Introduction to Seismic Inversion Methods (Course Notes Series, No. 2) (Course Notes Ser. : No. 2)

176 Pages·1988·9.982 MB·English

by  Brian H. Russell

Introduction to
Seismic Inversion Methods
Brian H. Russell
Hampson-RusseSllo ftwareS ervicesL, td.
CalgaryA, lberta
Course Notes Series, No. 2
S. N. Domenico, Series Editor
Societyo f ExplorationG eophysicists
Thesec oursen otesa re publishedw ithoutt he normalS EGp eer reviews.
They haven ot beene xaminedf or accuracya nd clarity.Q uestionso r
commentsb y the readers houldb e referredd irectlyt o the author.
ISBN 978-0-931830-48-8 (Series)
ISBN 978-0-931830-65-5 (Volume)
Libraryo f CongresCs atalogC ardN umber8 8-62743
Societyo f ExplorationG eophysicists
P.O. Box 702740
Tulsa, Oklahoma 74170-2740
¸ 1988 by the Societyo f ExploratioGn eophysicists
All rightsr eservedT. hisb ooko r portionsh ereofm ayn ot be reproduceidn anyf ormw ithoutp ermission
in writingf romt he publisher.
Reprinted1 990, 1992, 1999, 2000, 2004, 2006, 2008, 2009
Printed in the United States of America
]:n l;roduc t1 on (cid:127)o Selsmic I nversion (cid:127)thods Bri an Russell
Table of Contents
PAGE
Part I Introduction 1-2
Part Z The Convolution Model 2-1
2.1 Tr(cid:127)e Sei smic Model 2-2
2.2 The Reflection Coefficient Series 2-6
2.3 The Seismic Wavelet 2-12
2.4 The Noise Component 2-18
Part 3 Recursive Inversion - Theory 3-1
3.1 Discrete Inversion 3-2
3.2 Problems encountered with real data 3-4
3.3 Continuous Inversion 3-8
Part 4 Seismic Processing Consid erati ons 4-1
4. ! I ntroduc ti on 4-2
4.2 Ampil rude recovery 4-4
4.3 Improvemenot f vertical resolution 4-6
4.4 Lateral resolution 4-12
4.5 Noise attenuation 4-14
Part 5 Recursive Inversion - Practice 5-1
5.1 The recursive inversion method 5-2
5.2 Information in the low frequency component 5-10
5.3 Seismically derived porosity 5-16
P art 6 Sparse-spike Inversi on 6-1
6.1 I ntroduc ti on 6-2
6.2 Maximum-likelihood aleconvolution and inversion 6-4
6.3 The L I norm method 6-22
6.4 Reef Problem 6-30
P art 7 I nversi on appli ed to Thi n-beds 7-1
7.1 Thin bed analysis 7-2
7.Z Inversion comparis on of thin beds 7-4
Part 8 Model-based Inversion 8-1
B. 1 I ntroducti on . 8-2
8.2 Generalized linear inversion 8-4
8.3 Seismic1 i thologic roodeliln g (SLIM) 8-10
Appendix8 -1 Matrix applications in geophysics 8-14
Introduction to Seismic Inversion Methods Brian Russell
Part 9 Travel-time Inversion 9-1
g. 1. I ntroducti on 9-2
9.2 Numerical examples of traveltime inversion 9-4
9.3 Seismic Tomography 9-10
Part 10 Amplitude versus offset (AVO) Inversion 10-1
10.1 AVO theory 10-2
10.2 AVO inversion by GLI 10-8
Part 11 Velocity Inversion 11-1
I ntroduc ti on 11-2
Theory and Examples 11-4
Part 12 Summary 12-1
Introduction to Seismic (cid:127)nversion Methods Brian Russell
PART I - INTRODUCTION
Part 1 - Introduction Page 1 - 1
Introduction to Seismic Inversion Methods Brian Russell
I NTRODUCITO N TO SEI SMIC INVERSION METHODS
, __ _(cid:127) i i _ , . , , ! (cid:127) _, l_ , , i.,. _
Part i - Introduction
_ . .
This course is intended as an overview of the current techniques used in
the inversion of seismic data. It would therefore seema ppropriate to begin
by defining what is meant by seismic inversion. The most general definition
is as fol 1 ows'
Geophysical inversion involves mapping the physical structure and
properties of the subsurface of the earth using measurementsm ade on
the surface of the earth.
The above definition is so broad that it encompassesv irtually all the
work that is done in seismic analysis and interpretation. Thus, in this
course we shall primarily 'restrict our discussion to those inversion methods
which attempt to recover a broadband pseudo-acoustic impedance log from a
band-1 imi ted sei smic trace.
Another way to look at inversion is to consider it as the technique for
creating a model of the earth using the seismic data as input. As such, it
can be considered as the opposite of the forwar(cid:127) modelling technique, which
involves creating a synthetic seismic section based on a model of the earth
(or, in the simplest case, using a sonic log as a one-dimensional model). The
relationship between forward and inverse modelling is showni n Figure 1.1.
To understands eismic inversion, we must first understandt he physical
processes involved in the creation of seismic data. Initially, we will
therefore look at the basic convolutional model of the seismic trace in the
time and frequencyd omains,c onsidering the three componentosf this model:
reflectivity, seismic wavelet, and noise.
_ m i --.
Part I - Introduction Page 1 - 2
Introduction to Seismic InverSion Methods Brian Russell
FORWARDM ODELLI NG INVERSEM ODELLING( INVERSION)
i m ß , ß ß _ _
EAMROTHD EL
Input'
,
Process: MODELLING INVERSION
ALGORITHM ALGORITHM
EAMROTHD EL
Output' SEISMIC RESPONSE
i m mlm ii i ii
Figure1 .1 Fo.(cid:127)ard' andsInversMeo del,ling
Page I - 3
Part I - Introduction
Introduction. to Seismic Inversion Methods Brian l(cid:127)ussel 1
Once we have an understanding of these concepts and the problems which
can occur, we are in a position to look at the methodsw hich are currently
ß
used to invert seismic data. These methods are summarizedi n Figure 1.2. The
primary emphasis of the course will be on poststack seismic inversion where
o
the ultimate resul.t, as was previously Oiscussed, is a pseudo-impeaance
section.
We will start by looking at the most contanonm ethods of poststack
inversion, which are based on single trace recursion. To better unUerstand
these recurslye inversion procedures, it is important to look at the
relationship between aleconvolution anU inversion, and how Uependent each
method is on the deconvolution scheme Chosen. Specifically, we will consider
classical "whitening" aleconvolutionm ethods, wavelet extraction methods, and
the newer sparse-spike deconvolution methods such as Maximum-likelihood
deconvolution and the L-1 norm metboa.
Another important type of inversion methodw hich will be aiscussed is
model-based inversion, where a geological moael is iteratively upUated to finU
the best fit with the seismic data. After this, traveltime inversion, or
tomography,w ill be discusseda long with several illustrative examples.
After the discussion on poststack inversion, we shall move into the realm
of pretstack. These methoUs,s till fairly new, allow us to extract parameters
other than impedance, such as density and shear-wave velocity.
Finally, we will aiscuss the geological aUvantages anU limitations of
each seismic inversion roethoU,l ooking at examples of each.
Part 1 - Introduction Page i -
Introduction to Selsmic Inversion Methods Brian Russell
SEI S MCI I NVE RSOI N
.MET(cid:127)OS, ,,
POSTSTACK PRESTACK
INVERSION INVERSION
i i --
MODEI RLE-BCAUSTRREAVSEDLTIIMV E E WEAIFE VD L LINEAR
INVERSIO(cid:127) N,IN VES ION INVERSION NVERSIOUM ETHODS I METHO] DS
i ,,
!TOMOGRAPHY)
- "NARROWS PARSE-
BAND SPIKE
Figure 1.2 A summaryo f current inversion techniques.
Part 1 - Introuuction Page 1 -
Introduction to Seismic Inversion Methods Brtan Russell
PART2 - THEC ONVOLUTIOMNOADLE L
Part 2 - The Convolutional Model Page 2 -