Seismic imaging using internal multiples and overturned waves Alan Richardson

205 Pages·2015·8.66 MB·English

Seismic imaging using internal multiples and overturned waves
by
Alan Richardson
Submitted to the Department of Earth, Atmospheric and Planetary
Sciences
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Geophysics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
© Massachusetts Institute of Technology 2015. All rights reserved.
Author .............................................................
Department of Earth, Atmospheric and Planetary Sciences
February 27, 2015
Certified by ........................................................
Alison E. Malcolm
Associate Professor
Thesis Supervisor
Accepted by........................................................
Robert van der Hilst
Schlumberger Professor of Earth Sciences
Department Head
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Seismic imaging using internal multiples and overturned
waves
by
Alan Richardson
Submitted to the Department of Earth, Atmospheric and Planetary Sciences
on February 27, 2015, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Geophysics
Abstract
Incorporating overturned waves and multiples in seismic imaging is one of the most
plausible means by which imaging results might be improved, particularly in regions
of complex subsurface structure such as salt bodies. Existing migration methods,
such as Reverse Time Migration, are usually designed to image solely with primaries,
and so do not make full use of energy propagating along other wave paths. In this
thesis I describe several modifications to existing seismic migration algorithms to
enable more effective exploitation of the information contained in these arrivals to
improve images of subsurface structure. This is achieved by extending a previously
proposed modification of one-way migration so that imaging with overturned waves
is possible, in addition to multiples and regular primaries. The benefit of using this
extension is displayed with a simple box model and the BP model. In the latter, the
proposed method is able to image the underside of a salt overhang when even RTM
fails, although substantial artifacts are also present. Progressing to the two-way wave
equation, I explain three new ways in which a wavefield may be separated by wave
propagation direction, and use these in proposed modifications to the RTM algorithm.
Withthesemodifications,overturnedwavesandmultiplescanbeusedmoreeffectively,
as they no longer risk subtracting from the image contributions of primaries, their
amplitude is boosted to produce greater relative amplitude accuracy, and artifacts
usually associated with the use of these arrivals are attenuated. The modifications
also providetwo means of expressing image uncertainty. Among the results I show are
a demonstration of the superior image obtained using the proposed method compared
to the source-normalized imaging condition, and an improved image of a salt body
in the SEAM model. Finally, I describe another modification to RTM that further
reduces artifacts associated with the inclusion of multiples, exhibiting its effectiveness
with simple layer models, and on a portion of the SEAM model.
Thesis Supervisor: Alison E. Malcolm
Title: Associate Professor
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Acknowledgments
I wish especially to thank my family and Rebecca for their love. Our short lives can
sometimes seem difficult, but loving and being loved makes it easier to enjoy the time
that we have.
Other graduate students have told me how lucky they think I am to have, in their
opinion, the best advisor in the department. Alison is not only caring, dedicated,
and approachable, but I feel that she is also very skilled at advising, managing to
naturally transition me from a newcomer to geophysics and research into someone
who is comfortable working independently in these areas. Some of my colleagues
dread meetings with their advisors, but I have enjoyed looking forward to friendly
chats with Alison, and the happiness that I felt after the abundant reassurance and
encouragement she always gave to me during our meetings.
I am also very grateful to Total. Providing my funding for over four years has
allowed me to concentrate on my work without being concerned about how I would
continue to be paid. Perhaps more importantly, it was through my connection with
Total that I met some of the other people who have helped me over the past few
years. Especially in the early years of my PhD, Henri Calandra provided a useful
industrial perspective on my work. Terrence Liao supervised me during my first
summer internship, during which I wrote the RTM code on which I based almost all
of the subsequent research I have done. A friend told me that they had never heard
me talk as highly of anyone as I do about Paul Williamson. I have been impressed
on several occasions by how quickly he has understood what I have been trying to
explain, and how he has then able to immediately make insightful observations and
share some of his wisdom. I felt privileged that he kindly agreed to serve on my thesis
committee, where he made many useful suggestions.
Taylor Perron deserves no less of my admiration and gratitude, co-advising me on
one of my General Exam projects, participating in my General Exam committee, very
patiently and generously helping me to publish my first paper, and also forming part
of my thesis committee. As a further example of his generosity, Taylor provided the
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funding for the remainder of my time at MIT after the end of the Total sponsorship.
One of the ways in which the final member of my thesis committee, Mike Fehler,
has been instrumental in producing this thesis is very obvious, as he provided me with
the SEAM model that I used extensively to validate my ideas. Mike also made many
useful suggestions over the years on ways in which I might improve the presentation of
my work during practice sessions for SEG and ERL consortium meetings, and found
time to meet with me despite his very busy schedule.
The first research project I started working on when I came to MIT was with
Chris Hill, which became the project jointly advised by Taylor Perron. I very much
enjoyed the time that I spent with Chris, who shared my interest in high performance
computing, and he continued to provide encouragement to me even after I moved on
to working exclusively on my thesis research. Chris was a member of my General
Exam committee, and kindly worked on a General Exam project with me that was
outside his primary interest area.
One thing that struck me when I arrived at MIT was how much most of the ad-
ministrative staff cared about students. Sue Turback, the administrative assistant
of ERL during most of my time, went beyond even this. She sometimes jokingly re-
ferred to herself as “mom”, but, given her concern for the wellbeing of ERL’s students,
this was quite appropriate. It would have been difficult for anyone to replace Sue,
but Natalie Counts is doing an excellent job and always greets me with a friendly
smile. I must also thank ERL’s executive director, Anna Shaughnessy, who I know
would always do anything she can to help, and thoughtfully informed me whenever
there were leftovers from meetings. I never had to worry about working out how to
get reimbursed for attending conferences thanks to Terri Macloon. The staff of the
EAPS Education Office have also always been very kind and impressed me by their
dedication.
Life at MIT is certainly not devoted exclusively to research, and the friendships
I have developed with other students over the years have greatly enhanced my time
here. Although there are many others, I mention in particular Sudhish Kumar Bakku,
Di Yang, Ahmad Zamanian, Lucas Bram Willemsen, Andrey Shabelansky, Yuval Tal,
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Haoyue Wang, Ali Aljishi, Nasruddin Nazerali, Abdulaziz AlMuhaidib, Junlun Li,
Fuxian Song, Beebe Parker, Gabi Melo, Saleh Al Nasser, and Diego Concha, as
having been especially important parts of my life.
Another very important part of my life over the past five and a half years has
been the graduate residence known as “The Warehouse”. It has not only provided me
with the most perfect home that I could have wished for, but has also enabled me to
be part of a wonderful community outside of the department. Much of what makes
the Warehouse so nice is due to the housemasters, both the original, Steve and Lori
Lerman, and their successors, John Ochsendorf and Anne Carney.
In my first year at MIT I was a very grateful recipient of the Charles M. Vest
Presidential Fellowship, made possible by the generosity of the friends of Dr. Charles
Vest. As with the funding provided later by Total and Taylor Perron, this relieved
me from having to concern myself with anything other than my studies.
Although perhaps not as obvious a candidate for acknowledgment as the people
who have been part of my life, the creators of the software that I used extensively
in my research and thesis writing have also played a large role in making this work
possible. Particularly deserving of mention are Vim, Gnuplot, XƎLATEX, Asymptote,
and Matlab.
I was recently asked by another student what I considered to be the high point of
my time at MIT. While there are many tempting choices, such as the euphoric time
after passing my General Exam, or field work in St. Lucia with Dale Morgan, I chose
not a single experience, or even one directly related to MIT, but instead it was the
time I spent on many walks around Boston, particularly by the Charles River, that
stood out. It is a beautiful city, and one that I have very much enjoyed living in for
this portion of my life.
Finally, I am thankful to everyone who has made MIT the wonderful place that
it is, and to those who made it possible for me to be here. It has been an immense
privilege that I am unreservedly grateful for. I will cherish the memories of my time
here for the rest of my life, and am very sad that the time has come for me to leave.
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Contents
1 Introduction 29
1.1 Seismic imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.2 Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.3 Overturned waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2 Extending one-way migration to include multiples and overturned
waves 41
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.1.1 One-way migration . . . . . . . . . . . . . . . . . . . . . . . . 42
2.1.2 Attenuating multiples . . . . . . . . . . . . . . . . . . . . . . 43
2.1.3 Imaging with additional wave paths . . . . . . . . . . . . . . . 45
2.1.4 RTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.1.5 Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.1 Box model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.2 BP salt model . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3 Directional amplitude extraction during time-domain wave propaga-
tion 63
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
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3.2 Previously proposed methods . . . . . . . . . . . . . . . . . . . . . . 65
3.2.1 Poynting vectors . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.2 Local slowness . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.3 Frequency domain methods . . . . . . . . . . . . . . . . . . . 66
3.2.4 Windowed Fourier transform . . . . . . . . . . . . . . . . . . 68
3.3 New methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.1 Method 1: Plane wave decomposition followed by the Poynting
vector method . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.2 Method 2: Separated light cone stack . . . . . . . . . . . . . . 80
3.3.3 Method 3: Optimization . . . . . . . . . . . . . . . . . . . . . 84
3.3.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4.1 Crossing waves 1 . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.4.2 Crossing waves 2 . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4.3 Layer over halfspace . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.4 SEAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4 Improving RTM amplitude accuracy 105
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1.1 RTM amplitude errors . . . . . . . . . . . . . . . . . . . . . . 107
4.1.2 Illumination compensation . . . . . . . . . . . . . . . . . . . . 109
4.1.3 Multiples and overturned waves . . . . . . . . . . . . . . . . . 111
4.1.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2.1 Uncompensated images . . . . . . . . . . . . . . . . . . . . . 113
4.2.2 Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2.3 Illumination compensation . . . . . . . . . . . . . . . . . . . . 122
4.2.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
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