Table Of ContentFURTHER TITLES IN THIS SERIES
1 F.A. VENING MEINESZ
THE EARTH'S CRUST AND MANTLE
2 T. RIKITAKE
ELECTROMAGNETISM AND THE EARTH'S INTERIOR
3 D.W. COLLINSON, K.M. CREER and S.K. RUNCORN
METHODS IN PALAEOMAGNETISM
4 M. BATH
MATHEMATICAL ASPECTS OF SEISMOLOGY
5 F.D. STÄCEY and S.K. BANERJEE
THE PHYSICAL PRINCIPLES OF ROCK MAGNETISM
6 L. CIVETTA, P. GASPARINI, G. LUONGO and A. RAPOLLA
PHYSICAL VOLCANOLOGY
7 M. BATH
SPECTRAL ANALYSIS IN GEOPHYSICS
8 O. KULHANEK
INTRODUCTION TO DIGITAL FILTERING IN GEOPHYSICS
9 T. RIKITAKE
EARTHQUAKE PREDICTION
10 N.H. RICKER
TRANSIENT WAVES IN VISCO-ELASTIC MEDIA
11 W.L. PILANT
ELASTIC WAVES IN THE EARTH
12 A.J. BERKHOUT
SEISMIC MIGRATION
Imaging of acoustic energy by wave field extrapolation
13 V.C. DRAGOMIR, D.N. GHITAU, M.S. MIHAILESCU
andM.G. ROT ARU
THEORY OF THE EARTH'S SHAPE
14A A.J. BERKHOUT
SEISMIC MIGRATION
Imaging of acoustic energy by wave field extrapolation
B. Practical aspects
Developments in Solid Earth Geophysics
14B
SEISMIC MIGRATION
IMAGING OF ACOUSTIC ENERGY BY
WAVE FIELD EXTRAPOLATION
B. PRACTICAL ASPECTS
A.J. BERKHOUT
Department of Seismics and Acoustics
Delft University of Technology
Delft, The Netherlands
ELSEVIER
Amsterdam — Oxford — New York — Tokyo 1984
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Printed in The Netherlands
To Mabel,
Carina and Martin
VII
PREFACE
In volume Ά' an extensive treatment is given on the theoretical aspects of
migration. However, I appreciate that the somewhat 'heavy' mathematics in
volume 'A' is not easily accessible for every geophysicist. In addition,
technical and economical limitations may require some significant deviations
from what theory prescribes. Both afore mentioned reasons initiated the
creation of volume 'Β'.
In this volume I have explained the important aspects of migration largely
without mathematical arguments and I have spent ample time on user-oriented
problems and practical examples. Particularly, the choice of migration
technique in relation to the geological problem to be solved, received much
attention.
My frequent interaction with the staff of GeoQuest International Inc. on the
many practical problems with seismic migration, was essential for my
appreciation of the many pitfalls in migrating different types of real
seismic data. Particularly, I am very greatful to Don Larson for the many
fruitful discussions on matters related to implementation and application of
migration software. Thanks are also due to the management of GeoQuest for
allowing me to use some of their migration examples.
I am indebted to many friends, colleagues and students for their assistance.
In particular the comments of Cees Wapenaar during the proof-reading were
very helpful.
I also would like to thank Thijs de Graaff who generated all pre-stack
migration examples and Peter Mesdag who helped me with some of the
illustrative examples on migration arteffects.
III
I am very greatful to Hanneke Mulder who designed the lay-out, typed the
manuscript and coordinated all activities with the drawing and photographi
department. Without her help I would never have kept the deadline.
Many thanks are due to Bram de Knegt of the drawing department, who spent
many extra hours to advice us on the illustrations and to prepare the
hundreds of figures.
Finally, I would like to thank Ron Suiters and Cees Overweel of the
photographic department for their professional support.
Dr. A.J. Berkhout
Delft, September 1984
1
IINNTTRROODDUUCCTTIIOONN
UUnnttiil l ttooddaayy, ,thteh ecocommmmerecricailalyl lyavaavialailbaleb letectehcnhiqnuiqesu eisn isneissemisicm idcatad ata
aaccqquuiissiittiioonn aanndd pprroocceessssiinng gaarer estsitlli llgrgeraetaly tldyetdeertmerinmeidn ebdy bthye thCMeP CMpPripncriinpcle iple
aanndd ttiimmee sseerriiees smmetehtohdosd. s.ThTish isalasol soapapplipesl ietos ttohe thmeorem orreecernectley ntdleyvedleovpeeldo ped
3-D techniques which are largely a straightforward extension of the 2-D
3-D techniques which are largely a straightforward extension of the 2-D
oonneess. . MMaannyy wweell llknknoowwn nprporcoecdeudruerse sanadn dprporcoecsessess eshavhea vbeeebne ernefrinefedi netod taolmaolsmt ost
ultimate perfection, but it should be mentioned that most basic principles
ultimate perfection, but it should be mentioned that most basic principles
aarree llaarrggeelly y uunnttoouucchheedd: :
** ddaattaa ggaatthheerriinng gaarroouunnd da acocommmmono nmmid idpopionti nt(CM(CPM Pprpirnicnicpilpe)l e)
** vveelloocciittyy aannaallyyssisi sono nCMCMP Pggaaththeersr s
** NNMMOO ccoorrrreeccttiioonn aanndd CCMMPP ssttaacckkiinngg
* deconvolution
* deconvolution
** ttiimmee mmiiggrraattiioonn. .
IIt t isi simimpoprotratnat nttot oreraelailziez ethtaht awthwatheavteerv efrurftuhrert hererfirneefmineenmts enatrse abrreoubgrhot ught
iinnttoo tthhe eeexxisisttiinng gseseisismmic icprporcoecsessisnign gsosfotwftawrea, ret,he thvealvidaliityd itoyf tohef tChMeP CMP
pprriinncciipplel e ddeetteerrmmiinnees sththe euultlitmimatae tequqaulaitlyi tyof otfhe thfeinfail narlesruelst. ulFti.guFreig ular e 1a
sshhoowwss aa ttyyppiiccaal l ccoonnffigiguuraratitoino nwwhehreer ethteh eCMCPM Pprpinricnipcliep leapapplipesl iewsewll: elal : a
subsurface with plane reflecting boundaries. The 'CMP smearing' for a plane
subsurface with plane reflecting boundaries. The 'CMP smearing' for a plane
rreefflleeccttoor r wwiitht hddipi pananglge leα aanadn dhohmoomgoegneenoeuos uosvoevrbeurbrudredn ecnanc abne bseimspimly ply
ffoorrmmuullaatteedd bbyy ((ffiigg. . l1bb): ):
M = AX2sinacoso/4L , ((11))
0
wwhheerree Δ~ΧX eeqquuaalsl sthteh eoofffsfest etanadn dL LoQ tthhee lleennggtthh oof fthteh ezezreor-oo-foffsfest etrarya. yF.orF or
eexxaammppllee,, ffoor raa mmaaxxiimmuumm oofffsfest etof of202000 00m, ma, daipd iapngalne gloef 4o5f° 4aSond aan dzearoz-ero
ooffffsseet t rraayy oof f1010000 0m mthteh eCMCPM Psmsemaerainrgi ngis igsivgeinv ebny bAyL =~ L50=0 SOmO. m.
2
Figure la: Ray configuration in a CMP gather for plane reflectors.
Figure lb: Lateral smearing in a CMP gather for a plane reflector and a
homogeneous overburden.
Figure 2a shows a typical situation where the CMP principle largely fails.
For comparison, the rays of the related CDP gather are shown in figure 2b.
In chapter II we will see that NMO-corrected CDP gathers can be elegantly
generated by means of shot record migration. We may expect that shot record
migration will play a very important role in future seismic processing (2D
and 3D).
3
common midpoint
" AL *
Figure 2a: Ray configuration in a CMP gather for a situation where the CMP
principle largely fails.
common depth point
Figure 2b: Ray configuration in a CDP gather for the situation of figure 2a.
If we call seismic inversion the process to obtain a detailed and un-
distorted depth image of the subsurface then the entire seismic processing
philosophy should be centered around inversion which, almost needless to
4
say, ought to be at least two-dimensional. As a consequence, all processing
techniques that aim at a nice-looking time picture may be very valuable but
they solve only part of the problem. Generating agreeable time sections is
typically a "hang-up" from the sixties. In those years time domain process-
ing and statistical filtering were considered to be the ultimate techniques
to solve our problems. The generation of results in terms of a geologically
oriented depth image was often very remote. Let us illustrate the above with
an example:
Seismic migration is generally approached from a time series point
of view. The migration operator is considered as some 'time
variant filter* which eliminates diffractions and corrects dips.
The user should provide processing-oriented velocities (such as
stacking velocities as a function of time). The output consists of
a time section.
It is this type of thinking that kept the industry a long time from develop-
ing proper depth migration techniques. Fortunately there is an increasing
awareness that migration defines a multi-dimensional inversion process which
requires the specification of a macro acoustic model of the subsurface; its
output represents a detailed, high resolution, subsurface image in terms of
reflectivity as a function of depth.
In conclusion, we may state that the seismic industry has developed in the
past sophisticated data acquisition and processing techniques based on the
CMP principle and (statistical) filtering methods which are polished up to
great perfection; so far they have solved many seismic problems up to
satisfaction. This applies to both 2-D and 3-D techniques. However, looking
at the significant heavier demands we have to face in the near future on
accurate structural delineation (also in complicated situations) and high
spatial resolution, new principles should be utilized in order to solve also
the problems of tomorrow successfully.
One of the most important needs in seismic techniques is an alternative for
the CMP nucleus. CMP methods cannot generate results with a high lateral
resolution; in addition they largely fail in structurally complicated
situations. The solution to this problem is given by full pre-stack migrat-
ion, which can be elegantly formulated in terms of recursive pre-stack
downward continuation of common source point gathers ('shot records') into
