proprietary clones vim vi improved gvim or elvis The vi environment has a steep learning curve making it often unpopular among beginners If a person is envisioning working on Unix like systems a lot then taking the time to learn vi is also time well spent The vi editor is the only editor that is guaranteed to be on all Unix like systems All other editors are third party items that may have to be added on some systems sometimes with difficulty Similarly there is an editor called emacs that is popular among many users largely because it is possible to write programs in the LISP language and implement these within emacs There is a steep learning curve for this language as well There is often substantial configu
57. propagating wavefield The movie will run in a loop You may stop the movie by pushing the right mouse button You may reverse the movie by pressing the middle mouse button Effectively running the field backward in time is reverse time migration In seismic data we do not have a record of the down traveling field All we have is the record of that part of the reflected field that hits the surface of the earth where there are geophones The migration process finds the place where the downtravelling field and the reflected field overlay the reflector surface One way of looking at migration is that we would like to cross correlate the down traveling field with the time reversed reflected field The place where these fields correlate is at the reflector surface You may also see what the seismic data looks like recorded at the surface of the earth model by viewing the file hseis su via suximage lt hseis su perc 99 to see the direct arrival and the bowtie shaped reflected arrival Finally you may change the depths in the model by editing the file syncline unif2 or change the location of the source to see what varying these quantities changes in the data You may slow down the movie by increasing the value of the sleep parameter 6 2 Lab Activity 5 Hagedoorn s graphical migration The purpose of this lab example is to migrate the simple data in Figure 6 1a by Ha gadoorn s graphical method These synthetic data represent the z
58. punuoo 1u2224 ASIG Kosy amp 10J2241p BUDJAOM JUL pad uoupuuofur aSU asupyy ujuo uonpunofur sasn mdmo 2umusn 1o8ur 4asn ju244no amp pjdsiqz TUROYM SAISN ut PASSO IST oym AU p AWP Ud ovp njonb ysip amp vjdsi vjonb sanjpa 1u2uuo414Au2 uq saspyp puru amp pjdsiq aupu Auojuud 2umu see IIop ut sapf 1817 7d 178 amp 0J9241p ui S2pf Ir CF p s uondiisa q pueuluio snje1g 1uou1uoJliAUu 2 qU14DA Ju2uu041AU2 240UI24 4 2n D4 0 ADA AU2 128 uoissas puru PUT apou 3j0ui24 0j USOT PUDU SDUD pununuo2 2A0u2M SDI D PUDUULOD 210247 p4oasspd asuvyy Zp SD p amp uomo24ip aumua2y p amp uoj22uip 01 f apf aaow p amp u0po2uip aaoulay p amp uop2uip MAU 210247 p amp oro2uip 01 a8UuDYD uorjdrbsaq gaunu 2umu Auojosun 4 JUDU AUIS moog pu uou aumu seieun caumu 2umu see passed cP p Aw P cf f su p Tpu p ap yur pps pueururo JO 1 U0D 3ueuiuoJiAu UNIX Quick Reference card p2 25 Figure 2 4 Chapter 3 Lab Activity 2 viewing data Just as scratch paper is paper that you use temporarily without the plan of saving for the long term a scratch directory is temporary working space which is not backed up and which may be arbitrarily cleared by the system administrator Each computer in this lab has a directory called scratch that is provided as a temporary workspace for users It is in this location that you will be working with data Create your own scratch direct
59. ration required to get emacs working in the way the user desires A third editor is called pico which comes with a mailer called pine Pico is easy to learn to use fully menued and runs in a terminal window The fourth class of editor consists of the screen editors Popular screen editors include xedit nedit and gedit There is a windowed interfaced version of emacs called xemacs that is similar to the first two editors These are all easy to learn and to use Not all editors are the best to use The user may find that invisible characters are introduced by some editors and that there may be issues regarding how wrapped lines are handled that may cause problems for some applications More advanced issues such as those which might be of interest to a Unix system administrator narrow the field back to vi The choice of editor is often a highly personal one depending on what the user is familiar with or is trying to accomplish Any of the above mentioned editors or similar third party editors likely are sufficient for the purposes of this course 1 8 The Unix directory structure As with other computing systems data and programs are contained in files and files are contained in folders In Unix and all Unix like environments folders are called directories The structure of directories in Unix is that of an upside down tree with its root at the top and its branches subdirectories and the files they
60. rgest amplitudes are visible Image of sonar su data with perc 99 Clipping the top 1 percentile of amplitudes brings up the lower amplitude amplitudes of the plot Image of sonar su data with perc 99 and legend 1 Comparison of the default hsv0 hsv2 and hsv7 colormaps Rendering these plots in grayscales emphasizes the location of the bright spot in the COlOMIAES S aro any der Bnew ete ae ios Men do to diede di Image of sonar su data with perc 99 and legend 1 Image of sonar su data with median normalization and perc 99 Comparison of seismic su median normalized with the same data with no median normalization Amplitudes are clipped to 3 0 in each case Note that there are features visible on the plot without median normalization that cannot be seen on the median normalized data Cartoon showing the simple shifting of time to depth The spatial coor dinates do not change in the transformation only the time scale f is stretched to the depth scale z Note that vertical relief looks greater in a depth section as compared with a time section a Test pattern b Test pattern corrected from time to depth c Test pattern corrected back from depth to time section Note that the curvature seen depth section indicates a non piecewise constant v t Note that the reconstructed time section has waveforms that are distorted by repeated sinc interpolation The sinc interpolation applied in the depth
61. s as well as hundreds of library functions shell scripts and associated files Occasionally we would like to see the total scope of the package we are working with For an inventory of the SU programs typing 40 suname yields EC CWP Free Programs CWPROOT usr local cwp Mains In CWPROOT src cwp main CTRLSTRIP Strip non graphic characters DOWNFORT change Fortran programs to lower case preserving strings FCAT fast cat with 1 read per file ISATTY pass on return from isatty 2 MAXINTS Compute maximum and minimum sizes for integer types PAUSE prompt and wait for user signal to continue T time and date for non military types UPFORT change Fortran programs to upper case preserving strings X X In CWPROOT src par main A2B convert ascii floats to binary B2A convert binary floats to ascii CSHOTPLOT convert CSHOT data to files for CWP graphers DZDV determine depth derivative with respect to the velocity FARITH File ARITHmetic perform simple arithmetic with binary files FTNSTRIP convert a file of binary data plus record delimiters created FTNUNSTRIP convert C binary floats to Fortran style floats GRM Generalized Reciprocal refraction analysis for a single layer H2B convert 8 bit hexidecimal floats to binary More 3 Hitting the space bar shows the rest of the page The suname output shows every library function shell script and main program in the pac
62. s for each seismic trace Our 80 traces would then become 80 panels of sprayed traces We would then sum the corresponding traces on each panel Constructive interference would tend to enhance the region near the reflector and destructive interference would tend to eliminate everything else revealing only the reflector Does this method work Yes but it is subject to interference errors if the data are not densely sampled in space Because a point at 7 represents an impulse in the x t space corresponding 69 i Figure 6 5 The light cone representation of the constant velocity solution of the 2D wave equation Every wavefront for both positive and negative time t is found by passing a plane parallel to the x z plane through the cone at the desired time t We may want to run time backwards for migration Figure 6 6 The light cone representation for negative times is now embedded in the x z t cube A seismic arrival to be migrated at the coordinates 7 is placed at the apex of the cone The circle that we draw on the seismogram for that point is the set of points obtained by the intersection of the cone with the t 0 plane 70 Distance km 1 2 3 4 5 6 yee J e g ji alli Diffraction Figure 6 7 Hagedoorn s method of graphical migration applied
63. s set at 20 KHz and the low pass filter at 10 MHz A Gage Applied Compuscope 1602 digitizer computer card 16 Bit 2 Channel card with acquisition memory of 1 Million samples is used to perform the A D conversion and the data is displayed on a computer screen by means of GageScope 3 50 It is digitally recorded on the computer hard disk A sample rate of 2 5 MS s is chosen Nyquist frequency 1 25 MHz It is then re formatted to SEG Y and processed with Seismic Unix The data were acquired with a 5mm shotpoint and station interval zero offset and 1cm separation between lines In the directory cwpscratch Datal you will find a number of JPEG format files depicting the experimental setting described by Dr Tono The file dsc01324 su is an SU format file version of the image DSC01324 JPG cropped to remove parts of the image that are not the cross section This is not exactly the cross section of the data sonar su but it gives the idea Rarely are we able to slice into the actual model in this fashion 61 5 7 Homework Problem 2 Time to depth conversion of the sonar su and the radar su data Due Thursday 8 Sept 2011 Find the necessary velocities to permit the correct time to depth conversion of the sonar su and radar su data You will need to figure out the appropriate units because it is not possible for these non seismic datasets to have an accurate representation of the time sampling interval represented in the trace header fi
64. should see the same output by typing suplane gt junk su suxwigb lt junk su title suplane test pattern labeli time s label2 trace number amp Finally we often need to have graphical output that can be imported into documents In SU we have graphics programs that write output in the PostScript language supswigb lt junk su title suplane test pattern labeli time s label2 trace number gt suplane eps 2 1 Pipe redirect in lt redirect out gt and run in background amp In the commands in the last section we used three symbols that allow files and programs to send data to each other and to send data between programs The vertical bar is called a pipe on all Unix like systems Output sent to standard out may be piped from one program to another program as was done in the example of suplane suxwigb amp which in English may be translated as run suplane pipe output to the program suxwigb where the amp says run all commands on this line in background The pipe is a memory buffer with a read from standard input for an input and a write to standard output for an output You can think of this as a kind of plumbing A stream of data much like a stream of water is flowing from the program suplane to the program suxwigb The greater than sign gt is called redirect out and suplane gt junk su says run suplane writing output to the file junk su The gt is a b
65. sinc interpolation to the data points The bandwith of this sinc function is the the band from 0 to the Nyquist frequency of the data When resampling to a greater number of samples the Nyquist frequency of the output is greater than the Nyquist frequency of the input so there is no possibility of aliasing However if we subsample data the potential for aliasing exists To repeat the test we should be setting nt 64 to force the number of samples to be the same on both input and output suplane gt junk su suttoz lt junk su t 0 0 15 2 v 1500 2000 3000 gt junki su suztot lt junki su nt 64 z Z1 22 Z23 v 1500 2000 3000 gt junk2 su suxwigb lt junk su title test pattern amp suxwigb lt junki su title depth section amp suxwigb lt junk2 su title reconstructed time section amp AAA AHH The time to depth may be improved by truncating the additional values suwind itmax 64 lt junki su suxwigb title time to depth amp where suwind has been used to pass only the first 64 samples of each trace The short answer is that while the time to depth and depth to time conversions are ostensibly simply piecewise linear operations in this simple example the fact is that there is the potential for errors to be introduced by the interpolation process These errors may make only approximately invertible process The main problem is deciding how the v t and v z functions are to be interpolated As is seen in Fig 5 3 constant
66. st entries 113 Complex signal in the time domain xr 0 xi Ol xr N 1 xi N 1 114 Fourier transformed amplitude phase a 0 p 0 a N 1 p N 1 115 Complex time signal amplitude phase a 0 p 0 a N 1 p N 1 116 Real part of complex trace from O to Nyquist 117 Imag part of complex trace from O to Nyquist 118 Amplitude of complex trace from O to Nyquist 119 Phase of complex trace from O to Nyquist 121 Wavenumber time domain k t 44 122 Wavenumber frequency k omega 123 Envelope of the complex time trace 124 Phase of the complex time trace 125 Frequency of the complex time trace 130 Depth Range z x traces 143 Seismic Data Vertical Component 144 Seismic Data Horizontal Component 1 145 Seismic Data Horizontal Component 2 146 Seismic Data Radial Component 147 Seismic Data Transverse Component 201 Seismic data packed to bytes by supack1 202 Seismic data packed to 2 bytes by supack2 short nvs Number of vertically summed traces yielding this trace 1 is one trace 2 is two summed traces etc short nhs Number of horizontally summed traces yielding this trace 1 is one trace 2 is two summed traces etc short duse Data use 1 Production 2 Test int offset Distance from the center of the source point to the center of the receiver group negative if opposite to direction in which the line was shot
67. t In this course we will use the open source CWP SU Seismic Unix called simply Seis mic Unix or SU seismic processing and research environment This software collection was developed largely at the Colorado School of Mines CSM at the Center for Wave Phenomena CWP with contributions from users all around the world The SU soft ware package is designed to run under any Unix or Unix like operating system and is available as full source code Students are free to install Linux and SU on their PCs or use Unix like alternatives and thus have the software as well as the data provided for the course for home use during and beyond the time of the course 1 2 14 Steep learning curve The disadvantage that most beginning Unix users face is a steep learning curve owing to the myriad commands that comprise Unix and other Unix like operating systems The advantages of software portability and flexibility of applications as well as superior networking capability however makes Unix more attractive to industry than Microsoft based systems for these expert level applications While a user in an industrial envi ronment may have a Microsoft based PC on his or her desk the more computationally intensive processing work is done on a Unix based system The largest of these are clusters composed of multi core multiprocessor PC systems It is not uncommon these days for such systems to have several thousand cores which is to say subprocessors avail
68. ted seismic data or making depth sections from migrated time sections Sonar and GPR data usually have the attribute that the same piece of equipment is used as both source and receiver Furthermore this source receiver array is likely highly directional forming a beam of energy that travels straight down into the Earth Because the scattering occurs from roughness in the structures rough surface scattering of the subsurface and owing to the strength of the sources involved we may consider the reflection to have occurred from directly below the receiver To perform time depth conversion we need to know something about the velocities of the subsurface 5 3 Time to depth with suttoz depth to time with suztot The simplest approach to depth conversion is to use a simple velocity profile expressed as a function of time v t How can we have velocity as a function of time The idea is intuitive We expect the image to show reflectors These reflectors are the boundaries between media of different wavespeeds Given auxiliary information about geology well logs or the result of seismic velocity analysis we expect to be able to relate arrivals on the seismic section to specific depth horizons for which in turn we have wavespeed information 5 4 Time to depth conversion of a test pattern To see what the problem of time to depth and depth to time is all about we may try suttoz on a test pattern made with suplane suplane gt junk su
69. that are changed when we apply display gain Ultimately these numbers relate to the voltage recorded from a transducer a geophone hydrophone or accelerometer While in theory we should be able to extract information about the size of the ground displacement in say micrometers or the pressure field strength in say megapascals there is little reason to do this Owing to detector and source coupling issues and the fact that data must be gathered quickly we really are only interested in relative values 38 Chapter 4 Help features in Seismic Unix Scientific processing and data manipulation packages usually contain many commands Seismic Unix is no exception As with any package there are help features to help you navigate the collection of programs and modules The first thing that you must do with any software package is to locate and learn to use the help features in the package Usually these help mechanisms are not very helpful to the beginner but are really more like quick reference guides for people who are already familiar with the package There are a number of help features in SU here we will discuss only three 4 1 The selfdoc All Seismic Unix programs have the feature that if the name of the program is typed with no arguments a self documentation feature called a selfdoc is listed Try suplane suximage suxwigb sunormalize A A A A For example suplane yields SUPLANE create common offset data file
70. to the diffraction from a point scatterer Only a few of the Hagedoorn circles are drawn here but the reader should be aware that any Hagedoorn circle through a diffraction event will intersect the apex of the diffraction hyperbola circle drawn in Hagadoorn s method may be thought of as the impulse response of the migration operation 6 3 Migration as a Diffraction stack Another approach to migration is immediately apparent If we apply Hagedoorn s method to the diffraction from a point scatterer then we observe that the scatterer is recon structed However tangent vectors are not defined with regard to a point scatter In stead it must be the vector from the source receiver position to the scatterer that is being reconstructed In other words the reflected ray vector is the distinguished vector associ ated with the imaging point For a reflector surface this is the perpendicularly reflected ray vector See Figure 6 7 Furthermore we might ask why is it necessary to draw Hagedoorn s circles at all Suppose that we were to sum over all possible diffraction hyperbolae Then the largest arrivals would exist only where a hyperbola we sum on hits a hyperbola in the data The sum would then be placed at a point at the apex of the hyperbola passing through our data This type of migration is referred to as a diffraction stack We sum or stack data but we do this over a diffraction curve Furthermore the output need not be a 71
71. to time calculation has not had an anti alias filter applied 30 32 33 34 35 37 54 5 3 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 a Cartoon showing an idealized well log b Plot of a real well log A real well log is not well represented by piecewise constant layers c The third plot is a linearly interpolated velocity profile following the example in the text This approximation is a better first order approximation of a teal sell logs sieste etna aa em D a de i er Roe tib E EEA a Synthetic Zero offset data b Simple earth model The Hagedoorn method applied to the arrivals on a single seismic trace Hagedoorn s method applied to the simple data of Fig 6 1 Here circles each centered at time t 0 on a specific trace pass through the maximum amplitudes on each arrival on each trace The circle represents the locus of possible reflection points in x z where the signal in time could have originated orte pu uec eee Oe eB el tO RUE B EL ed The dashed line is the interpreted reflector taken to be the envelope of the uuo FL CT Pc LrcPDP wee The light cone representation of the constant velocity solution of the 2D wave equation Every wavefront for both positive and negative time t is found by passing a plane parallel to the x z plane through the cone at the desired time t We may want to run time backwards for migration The light cone representation for negative times
72. type the dollar sign directory In these notes the symbol will represent the commandline prompt The user does not type this Because there are a large variety of possible prompt characters or strings of characters that people use for the propmt we show here only the dollar sign as a generic commmandline prompt On your system it might be a a gt or some combination of these with the computer name and or the working directory and or the commandline number echo SHELL lt returns the value of the users i working shell environment type this dollar sign The command echo SHELL tells your working shell to return the value that denotes your working shell environment In English this command might be translated as print the value of the variable SHELL In this context the dollar sign in front of SHELL should be translated as value of Common possible shells are bin sh lt the Bourne Shell bin bash lt the Bourne again Shell bin ksh K shell bin zsh Z shell bin csh C shell bin tcsh T shell The environments sh bash ksh and zsh are similar We will call these the sh family The environments csh and tcsh are similar to each other but have many differences from the sh family We refer to csh and tcsh as the csh family 1 6 Setting the working environment Each of these programs have a specific syntax which can be quite complicated Each is a language that all
73. uffer which reads from standard input and writes to the file whose name is supplied to the right of the symbol Think of this as data pouring out of the program suplane into the file junk su The lest than sign lt is called redirect in and suxwigb lt junk su amp says run suxwigb reading the input from the file junk su run in background e pipe from program to program 21 a trace number b trace number 10 20 30 10 20 30 204 0 05 J 0 10 no 605 time s ne w eer nal Freq Hz 0 154 l1 0 204 100 1204 0 254 suplane test pattern Figure 2 2 a The suplane test pattern b the Fourier transform time to frequency of the suplane test pattern via suspecfx e gt write data from program to file redirect out e lt read data from file to program redirect in e amp run program in background 2 2 Stringing commands together We may string together programs via pipes and input and output via redirects gt and An example is to use the program suspecfx to look at the amplitude spectrum of the traces in data made with suplane suplane suspecfx suxwigb amp make suplane data find the amplitude spectrum
74. unif2 scratch yourusername Temp1 cp cwpscratch Datal XSyncline scratch yourusername Temp1 Now cd scratch yourusername Temp1 If you type more syncline unif2 0 0 4000 0 1 99999 0 1000 500 1100 1000 1300 2000 1000 2700 1100 3200 1000 4000 1050 1 99999 you will see the input data for a wavespeed profile building program called unif2 The contents of this file define two boundaries in a velocity model The data for the two boundaries is separated by the values 1 99999 The values in the column on the left are horizontal positions and the values on the right are depths This model defines the same simple syncline model seen in Fig 6 1 We now look at the contents of the shell script XSyncline more XSyncline bin sh Shell script to build velocity profiles with unif2 input parameters modelfile syncline unif2 velfile syncline bin 65 n1 200 n2 400 di 10 d2 10 use unif2 to build the velocity profile unif2 lt modelfile method i ninf 2 nx n2 nz n1 v00 1000 2000 ninf 1 method spline gt velfile view the velocity profile on the screen ximage lt velfile wbox 400 hbox 200 ni n1 n2 n2 di d1 d2 d2 wbox 800 hbox 400 legend 1 title Syncline model labeli depth m label2 distance m units m s amp provide input for sufdmod2 xs 1000 zs 10 hsz 10 vsx 1000 verbose 2 vsfile vseis su ssfile sseis su hsfile hseis su tmax 3 0 mt 10 labeli Depth m l
75. velocity m s 0 2000 3000 4000 5000 6000 pe f 1 1 a 1500 2000 3000 M s velocity Pr 112 5 10004 Depth m 162 5 15004 Well Log c 1500 2000 300 M S velocity 131 25 193 75 Figure 5 3 a Cartoon showing an idealized well log b Plot of a real well log A real well log is not well represented by piecewise constant layers c The third plot is a linearly interpolated velocity profile following the example in the text This approximation is a better first order approximation of a real well log 57 try to figure out the depths Z1 Z2 and Z3 necessary to undo the operation suztot lt junki su z Z1 Z2 Z3 v 1500 2000 3000 gt junk2 su suxwigb lt junk2 su title time section reconstructed amp Please note you don t literally type z Z1 Z2 Z3 what you want is to find three numbers representing depths to substitute in for Z1 Z2 and Z3 The first value 71 0 You will notice that on the junk1 su data the picture does not start getting distorted until after about depth 105 This gives a clue as to the place where the faster speeds kick in You will further notice that the junk2 su data does not look very much like the junk su data The first think that you should notice is that the original junk su data only goes to about 24 seconds but the junk2 su data goes to more than 5 seconds It is a good idea to see if the header values have changed by using surange The original
76. vertical slice through the data In SU we may view a wiggle trace display of data via the program suxwigb For example viewing the sonar su data as wiggle traces is done by redirecting in the data file into suxwigb suxwigb lt sonar su amp the ampersand amp means run in background 27 This should look horrible The problem is that there are 584 wiggle traces side by side Place the cursor on the plot and drag while holding down the index finger mouse button This is called a rubberband box Try grabbing a strip of the data of width less than 100 traces by placing the cursor at the top line of the plot and holding the index finger mouse button while dragging to the lower right Zooming in this fashion will show wiggles The less on here is that you need a relatively low density of data on your print medium for wiggle traces Place the mouse cursor on the plot and type q to kill the window Try the seismic su and the radar su data as wiggle traces via suxwigb lt seismic su amp suxwigb lt radar su amp In each case zoom in on the data until you are able to see the oscillations of the data 3 1 2 Image plots The seismic data may be thought of as an array of floating point numerical values each representing a seismic amplitude at a specific t x location A plot consisting of an array of gray or color dots with each gray level or color representing the respective value is called an im
77. x like system has a system manual page called a man page that gives a terse description of its usage For example type man ls man cd man df man sh man bash man csh to see what the system says about these commands For example 17 man 1s LS 1 User Commands LS 1 NAME ls list directory contents SYNOPSIS ls OPTION FILE DESCRIPTION List information about the FILEs the current directory by default Sort entries alphabetically if none of cftuvSUX nor sort Mandatory arguments to long options are mandatory for short options too a all do not ignore entries starting with A almost all do not list implied and MORE The item at the bottom that says MORE indicates that the page continues To see the rest of the man page for Is is viewed by hitting the space bar View the Unix man page for each of the Unix commands you have used so far Most Unix commands have options such as the Is a which allowed you to see files beginning with dot or ls 1 which shows the long listing of programs Remember to view the Unix man pages of each new Unix command as it is presented 18 Chapter 2 Lab Activity 1 Getting started with Unix and SU Any program that has executable permissions and which appears on the users PATH may be run by simply typing its name on the commandline For example if you have set your path correctly you should be able to do the following
78. xtra storage most system administrators restrict the amount of backed up space to a relatively small area of a computer system To restrict user access quotas may be imposed that will prevent users from using so much space that a single user could fill up a disk However in scratch areas there usually are no such restriction so it is preferable to work in these directories and save only really important materials in your home directory Users should be aware that administration of scratch directories may not be user friendly Using up all of the space on a partition may have dire consequences in that the 13 administrator may simply remove items that are too big or have a policy of removing items that have not been accessed over a certain period of time A system administra tor may also set up an automated grim file reaper to automatically delete materials that have not been accessed after a period of time Because files are not always automatically backed up and because hardware failures are possible on any system it is a good idea for the user to purchase USB storage media and get in the habit of making personal backups on a regular basis A less hostile mode of management is to institute quotas to prevent single users from hogging the available scratch space You may see a scratch directory on any of the machines in your lab but these are different directories each located on a different hard drive This can lead to confusion as a
79. you try editing files in some of these other directories you will find that you likely do not have permission to read write or modify the contents of many those directories Unix is a multi user environment meaning that from an early day the notion of protecting users from each other and from themselves as well as protecting the operating system from the users has been a priority from day one In none of these examples have we used a browser yet there are browsers available on most Unix systems There is no fundamental problem with using a browser with the exception that you have to take your hands off the keyboard to use the mouse The browser will not tell you where you are located within a terminal window If you must use a browser use column view rather than icon view as we will have many levels of nested directories to navigate 1 9 Scratch and Data directories Directories with names such scratch and data are often provided with user write permission so that users may keep temporary files and data files out of their home direc tories Like scratch paper a scratch directory is usually for temporary file storage and is not backed up Indeed on any computer system there may be scratch directories that are not called by that name Also such directories may be physically located on the specific machine were you are seated and may not be visible on other machines Because the redundancy of backups require e

GPGN 461/561 Lab Fall 2011 - Center for Wave Phenomena

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