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`Ex. PGS 1042
`EX. PGS 1042
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`Elements Of
`3-0 Seismologq
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`Ex. PGS 1042
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`Elements Of
`3-0 Seismologq
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`~'!".!;.).~
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`-j;.>---;'.•~o
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`Ex. PGS 1042
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`Copyright© 1999 by Christopher L. Liner
`All inquiries should be referred to Penn Well Publishing
`1421 South Sheridan/P.O. Box 1260
`Tulsa, Oklahoma 74101
`
`Cover Design by Matt Berkenbile
`Book Layout by Geoff Harwood with Stormgrafx
`
`All rights reserved. No part of this book may be reproduced, stored in a
`retrieval system, or transcribed in any form or by any means, electronic or
`mechanical, including photocopying and recording, without the prior written
`permission of the publisher.
`
`Printed in the United States of America
`
`1 2 3 4 5 04 03 02 01 00
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`iv
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`Ex. PGS 1042
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`i~lements of 3-D Seismology
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`<I>
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`CMP Fold
`For a 3-D survey to yield good data quality, the target fold should
`be about one-half of the fold required to shoot good 2-D data in the
`area. This is a result of migration and dip moveout which result in more
`mixing of 3-D data than occurs in 2-D.
`Some points on fold
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`l. High fold costs more at acquisition time
`2. Low fold (< 10) 3-D has been successful
`3. Lower fold with right bin size may be better than high fold
`with too large a bin
`
`Spatial Aliasing
`Spatial aliasing is an effect of trace spacing relative to frequency,
`velocity, and slope of a seismic event. With adequate trace spacing, the
`points along a seismic event are seen and processed as part of the con(cid:173)
`tinuous event. When trace spacing is too coarse, individual points do
`not seem to coalesce to a continuous event, which confuses not only the
`eye but processing programs as well. This can seriously degrade data
`quality and the ability to create a usable image.
`Figure 7-6 shows one way of defining spatial aliasing. In this view
`spatial is based on trace-to-trace delay associated with a dipping reflec(cid:173)
`tor. Since the delay is related to trace spacing, the issue is really one of
`midpoint interval. This, in turn, is related to shot and receiver interval.
`For 2-D data, midpoint spacing, M;, shot interval, Si, and receiver
`group interval, R;, are related by
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`M· = _!_ Min(S. P.)
`2
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`"Llj
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`I
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`To avoid spatial aliasing on the stack section we require
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`M-<
`'
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`vint
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`4 /max Sin()
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`(7.10)
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`(7.11)
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`104
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`Ex. PGS 1042
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`Chapter 7 Survey Predesign J
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`<I>
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`where vint is the interval velocity near (or immediately above) the target,
`Jmax is maximum signal frequency and 8 is the physical dip angle of the
`·reflecting bed. When interval velocity is not known, average velocity can
`be used. But this will give a bin size estimate that is smaller than
`required. The design condition is rightly based on maximum frequen(cid:173)
`cy, but the dominant frequency is often used. This means high fre(cid:173)
`quency components risk being aliased.
`Spatial aliasing is not difficult to recognize on real data, (Figure 7-
`7). The main problem with spatial aliasing is the detrimental effect it
`has on two very expensive processes: dip moveout and migration.
`Figures 7-8 and 7-9 give a migration example.
`We note for design purposes that diffraction limbs (Figure 7-4)
`appear as e = 90° events. The SinO term is sometimes invoked to justify
`a non-square bin in 3-D shooting. However, this increases risk of spa(cid:173)
`tially aliasing the data, so the safe design rule is to use e = 90°. In this
`case, the midpoint spacing condition reduces to M; < A.dom/4. This agrees
`with the minimum bin size requirement, Adom/4, for a 3-D survey as dis(cid:173)
`cussed i~ chapter 14.
`The unaliased midpoint interval grows with depth due to increas(cid:173)
`ing velocity and decreasing frequency.
`Some points on spatial aliasing
`
`1. Safe direction is smaller
`2. Will be different for shallow and deep targets
`3. Use !max and e = 90° for safest midpoint interval
`4. Smaller midpoint interval costs more at acquisition time
`5. Same equation for 2-D midpoint interval and 3-D bin size
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`<
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`l
`1
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`105
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`Ex. PGS 1042
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`<P
`JElements of 3-D Seismology
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`2-0 survev Size
`This calculation shows how much disk space is needed to store a
`moderate 2-D seismic line in SEGY format:
`
`1sample value
`=
`6 sees data @ .004 sec sample rate =
`1,500 * 4 + 240(header)
`=
`96 channel* 800 shots
`=
`76,800 traces* 6,240 bytes/trace
`=
`add line headers 3600 bytes
`=
`479,232,000 I (1,024)A2
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`4 bytes (floating point\#)
`1,500 samples/trace
`6,240 bytes/trace
`76,800 traces
`479,232,000 bytes
`479,235,600 bytes
`457 Mb
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`From the typical RAM and disk storage numbers above, we con(cid:173)
`clude that the 2-D seismic line can fit
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`1. in RAM of a large wk or small sc
`2. on disk of a wk or pc
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`The RAM issue is important because some processes (e.g.,
`prestack migration) want to hold the entire data set, plus work space, in
`RAM. If it can't all be stuffed into RAM, we are left with a significant
`data management problem.
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`3-D survev Size
`Do things get better for 3-D seismic data? Hardly. Large 3-D sur(cid:173)
`veys today can contain hundreds of millions of prestack traces. This cal(cid:173)
`culation shows the size of a medium-sized 3-D data set composed of 500
`2-D lines like the one above:
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`206
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`Ex. PGS 1042
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`Chapter 17 Computing Needs
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`f<f>
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`(_l)
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`500 2-0 lines
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`= 500 lines* 479,235,600 bytes/line
`= 2.39616*10A11 bytes
`-
`228 515Mb
`- 223Gb
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`[38,400,000 traces!]
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`This amount of data will not fit in RAM of any existing sc (not
`even close), but we could probably find enough pasture for it on the
`disk farm.
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`Processing Speed
`RAM and disk storage are part of the seismic computing bottle(cid:173)
`neck; the other problem is processing speed. It is of little use to squeeze
`a mass of seismic data into computer RAM if, once there, it takes 2 or 3
`years to process it.
`The fundamental unit of processing is the flop. To confuse the
`uninitiated, the flop is both an operation, floating point operation, and a
`rate, floating point operations per second. Here is a table of processing
`speed units.
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`flop
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`=
`=
`sqrt()
`=
`1 megaflop =
`1 gigaflop
`=
`1 teraflop
`=
`1 petaflop =
`1 exaflop
`=
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`floating point operation +*I
`floating point operation per second
`10 15 floating point operations
`1QA6 flop = 1 Mflop
`1QA9 flop = 1 Gflop
`1QA12 flop= 1 Tflop
`10A15 flop= 1 Pflop
`1QA18 flop= 1 Eflop
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`As with petabyte and exabyte, the last two terms are not yet in
`common use. We don't have machines that fast. The current world
`speed record for computer processing is around 1 teraflop in perform(cid:173)
`ance.
`The alert reader will see inconsistent use of prefixes between
`megabyte and megaflop. A megabyte is 1,0242 bytes, but a megaflop is
`2
`1,000 flops.
`There are many different approaches to achieving high flop rates.
`None of them are cheap. Some typical, and not so typical, processing
`speeds are:
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`207
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`Ex. PGS 1042
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`j Elements of 3-D Seismology
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`(p
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`pc =
`wk =
`sc:
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`10 Mflop
`60 Mflop
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`(1 cpu)
`(1 cpu)
`
`Cray 2
`SGI Power Challenge
`Hitachi SR2201
`IBM SP2/402
`Gray T30 MC512-8
`Intel XP/S
`SGI T3E900
`SGI T3E1200
`Intel ASCI Red
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`= 1.6 Gflop
`= 110 Gflop
`= 220 Gflop
`= 690 Gflop
`= 510 Gflop
`= 700 Gflop
`= 800 Gflop
`= 900 Gflop
`= 1.3 Tflop
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`(4 cpu)
`(288 cpu)
`(1,024 cpu)
`(402 cpu)
`(512 cpu)
`(3,680 cpu)
`(1,324 cpu)
`(1,084 cpu)
`(9, 152 cpu)
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`We should all realize that any list of supercomputer speed 1s
`extremely volatile. It certainly needs to be updated every 6 months or
`so. The list given here is a mix. Some machines (like the Cray 2) are no
`longer in production. The fastest machine listed (Intel ASCI Red) has
`been online since 1997.
`For the latest and greatest information on such things, visit the
`TOP500 web site which aspires to keep an up-to-date list of the world's
`fastest supercomputer installations. The URL is
`http: I lwww.netlib.orglbenchmarkl top500 I top500.list.html
`
`Speed and 3-D Migration
`Prestack migration is the classic example of our need for this
`expensive speed. Assume that migration involves 10,000 floating point
`operations per data sample. This is the effort it takes to broadcast each
`input amplitude along an image surface that resembles a lumpy bowl.
`A major part of this work is tied up in calculating the exact geometry of
`the lumpy bowl.
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`Ex. PGS 1042
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`Chapter 17 Computing Needs J
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`<fJ
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`We can estimate how much time is required for 3-D prestack
`depth migration the medium-sized 3-D data set:
`
`Data size:
`
`1,500 samp/trace * 38,400,000 traces
`= 5.76 x 10A10 data samples
`= 10,000 operations/sample
`= 5.76 X 10A14
`333 days
`(disk?,RAM?,speed?,I/O?,forget it!)
`90 days
`(disk?,RAM?,speed?,I/O?,good luck!)
`100 hours
`(RAM?,I/O?,dedicated?)
`87 minutes
`(RAM?,I/O?,dedicated?)
`9 minutes
`(RAM?,I/O?,dedicated?)
`7.4 minutes
`(RAM?,I/O?,dedicated?)
`
`Assume migration
`total floating point operations
`=
`pc
`=
`wk
`Crny2
`=
`SGI Power Challange
`=
`=
`SGI T3E1200
`Intel ASCI Red
`=
`
`The qualifier "dedicated" is added to highlight the fact that it is
`unusual to have a super computer working on only one problem at a
`time. More likely, jobs are queued up like traffic on a Los Angeles free(cid:173)
`way, thus slowing work on any given job. There also are issues of disk
`storage, data transfer rates, and grossly insufficient RAM. We should
`therefore consider these estimates extremely optimistic.
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`Ex. PGS 1042
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