theleadingedge201310 dl

October 2013, Vol. 32, No. 10

Special Sections:

Geohazards 3D VSP

Special Sections:

Geohazards 3D VSP

Tel: +1 713 860 2100 Email: [email protected]

For more information, contact TGS at:

2013 TGS-NOPEC GEOPHYSICAL COMPANY ASA. ALL RIGHTS RESERVED.

WWW.TGS.COM

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TGS Clari-Fi is a proprietary three step processing solution which allows broadband pre-stack seismic data to be generated from conventionally acquired seismic data such as using single sensor streamers towed at a constant depth.

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1178 The Leading Edge October 2013

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ts1192...... RoundtableA timely and necessary antidote to indirect methods and so-called P-wave

FWI, A. Weglein

1206 ..... Acquisition and ProcessingComparing the MEMS accelerometer and the analog geophone, J. Wei

Special section: Geohazards1212 ...... Introduction to this special section: Geohazards, C. Torres-Verdn

1214...... Recent advances and trends in subsea technologies and seafloor properties characterization, H. Djikpesse, J. F. F. Sobreira, A. Hill, K. Wrobel, R. Stephen, M. Fehler, K. Campbell, O. Carrire, and S. Ronen

1222...... A new, fully integrated method for seismic geohazard prediction ahead of the bit while drilling, C. Esmersoy, A. Ramirez, S. Teebenny, Y. Liu, C. Shih, C. Sayers, A. Hawthorn, and M. Nessim

Special section: 3D VSP1234 ..... Overview and introduction to this special section: 3D VSP, J. S. Gulati and R. R. Stewart

1238...... Images, anisotropy, multiples, and more from an unconventional 3D VSP, A. Campbell, S. Leaney, J. Gulati, J. Leslie-Panek, and E. Von Lunen

1246...... Steam-injection monitoring in South Omanfrom single-pattern to field-scale surveillance, D. Kiyashchenko, J. Lopez, W. Berlang, B. Birch, M. Zwaan, R. Adawi, G. Rocco, and S. Ghafri

1258...... VSP imaging using free-surface multiples: A case study from the Gulf of Mexico, J. OBrien, B. Farmani, and B. Atkinson

1268...... Monitoring CO2 injection for carbon capture and storage using time-lapse 3D VSPs, M. L. Couslan, S. Ali, A. Campbell, W. L. Nutt, W. S. Leaney, R. J. Finley, and S. E. Greenberg

1278...... Distributed acoustic sensing for reservoir monitoring with VSP, A. Mateeva, J. Lopez, J. Mestayer, P. Wills, B. Cox, D. Kiyashchenko, Z. Yang, W. Berlang, R. Detomo, and S. Grandi

Departments1182 .......Editorial Calendar1184 .......Presidents Page1186.......From the Other Side1188.......Foundation News1284.......Outstanding Reviewers1286.......Announcements1290.......Meetings Calendar1292.......Postal Report 1294.......Personals1294.......Membership1296.......Classifieds1298.......Advertising Index1300.......Interpreter Sam

Cover design by Kathy Gamble. Cover photo courtesy of Al Widynowski, Nexen Energy ULC.

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workflow from reconnaissance to crossplotting. Whether its

traditional seismic interpretation, powerful pre-stack analysis, or

interactive pore-pressure prediction, the seamless integration of

DUG Insight enables trouble-free transition between people and

projects.

You can even migrate data from Kingdom+ or Petrel* with ease, so

theres never been a better time to see whats new in DUG Insight 3.

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the way you interpret your data. Download your free, no-obligation,

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StEVEn DAVIS, SEG executive director; tED BAkAMjIAn, director, publications; DEAn ClARk, editor; jEnny kuCERA, associate editor; SPRInG HARRIS, assistant editor; kAtHy GAMBlE, graphic design manager; tOnIA GISt, senior graphic designer; jIll PARk, graphic designer; MERRIly SAnzAlOnE, manuscript tracking specialist. Advertising information and rates: HEAtHER WAlkE, phone 1-918-497-5524. Editorial information: phone 1-918-497-5535; fax 1-918-497-5557; e-mail [email protected].

Subscription information: e-mail [email protected].

The Leading edge (Print ISSN 1070-485X; Online ISSN 1938-3789) is published monthly by the Society of Exploration Geophysicists, 8801 S. Yale Ave., Tulsa, Oklahoma 74137 USA; phone 1-918-497-5500. Per iodicals postage paid at Tulsa and additional mailing offices. Print subscriptions for members of the Society in good standing are included in membership dues paid at the World Bank III and IV rate. Dues for Active and Associate members for 2013 vary depending on the three-tiered dues structure based on World Bank classification of the members

country of citizenship or primary work residence. Dues are US$90 (World Bank IV countries), $48 (World Bank III countries), and $12 (World Bank I and II countries). Dues for all Student members regardless of country of citizenship or primary residence are $21 and include online access to journals. Students may receive TLE in print by paying an additional $36. Print and online single-site subscriptions for academic institutions, public libraries, and nonmembers are as follows: $180, Domestic (United States and its possessions); $220 Canada, Mexico, Central and South America, Caribbean; and $220 Europe, Asia, Middle East, Africa, and Oceania. For corporations and government agencies, print and online single-site subscriptions are: $965, Domestic (United States and its possessions); $1,005 Canada, Mexico, Central and South America, Caribbean; and $1,005 Europe, Asia, Middle East, Africa, and Oceania. Print-only subscriptions for corporations and government agencies are: $395, Domestic (United States and its possessions); $435 Canada, Mexico, Central and South America, Caribbean; and $435 Europe, Asia, Middle East, Africa, and Oceania. Rates are subject to change without notice. Subscriptions to the SEG Digital Library include subscriptions to TLE. Subscribers to GeoScienceWorld are entitled to a $30 discount off print-only subscriptions to TLE. See www.seg.org/publications/subscriptions for ordering information and details. Single-copy price is $17 for members and $35 for nonmembers. Postage rates are available from the SEG business office. Advertising rates will be furnished upon request. No advertisement will be accepted for products or services that cannot be demonstrated to be based on accepted principles of the physical sciences. Statements of fact and opinion are made on the responsibility of the authors and advertisers alone and do not imply an opinion on the part of the officers or members of SEG. Unsolicited manuscripts and materials will not be returned unless accompanied by a self-addressed, stamped envelope. Copyright 2013 by the Society of Exploration Geophysicists. Material may not be reproduced without written permission. Printed in USA.

POSTMASTER: Send changes of address to The Leading edge

Box 702740, Tulsa, OK 74170-2740 USA

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d Chairmantad SmithApache Corporation2000 Post Oak Blvd. Suite 100Houston, TX 77056, USATel: [email protected]

Ezequiel F. GonzalezShell Exploration and Production150 N. Dairy AshfordHouston, TX 77079, USATel: [email protected]

Shuki RonenSeabed [email protected]

julie Shemeta MEQ Geo Inc.Highlands Ranch, CO, USATel: [email protected]

tracy j. Stark Stark Realty, Inc. 5021 Sparrows Point DrivePlano, TX 75023, [email protected]

Carlos torres-Verdn University of Texas Department of Petroleum and Geosystems Engineering1 University Station, Mail Stop C0300 Austin, TX 78712-0228, USATel: [email protected]

PresidentDon W. Steeplesc/o University of KansasDept. of Geology903 Juniper Box 99Palco, KS 67657, USATel: +1-785-737-4536 President-Elect Christopher linerUniversity of ArkansasDepartment of Geosciences218 Ozark HillFayetteville, AR 72701Tel: [email protected]

First Vice-President Dennis A. CookeThe University of AdelaideSantos Building/Australian School of PetroleumAdelaide, South Australia, 5005 AustraliaTel: +61-(0)[email protected]

Second Vice-President Robert R. StewartUniversity of HoustonEarth and Atmospheric SciencesSR1 131CHouston, TX 77204, USATel: [email protected]

Treasurer Gary G. Servos16606 Big Creek Falls Ct.Spring, TX 77379, USATel: [email protected]

Editor Evert SlobDelft University of TechnologyStevinweg 12628 CN, Delft, The NetherlandsTel: [email protected]

Past-President David j. MonkApache Corporation2000 Post Oak Blvd.Houston, TX 77056, USATel: [email protected]

Director at Large Samir Abdelmoaty288 Zone WawSouth Academy Division, 5th DistrictNew Cairo, Cairo, EgyptTel: +20100 166 [email protected]

Director at Large Guillaume CamboisPGSLilleakerveien 4CP.O. Box 251 Lilleaker0216 Oslo, NorwayTel: + 47 4143 [email protected] Director at Large Gustavo j. Carstens Calle 6 e/526 y 527 #550 1900 La Plata, Buenos Aires, Argentina Tel: +54 911 4439 4805 [email protected]

Director at Large Christine E. krohnExxonMobil Upstream Research3319 Mercer StreetHouston, TX 77252, USATel: [email protected]

Director at Large Alfred liawAnadarko Petroleum Corporation1201 Lake Robbins Dr.The Woodlands, TX 77380, USATel: [email protected]

Director at Large Edith j. MillerChevron U.S.A. Inc.1500 Louisiana St., 20-040Houston, TX 77002, USATel: [email protected]

Chair of the CouncilMike GraulTexSeis, Inc.10810 Katy Freeway, Ste. 201Houston, TX 77043, USATel: [email protected]

The leader in shale research

There at the beginning. Here for the future.www.ou.edu/mcee

When you think of petroleum engineering and petroleum geology programs, theUniversity of Oklahomas Mewbourne College of Earth & Energy might be the firstcollege that comes to mind, and it should be.

n At the forefront of the horizontal shale revolution since the Barnett Shale

n The first college to establish a frontier shale research laboratory

n Trains our students on the dual-beam scanning electron microscope where the classroom meets the shales

n Has graduated more petroleum engineers and petroleum geologiststhan any other college in the world, over 10,000 and counting

n A trusted partner of the oil and gas industry for the past 100 years and a technology leader for the future

The leader in shale research

There at the beginning. Here for the future.www.ou.edu/mcee

When you think of petroleum engineering and petroleum geology programs, theUniversity of Oklahomas Mewbourne College of Earth & Energy might be the firstcollege that comes to mind, and it should be.

n At the forefront of the horizontal shale revolution since the Barnett Shale

n The first college to establish a frontier shale research laboratory

n Trains our students on the dual-beam scanning electron microscope where the classroom meets the shales

n Has graduated more petroleum engineers and petroleum geologiststhan any other college in the world, over 10,000 and counting

n A trusted partner of the oil and gas industry for the past 100 years and a technology leader for the future


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arIssue ..Special Section theme .............................. Due date .........Guest editors

2013Nov .......Offshore and onshore broadband seismology ....................past due .................... Shuki Ronen*, [email protected]........................................................................................................................................... William Goodway*, [email protected] ........Unconventional resources technology ................................past due .................... Tad Smith*, [email protected]........................................................................................................................................... Carlos Torres-Verdn*, [email protected]........................................................................................................................................... Ezequiel Gonzalez*, [email protected] ........Middle East .........................................................................past due .................... Chris Liner*, [email protected] Adel El-Emam, [email protected] Said Mahrooqi, [email protected] Feb ........4D .......................................................................................15 Oct 2013 .............. William Goodway*, [email protected]........................................................................................................................................... Alan Jackson, [email protected] .......Rock physics ......................................................................15 Nov 2013 ............. Tad Smith*, [email protected]........................................................................................................................................... Carlos Torres-Verdn*, [email protected]........................................................................................................................................... Ezequiel Gonzalez*, [email protected] ........Offshore / OTC ....................................................................15 Dec 2013 ............. Dean Clark, [email protected] .......Reservoir description with seismic and well-logs ..............15 Jan 2014 ............. Carlos Torres-Verdn*, [email protected] ........Attenuation dispersion .......................................................15 Feb 2014 .............. Chris Liner*, [email protected] .........Regional issue: Latin America ............................................15 Mar 2014 ............ Ezequiel Gonzalez*, [email protected] .......Regional issue: China ........................................................15 Apr 2014 ............. Jenny Kucera, [email protected] ........Imaging migration .............................................................15 May 2014 ............ Biondo Biondi, [email protected]........................................................................................................................................... Paul Sava, [email protected]........................................................................................................................................... Dave Nichols, [email protected] ......... Hydrofracturingmodern and novel methods ..........................15 Jun 2014 ................Steve Laubach, [email protected] Jon Olson, [email protected]........................................................................................................................................... Carlos Torres-Verdn*, [email protected] .......New sensors / nanotechnology ...........................................15 Jul 2014 ............... Shuki Ronen*, [email protected] ........Humanitarian geophysics ....................................................15 Aug 2014 ............. Lee Liberty, [email protected]........................................................................................................................................... Rhonda Jacobs, [email protected]........................................................................................................................................... Louise Pellerin, [email protected]

(* Current TLE Board member)

notice to authorsTLE publishes articles on all areas of applied geophysics and disciplines which impact it. To submit a paper for possible publication in a specific issue, please e-mail an inquiry to the appropriate guest editor for that issue. Authors are encouraged to submit their papers at any time, regardless of whether they fit the schedule. To submit an article on an unscheduled topic, contact Dean Clark, TLE editor, [email protected] or 1-918-497-5535.

Electronic submission of articlesElectronic submissions should include the manuscript file, figures and other graphics, a PDF of the manuscript and figures, and the authors contact information. These files can be uploaded to an FTP site (the preferred method) or burned to a CD and mailed to the appropriate editor. Once accepted for TLE, the files will be opened and edited on a Mac or a PC using various software applications. To simplify conversion, figures should be submitted in TIFF, PDF or EPS (.tif, .pdf or .eps) file formats, with a resolution of at least 300 dpi (pixels per inch). High-resolution images can be placed in Word or PowerPoint if

placed large on the page; these will be converted to PDF format. Once the paper is accepted, please also mail the appropriate editor a printed color copy of the manuscript with any figures, tables, and equations to be included. For assistance with electronic submission, contact Tonia Gist, [email protected] or 1-918-497-5575. More details are online at http://www.seg.org/resources/publications/tle/submission-guidelines.

notice to lead authorsLead authors of articles published in TLE who are not members of SEG should apply for a one-year free membership and subscription to TLE by contacting Member Services, fax 1-918-497-5557 or [email protected]. Lead or corresponding authors also are required to sign a copyright transfer agreement, which gives TLE permission to publish the work and details the magazines and the authors rights. TLE staff will send a form to be signed and sent back after the article is accepted for publication. The form can be downloaded at http://www.seg.org/documents/10161/74670/SEG_Copyright_form.pdf.


Iwant to make three points here, and two of them relate to the importance of volunteers in SEGs activities and programs. The first point involves volunteering time and expertise, the second involves volunteering resources, and the third emphasizes the increasingly important role of our female colleagues.

Operating the myriad worldwide programs of SEG re-quires nearly 100 dedicated staff members who take direction from an army of volunteers, led by the Board of Directors. As our programs have grown to major international scope, our membership has also become more international with 65% of our current members residing outside the United States. Many members are eager to volunteer to assist with SEG programs, but may not know how or where to volunteer, or whom to contact.

In my position statement when I was a candidate for pres-ident-elect in 2012, I proposed that we use SEGs Web site to provide a database where those willing to serve in a voluntary capacity can register for activities in which they would like to be involved. SEG staff is on schedule to make this volunteer registry a reality during my term as president.

Conceptually, here is how it will work. Assume that you are living in a country with only a few SEG members and that you would like to volunteer to assist with SEG activities, but you do not know any committee chairs, associate editors, or others who need volunteers to help carry out SEGs activi-ties. You would be able to go to the SEG Web site and click on the box for volunteering which would lead to a menu of possible volunteer activities. These could include reviewing manuscripts in specific subject areas, reviewing abstracts for meetings, serving on committees, or being a candidate for of-fice or for the SEG Council, for example.

Now assume instead that you are on the Technical Pro-gram Committee for the SEG Annual Meeting and that you need reviewers for some of the 1500 abstracts that have been submitted. Your favorite reviewers have been overloaded and are starting to respond more slowly, or are starting to com-plain of being swamped. You will be able to go to the volun-teer registry and look for contact information for individuals who have volunteered to review abstracts in your (and their) area of expertise.

Society of Exploration Geophysicists

Presidents PagePoints to ponder

The volunteer registry has the potential to identify an army of new volunteers to help with the many tasks required to keep SEG functioning.

My second point has to do with volunteering resources to help keep SEGs worldwide programs operating. Many in-dividuals and corporate sponsors of SEGs activities fit into this volunteer category, with several contributing hundreds of thousands of dollars annually through the SEG Foundation. I want to highlight one program in particular because I saw it in action in August of this year.

The SEG/ExxonMobil Student Education Program (SEP) has been in operation since 2008, and has provided travel grants and a free, intensive 2.5-day geophysical educational experience to nearly 500 students from 50 countries. In ad-dition to the last several SEG annual meetings in the United States, venues have included the Netherlands, Bahrain, Chi-na, Russia, Romania, Poland, Turkey, Serbia, Germany, and Brazil. ExxonMobil has voluntarily contributed more than US $1 million to this program. I had the opportunity to speak to the class of 30 Latin American students in the SEP in Rio in August.

Later, at the Brazilian Geophysical Societys conference, several students came up to me individually and praised the SEP in glowing terms. Based on what I heard from these students, this corporate philanthropy will repay ExxonMo-bil multiple times in the coming decades, and SEG will also continue to benefit for the remainder of the careers of many of these students.

I believe Audrey Galvo, a graduate student at Universi-dade Federal Fluminense, Brazil, captured the essence of the typical praise in her letter of appreciation to ExxonMobil, from which I quote in part:

This exchange of experience provided me further knowl-edge and new insights, outperforming all my expectations. And I would like to make a special thanks to ExxonMobil for sending us competent instructors that were well rep-resented by Sue, Virginia, and Isabela. I, as a woman, was delighted to see that in the geophysics world, women are increasingly recognized for their efforts and abilities.

In closing with my third point, I want to emphasize the importance of Audreys last sentence. The Board of Directors is acutely aware that our highly deserving female colleagues have been under-represented on the award stand at the SEG Annual Meeting. Please help us address this issue by sending the Honors and Awards Committee an award nomination for one or more of our many outstanding female colleagues. Tempus nunc est! (The time is now!)

Don SteepleSSEG President

The SEG/ExxonMobil Student Education Program (SEP) has been in operation since 2008, and has provided travel grants and a free, intensive 2.5-day geophysical education-al experience to nearly 500 students from 50 countries.

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In the January FTOS, the subject was fracturing as a method to stimulate a cranky well. I went back to the early days of oil exploration and production. You may recall that there was a certain amount of ex-

perimentation in those days. I mentioned the idea of put-ting gun powder in an earthen pot and lowering it on the end of a long pipe. A burning, red-hot ember was dropped down the pipe. Seems a little strange, but it worked, worked too well. It blew out all of the tools and damaged the rig. But it brought the well in. In summary, I went from those early efforts to the use of nitroglycerine. Hydraulic fractur-ing didnt show up until 1954. I assumed that fracturing potentially producing wells was done hydraulically. Interest-ingly, one of the first methods to use nitro was the Roberts Torpedo. After a lot of litigation and travail with nitro, the name was changed to The Otto Cupler Torpedo Co., and it lives on today!

This last bit is from an introduction to a book currently under construction titled

and written by Rick F. Tallini, president of the Otto Cupler Torpedo Co. You can find it on the Internet at http://allenwl.com/logwell/tales/menu/index.html. It has a lot of stories about using nitro for fracturing oil wells.

A question for us to ponder and consider: Is the Roberts Torpedo being used today to bring in oil wells? It is probably cheaper than extensive hydrau-lic fracturing. There might be just a little difficulty trying to frac a horizontal well in stages with nitro!______________________________

Ron Weatherhill sent the Geo-physical Society of Houston a box of geophysical memorabilia for its Geo-Science Center. Of interest was the 1981 Houston Geological Society pub-lication about Houstons active surface faulting. Ron wrote:

If you subscribe to the theory that what goes around comes around, then

The Leading Edge

From the other sideA column by Lee Lawyer with stories about geophysics and geophysicists

you should know that the HGS publication on urban faults in the Houston area was given to me as a door prize on the one and only occasion I attended a monthly luncheon meeting of the Houston Geological Society many moons ago. The title was Houston Area Environmental Geology: Surface Faulting, Ground Subsidence, Hazard Liability.

My career in the doodlebugging business started in 1957 in Iraq where the following year they had a revolution that deposed the king, his prime minister, and ushered in a mili-tary government headed by some general whose name es-capes me. I was working as junior observer on an SSL crew in the desert at the time, and we continued working as if nothing had happened. Of course, we downed a few beers in the evening to celebrate, though exactly what I know not as we supped copious amounts of beer most evenings.

Twelve years later I was on a seismic crew in Libya with GSI and survived another revolution that toppled the king, his government, and ushered in a military govern-ment headed by Mohammed Gadhafi. I was on local leave in Tripoli at the time, heading downtown with my fam-ily, when I saw the street ahead was completely blocked by a crowd waving banners and advancing toward us. I have never made a faster U-turn. Back to home base!

Ron, I may have asked you this before, but do you think there is a causal relationship between your involvement in acquiring seismic data and revolution? Clearly the data sup-port this. You may wish to seek asylum in a country where you have not acquired seismic data.

To contact the Other Side, call or write L. C. (Lee) Lawyer, Box 441449, Houston, TX 77244-1449 (e-mail [email protected]).

Groundbreaking was on 12 September 2013 for a second building on SEGs Geophysical Resource Campus in Tulsa, USA. (left to right) Dave Monk, SEG president; Steven Davis, SEG executive director; Phil Lakin, Tulsa city councilor; Gary Servos, SEG treasurer and former chairman of the Real Estate Corporation; and Robert Wyckoff, chairman of the SEG Real Estate Corporation. More information about this new chapter for the Society, and some history, will be in next months FTOS.

DiscoverYourPotential

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DiscoverYourPotential

www.lmkr.com/geographix

GeoGraphix Geoscience | Services | GeoTechnology Applications | Information Management

LMKR is a petroleum technology company with an extensive solutions portfolio that includes reservoir-centric

interpretation, modeling and analytics software, mobile technology solutions, E&P data services as well as

geoscience and information management consulting solutions

By unleashing the

power of GeoGraphix

Make this well better than your last through integrated

multi-dimensional geological interpretation

Maximize your reservoir understanding through seamless

interpretation of seismic and geological data

Optimize your field development efficiency with quick and

easy field planning tools

See where your next BIG opportunity lies with state of the art

mapping & 3D visualization

Geology

Geophysics

Field Planning

Visualization


The Leading Edge

Foundation NewsTrustee Associates need your help to support SEG programs

Trustee Associates represent the financial backbone of the SEG Foundation, allowing us to create new programs and support existing programs. A Trustee Associate (TA) is an individual or family who has donated or pledged to donate at least US $10,000 to the SEG Foundation. Contributions made through the SEG Foundation currently help to support 18 different SEG programs designed to Advance Geophysics Today and Inspire Geoscientists for Tomorrow. To highlight just a few of these beneficial programs: contributions this year supported 133 scholarship students pursuing studies in geophysics, allowed student participation in 15 field camps offering hands-on experiences in applied geophysics, and provided more than 140 travel grants that allowed students from around the world to attend educational and leadership workshops and conferences. SEG continues to demonstrate the importance of our futurenow with 282 Student Chapters worldwide!

A sincere thank you to our 240 TAs for their contribu-tions to the SEG Foundation because you have made a dif-ference. It is noteworthy that during the past four years, 52 new Trustee Associates have joined our mission. However, we need more TAs and wed like to tell you why.

Managing our programs requires staff time and materials. The SEG Foundation has a number of endowments total-ing more than $13 million from which we target an annual spending rate of 35% to support the various programs. In addition, our corporate sponsors annually support multiple programs ranging from $50,000 to $250,000 per year. All to-gether, more than $2 million on average is funded annually through the Foundation for actual grants and expenses to run our SEG programs. Although there are some administrative costs built into the corporate gifts, and the SEG Foundation sees a small fee from managing the endowments, SEG is still required to partially support the operations of these programs each year. The Foundation would like to be able to do moreto fully support and further build these programs. To achieve

Eric Jones with Trustee Associate Chairman Mike Forrest.

Trustee Associate Jim Payne with Trustee Associate Vice Chairman Peter Duncan.

Trustee Associates Arlyn and Martin Shields at the April TA event in Galveston, Texas.

Trustee Associates and guests gather at the April TA event in Galveston, Texas.


Hank Hamilton, chairman of TGS, is an active volunteer/donor with SEG and SEG Foundation. He currently serves as a director on the SEG Foundation Board and also as chairman of the Development Committee.

The SEG Foundation is proud to recognize Hamilton as our first Sustaining Trustee Associate (TA). Since becoming a Trustee Associate in 2010, he has been committed to promot-ing the good work of the Foundation and finding others who share his same interest.

Hamilton said, I originally decided to become a Trustee Associate after reading an article in TLE by Mike Forrest that encouraged folks who have enjoyed rewarding careers in geophysics to give back to this wonderful profession. That message really resonated with me. After having the opportunity to get a closer look at the wonderful impact of the various programs that the Foundation supports, the decision to follow up and be-come a Sustaining TA was an easy one.

Thank you, Hank, for your continued support!Attendees Russell Pruitt, John Terwilliger, and John Plappert at the May

Trustee Associates event in Austin, Texas.Hank Hamilton

Sustaining Trustee Associate Spotlight: Hank Hamilton

The SEG Foundation proudly recognizes our Trustee Associates who have made a commitment to the Annual Fund this year in support of sustaining our impactful SEG programs and SEG Foundation activities.

Richard A. and Fran BaileWilliam N. BarkhouseDavid C. Bartel

Glenn and Lorie BearMike ForrestHank Hamilton

Prentiss C. HavensAlfred and Julie LiawVicki Messer

Scott Petty, Jr.Jack and Catherine ThreetJin Ming Zhou

SustainingTrustee Associates

15 August 2013

this, we would like to gain the support of 500 members, each giving an average of $2000 per year to the SEG Foundation annual fund, either as a new Trustee Associate or Sustaining Trustee Associate.

So whats in it for you? For starters, a good feeling and a sense of pride that you are giving back a little for all that this industry has offered to you. But there are some more tangible, even fun, benefits as well. Networking is an important part of being a Trustee Associate. During the past three years, we have had an annual Day at the Beach in Galveston, Texas, (60 peo-ple attended this past April) and an early December reception at Lakeside Country Club in Houston, Texas (90 people attended last year). Both events received enthusiastic support, and will be repeated in the future. Trustee Associates also are invited to the SEG Foundations Donor Luncheon and the Presidents Recep-tion, both held annually at the SEG Annual Meeting.

This year, we have a robust goal of finding 40 new Trustee Associates to join our mission, and you could be one of them. You may be contacted by a SEG Foundation board member or Development Director Paul Allison in Houston ([email protected]) to encourage you to become part of this special group. However, you are also welcome to contact me, Mike Forrest, at [email protected] or me, Peter Dun-can at [email protected] to learn more about our programs and opportunities. We welcome everyone with a love for our geophysical community and who want to see it flourish in the future.

Join your colleagues; join us by becoming a new Trustee Associate. Its easy to contribute via the Foundation Web site by logging into your membership account at www.seg.org/do-nate. Just add a note such as TA first installment, or if you are a current TA, just state Sustaining TA. Or if youd rather, drop a check in the mail made out to SEG Foundation.

Thank you for your support! Mike ForreSt

SEG Foundation Director and Chairman of the Trustee Associates

peter Duncan SEG Foundation Director and Vice Chairman of the

Trustee Associates


The SEG Foundation recognizes a special leadership group of contributors, known as the Trustee Associates. Below, these members are acknowledged by their cumulative support of the Foundation.

$1,000,000 anD Up

$250,000 to $499,999

Robert and Margaret SheriffL. Decker Dawson

Richard A. and Fran BaileAubra E. Tilley

Scott Petty, Jr. and The Petty Foundation

Thomas R. LaFehrFred and Kathi Hilterman

Jeff and Amie SpringmeyerHank HamiltonRichard Degner

Stanley H. and Shirley A. Ward Trust* Rutt Bridges Charles and Jean Smith, Jr. David W. Worthington

$100,000 to $249,999

$50,000 to $99,999Frans H. and Alice B. Ham-mons*Mike ForrestAlexander Mihai and Catherine Ann Popovici

Gary and Lorene ServosDonald W. and Nancy FryeLeon and Pat ThomsenKurt-Martin StrackRodney Cottrell

Larry and Connie GallowayNorman* and Shirley DomenicoRichard and Shirley HuntJames D. and Stella M.

RobertsonJames L. and Arlene H. PayneJesse and Cathy MarionMike and Donna BahorichBill and Debbie Mitcham

David E. LumleyCecil H. Green*

$25,000 to $49,999David C. BartelWilliam N. BarkhouseJack and Catherine ThreetLee and B.J.* LawyerJohn W. C. Sherwood

Ian G. JackJames L. AllenDavid LammleinGerald W. Hohmann Trust*Kenneth and Kim Zonge

Elwin PeacockBrian and Elaine RussellJeff Hume and Cindy BerlierCraig and Betsy BeasleyMike and Susan Graul

Wm. E. LaingJames* and Ruth HarrisonArthur ChengCung VuD. Wayne Turner

Rocky RodenClaire and Joe Greenberg

Anonymous Donor Anonymous Donor

$10,000 to $24,999 Robert B. PeacockCharles WeinerMarvin and Jene HewittR ichard and Barbara SchneiderBarry and Lee DaviesJohn and Elizabeth GibsonPeter M. DuncanDorothy LaCoste*Tom and Carolyn HamiltonPrentiss C. HavensHenry L. Grant*Martin Stupel and Catherine LappeJames and Patty DiSienaSusan Mastoris PeeblerJohn SumnerKen LarnerBenegene Kring*

Richard and Nancy WhiteMary L. FlemingLarry FunkhouserRaymond FarrellThe Zonge Family TrustJames R. StrawnKim and Karen El-TawilT. Norman CrookRed OlanderWilliam and Evangeline AbrielPaul C. MitchamDavid C. DeMartiniJames B. Coffman*Robert and Michelle HobbsMichael G. LoudinAlfred and Julie LiawGlenn and Lorie BearKayleen RobinsonE. J. Northwood*

Dave K. AgarwalPeter PangmanMark and Kim LeonardRonald and Mary BrackenFritz P. KronbergerPaul M. FergusonSam L. EvansRhonda and John JacobsEarl and Reba Griffin*Allen L. GilmerBill LangleyRobert and Esther GraebnerMichael and Lynn Schoenberger Sally G. ZinkeFred AminzadehMike MuellerRichard S. BishopGene and Carlene SparkmanErnie and Donna Siraki

Chuck PengRobert PeeblerWilliam and Linda PearsonMagne ReiersgardDon PaulFrank D. BrownJie ZhangZhiming LiGary E. JonesRobert and Vivian TalleyHugh E. Rowlett, JrMichael P. ThorntonMartin L. Shields Floyd F. FosterMichael and Dana PadgettDominique RobertJohn CastagnaFred HoffmanRobin Pearson

Scott and Rachel BrannanJim and Kelly BrothersSteve CrowellSteven H. DavisRocco and Julie DetomoCarlos GuzmanMartin E. Hansen Driscoll A. HenkhausBill KampsHenry S. PettingillSimon Robinson and Lia MillsPaul SchlirfMike SeidnerC. David SmithMarta Weeks

*deceased

Richard C. Anderson* Ronald G. Antonation Ralph W. BairdDouglas D. Barman Timothy B. Berge, Sr.Brad and Roz BirkeloJohn W. Bissell John E. BobbittOrval R. Brannan* Glenn R. Breed Albert (Al) P. Brown Alistair R. BrownEugene R. BrumbaughJohn R. Butler, Jr. Lawrence J. Cernosek Richard D. Chimblo Roy E. Clark, Jr.Lucius R. CorbettNeal P. Cramer, Sr.

Steve and Susan Danbom Charles W. DickM. Howard Dingman, Jr. Charles E. Edwards Richard V. Edwards, Jr. Theodore D. Einarsson Jon A. Ferris James H. FrasherWilliam S. French Richard J. Gardner Pierre L. Goupillaud Theodore S. Green*Gordon M. Greve James K. Grigsby E. J. Grivetti Ernest M. Hall, Jr. Jack H. Hamilton* Kathleen Hogenson David S. Holland*

Gary M. HooverPaul S. Horvath Albert Hrubetz Alan R. Huffman David F. Jewell, Jr. Stanley B. Jones* James B. Jordan* Alf Klaveness* Jack A. KruppenbachJohn D. Laker B. L. Langston Walter S. Lynn Wulf F. MassellRed McCombs Dolan K. McDaniel Raymond H. MendezVicki Messer Richard F. MilesLee Miller

Billy F. Mitcham, Sr.* David and Lorraine MonkRussell D. Nash*Robert and Penny NeeseEdwin B. Neitzel*P. Dennis OBrien George E. Parker Robert H. Peacock Walter D. PharrisJoseph G. Putman III* Jeff RaynerWilliam E. Richardson*Louis I. Schneider, Jr. William A. SchneiderVictor M. Shainock Anna Shaughnessy Damir S. Skerl C. O. SmithDaniel L. Smith

Jackie D. StewartJohn W. Stockwell, Jr.Booth B. Strange*Yonghe and Grace Sun Ben B. ThigpenMaurice E. Trostle* H. A. Wakefield Peyton WeemsDavid WegnerMargaret M. Welch Jack C. Weyand*Courtenay WhiteFrank Wipff*Michael Wisda Kay D. WyattRobert A. WyckoffTerry and Nadine Young Jin Ming Zhou

5 September 2013

$500,000 to $999,999Debra and Mark Gregg

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and planning optimum operations. Weatherford offers industry-leading formation

evaluation technologies and services that will make a real difference to your assets:

38 cutting-edge laboratories in 22 countries Unique LWD and MWD measurements for well placement Distinct wireline logging and cased reservoir evaluation Surface logging services and wellsite geochemistry 350 global petroleum consultants

Transform hard data into meaningful decisions.

At Weatherford, were here to help you, every step of the way.

Contact and collaborate with us at

[email protected]

Formation Evaluation | Well Construction | Completions | Production 2013 Weatherford. All rights reserved.

From Data to Decisions.indd 1 8/8/2013 1:27:41 PM


R o u n d t a b l e

Editors note: The following article brings to light a cautionary concern (and a set of fundamental and substantive issues, related to indirect methods, in general, that benefits from a broader and deeper under-standing and perspective), regarding the validity of basic assumptions made in FWI. It was slated to appear in the special section on FWI in September. The article also describes and exemplifies a direct inverse method for the same FWI-type objectives. However as that issue was fully subscribed, given the popularity of FWI, it was decided, in conjunction with the sections guest editors (Antoine Guitton, Tariq Alkhalifah, and Chris Liner) that the article appear in the October TLE. In the introduction to the FWI section, the guest editors pose some admonitory questions: Are we heading in the right direction? Are we in the right valley? Or within a bigger context, is FWI the way to go? In this context, Wegleins article is a timely and pertinent riposte that will be of significant interest and may elicit a degree of controversy to those working in the FWI field.

A central purpose of this article is to bring an alternative voice, perspective, and understanding to the latest geophysical stampede, technical bubble, and self-proclaimed seismic cure-all, the so-called full-waveform inversion or FWI. If you think this is exaggerated, I refer to the advertisement/announcement of the 2013 SEG Workshop on FWI whose opening line is, Full-waveform inversion has emerged as the final and ultimate solution to the Earth resolution and imaging objective.

Besides representing language, attitude, and a viewpoint that have no place anywhere in science, and, in particular, in exploration seismology, the fact is that the method, as put forth, is from a fundamental and basic-principle point of view (aside from, and well before, any practical considerations and track record of added-value are considered) hardly deserving of the label inversion, let alone all the other extreme and unjustified claims and attributes, as being the deliverance and the last and final word on the subject.

From a direct-inversion point of view, and for the algo-rithms that are derived for solving the exact same problem of estimating, for example, the location of velocity anomalies and shallow hazards, and velocity changes at the top and base salt, all the current approaches to so-called full-waveform inver-sion are: (1) always using the wrong data, (2) always using the wrong algorithms, and (3) all too often, using the wrong Earth model, as well. Making this clear is one purpose of this article.

The issue being discussed in this article is not a matter of semantics and is not a labeling/mislabeling issue; it is the substantive issue of what data and what algorithms are called for by direct inversion to achieve certain seismic processing objectives. In particular, the focus here is on objectives that rely on the amplitude of reflection data as a function of in-cident angle to determine changes in, e.g., P-wave velocity, AVO parameters, or so-called FWI.

Another purpose of this article is to propose and exem-plify an alternative and direct inverse solution that actually

A timely and necessary antidote to indirect methods and so-called P-wave FWIArthur B. Weglein, University of Houston

deserves the label inversion and could be useful for those goals and objectives, and perhaps can actually earn, deserve, and warrant a label of FWI, although never as the ultimate and final solution. The direct-inversion approach provides not only a method but also a framework and platform for understanding when it will and will not work. All current so-called FWI methods are indirect model-matching methods, and indirect methods can never provide that capability and clarity. Model-matching run backward, or solving a forward problem in an inverse sense, resides behind all the current indirect P-wave-only so-called FWI and is never equivalent to a direct inverse solution for any nonlinear problem, nor does it even represent a fully and completely aligned goal and property of a direct inverse solution.

A third and perhaps the most important goal of this article is to provide a new, comprehensive overview and bridge for these two approaches for those who may be following, apply-ing, and/or considering the current so-called indirect model-matching FWI approach and those proposing, interested in, or providing a road to a direct inverse methodology. It will be shown how these two approaches have the same starting point, and in fact, have the same exact generalized Taylor series ex-pansion for modeling data and for expressing the actual data in terms of a reference model and reference data and the difference between actual and reference properties. The two approaches differ in how they view each of the same terms of that forward series. One view of those individual terms leads to a Taylor series form that does not allow a direct inverse series and that leaves as the only option the running of a forward (linear truncated) series in an inverse sense. That forward description viewed as only a generalized Taylor series results in, and provides no other choice other than, an indirect model-matching approach (e.g., as seen in AVO and the so-called FWI methods). This is the mainstream/conventional view of the forward description as a Taylor series, and, while easy to understand, that view precludes a direct inverse, and therefore explains the widespread use of indirect model-matching approaches. Another view of those individual terms in the forward Taylor series that derives from the fundamental equation of scattering theory (the Lippmann-Schwinger equation) recognizes that the forward Taylor series is a special class of generalized Taylor seriesa generalized geo-metric series. Further, it is a geometric series for a forward prob-lem, and it has a geometric series for a direct inverse solution. Without understanding and calling upon the scattering-theory equation, that recognition of the forward series as being geo-metric is not possible, and a direct inverse solution would not be achievable. All of the consequences and differences between the forward model-matching approach leading to methods such as so-called FWI and the direct inverse methods, derived from the inverse scattering series, have that simple, accessible, and under-standable origin. The details, arguments, and examples behind these three objectives and goals are provided below.


R o u n d t a b l eR o u n d t a b l e

Lets begin. Seismic processing is an inverse problem, in which measurements on or near the surface of the Earth are used to make inferences about the nature of the subsurface that are relevant to the exploration and production of hydrocarbons.

There was a time, not too long in the past, when a dis-cussion of any method for solving inverse or data-processing problems always began with a definition of direct and indirect methods. The latter was deemed the less respectable and the lesser choice between the two, considered out of despera-tion and resignation and offered with hesitation and apology. It was associated among inversionists with searching and model matching rather than with seeking a direct, clear, and definitive solution through a math-physics analysis.

It appears that earlier, healthy understanding and respect for the framework and definitiveness of direct inverse meth-ods have largely given way or have been pushed aside, with serious and substantive negative and injurious conceptual and practical consequences. Among the latter manifestations and consequences is the totally mislabeled and ubiquitous phe-nomenon of so-called full-wave inversion (FWI) methods. Among FWI references are Brossier et al. (2009), Crase et al. (1990), Gauthier et al. (1986), Nolan and Symes (1997), Pratt (1999), Pratt and Shipp (1999), Sirgue et al. (2010), Symes (2008), Tarantola (1984, 1986), Valenciano et al. (2006), Vigh and Starr (2008), and Zhou et al. (2012).

This note advocates (whenever possible) direct methods for solving processing problems and providing prerequisites. Direct methods offer many conceptual and practical benefits over indirect methods. Advantages of direct methods begin with actually knowing that you are solving the problem that you are interested in solving.

How can you recognize a direct versus an indirect meth-od? Consider the quadratic equation

, (1)

and the solution

. (2)

Equation 2 is a direct solution for the roots of Equation 1. On the other hand, if you see a cost function involved in a solution, the solution is indirect. Also, if you see a modeling equation being solved in an inverse sense, or an iteratively linear updating, those are each direct indicators of an indirect solution and a model-matching approach, which too often can start with an incorrect or insufficient modeling equation and a matching of fundamentally inadequate data. The only time that a forward problem solved in an inverse sense can be equivalent to a direct inverse solution is when the direct inverse solution is linear. For example, locating reflectors at depth with a known velocity model is linear, and, hence, e.g., (asymptotic) RTM is a modeling run backward (i.e., in an inverse sense) to directly determine structure. Another trans-parent example is given by the forward geometric series

(3)and the inverse

(4)

when |S/a |. < 1

If, rather than these nonlinear relationships among S, a, and r, we instead imagine an exact linear relationship that S, a, and r might satisfy, e.g.,

, (5)

then we have the forward problem of solving for S given a and r, and the inverse problem becomes solving for r in terms of S and a. The direct inverse solution r = S/a is equivalent to the forward problem solved in an inverse sense, solving S = ar for r in terms of S and a. However, if the forward relationship assumed among S, a, and r is a quadratic relationship (an ap-proximate of the actual nonlinear forward problem given by Equation 3), we have

. (6)

Then, solving the forward problem, Equation 6, in an inverse sense is a quadratic solution with two roots that can be real or imaginary, whereas the solution to Equation 4 is a single real solution for r. In place of Equation 6, think of the linearized forward Zoeppritz equation for RPP solved in an in-verse sense, and the point is clear. This simple and transparent example demonstrates a pitfall of thinking that a direct inver-sion is equivalent to a forward problem solved in an inverse sense. Another example, pointed out in Weglein et al. (2009), is the direct inverse solution for predicting and removing free-surface and internal multiples, from the inverse-scattering se-ries, where these two distinct algorithms are independent not only of subsurface information, they are also independent of whether we assume the Earth is acoustic, elastic, anelastic, het-erogeneous, and anisotropic. The multiple-removal algorithms (which are direct and nonlinear) do not change one line of code when you change your mind about the Earth model type you want to consider. Can you imagine a model-matching and subtraction method or linear-updating method for predicting and removing multiples, with any cost function, L1, L2, LP, that would be independent of subsurface properties and the type of Earth model you are using to generate the synthetic data? It is hard to overstate the significance of this point. The widely recognized benefit to industry from effectively removing free-surface and internal multiples using algorithms derived from the inverse scattering series, for offshore and onshore plays, never would have occurred if the indirect inversion, model-matching, and iterative updating, and FWI-like thinking, were the approaches pursued for removing multiples.

In general, we look at inversion as a set of tasks: free-surface and internal-multiple removal, depth imaging, and nonlinear AVO. For the purposes of this article and for dis-cussing FWI, the focus is entirely on how the ISS addresses that parameter estimation task in isolation, and as if all other tasks (e.g., multiple removal) had been previously achieved.


R o u n d t a b l e

Indirect methods such as flat common-image gathers (CIG) were developed as a response to the inability to directly solve for and adequately provide a velocity model for depth imaging, and those CIGs represent a necessary condition at the image that an accurate velocity would satisfy. References for CIGs are Anderson et al. (2012), Baumstein et al. (2009), Ben-Hadj-ali et al. (2008, 2009), Biondi and Sava (1999), Biondi and Symes (2004), Brandsberg-Dahl et al. (1999), Chavent and Jacewitz (1995), Fitchner (2011), Guasch et al. (2012), Kapoor et al. (2012), Rickett and Sava (2002), Sava et al. (2005), Sava and Fomel (2003), Sirgue et al. (2009, 2010, 2012), Symes and Carazzone (1991), Tarantola (1987), and Zhang and Biondi (2013). Many wrong velocity models can and will also satisfy a flat common-image-gather criterion, especially under com-plex imaging circumstances. Indeed, unquestioned faith in the power of satisfying the flat CIG criterion can and does con-tribute to dry-hole drilling. Mathematicians who work on the latter types of CIG problems would better spend their time describing the underlying lack of a necessary and sufficient condition, and the consequences, rather than dressing up and obfuscating the necessary but insufficient condition in fancy, rigorous, and abstract new clothes.

It seems that the recent surge of interest in estimating changes in velocity is fueled by: (1) the improved ability to produce low-frequency and low-vertical-wavenumber infor-mation from new acquisition and improved deghosting; (2) the implicit admission of serious problems with methods to estimate velocity models (e.g., with tomography, iterative flat CIG searching, and the like); and, of course, (3) the persistent and unacceptable dry-hole drilling rate. Today, for example, we basically remain fixed and without significant progress (at a one-in-ten success rate) in drilling successful exploration wells in the deep-water Gulf of Mexico (Hawthorn, 2009; Iledare and Kaiser, 2007).

Indirect methods should be considered only when direct methods are not available or are inadequate, or when you can-not figure out how to solve a problem directly. Indirect meth-ods are often and reasonably employed to allow a channel or an adjustment (a dial) for phenomena and components of reality that are outside and external to the physics of the system you have chosen and defined. Of course, there always are, and al-ways will be, phenomena outside your assumed and adopted physics and system that must be accommodated and that are ignored at your peril. Thats the proper realm and role for in-direct methods. Even then, however, they need to be applied judiciously and always with scrutiny of what resides behind cost-function-criteria assumptions. When a direct method to predict the amplitude and phase of free-surface multiples, such as inverse-scattering-series free-surface-multiple removal, includes the obliquity factor, and has the direct satisfaction of prerequisites such as source and receiver deghosting and wave-let estimation, then the better the direct method of providing the prerequisites performs, the better the free-surface demul-tiple provides the amplitude and phase of the free-surface mul-tiples. If at any stage you decide you can roll in obliquity, source and receiver deghosting, and wavelet estimation into a catch-all energy-minimization adaptive subtraction, you run

into the serious problem: No matter how much better you achieve a satisfaction of energy minimization, you still have no guarantee that that improved energy minimization aligns with and supports free-surface-multiple removal while preserv-ing primaries. In fact, removal of multiples can increase en-ergy (e.g., when you have destructive interference between a primary and a multiple), and it is widely understood that the energy-minimization criteria are among todays greatest impediments to effectively removing free-surface and internal multiples for complex onshore and marine plays. The crite-ria behind the indirect adaptive step matter. Within the area of free-surface and internal-multiple attenuation, the rush to and overreliance on energy-minimization adaptive subtraction contributes to the inability to effectively and surgically remove multiples at all offsets and without damaging primaries. That specific issue was discussed in a recent report to the M-OSRP consortium on seeking adaptive criteria (Weglein, 2012) that serve as an alternative and replacement for energy minimiza-tion for free-surface multiple removal. However, the trend of using indirect methods for phenomena and processing goals within the system, and for providing prerequisites within the system, is in general a conceptual and practical mistake. There has been a dangerous and growing tendency to solve everything inside and outside the system by using indirect methods and cost functions. Of course the need for ever-faster computers is universally recognized and supported. However, the growth in computational physics, often at the expense of mathematical physics, and the availability of ever-faster computers, encourag-es the rush to cost functions and to searching without think-ing, and thus represents a ubiquitous, misguided, and unfor-tunate trend, with solutions that arent. When we give up on physics and determinism, we look at statistics and searching, and indirect methods become a natural choice and are always readily available, along with their drawbacks and consequences.

A direct method provides a framework of precise data needs, and it delivers a straight-ahead formula that takes in your data and actually solves and explicitly and directly outputs the solu-tion that you seek. Indirect methods can never provide that clarity or confidence. Model-matching and iterative updating by any fancy name, such as a new Frechet derivative, and the so-called full-wave inversion, are model-matching and are never, ever, equivalent to a direct inversion for the Earths elas-tic mechanical property changes. The distinction is significant and has both conceptual and mercantile consequences.

Here is an example of the difference. Suppose someone said that you could take a single seismic trace that is a single function of time, and invert simultaneously for velocity and density, each as a function of depth in a 1D Earth.

Today, you might reasonably be cautious and concerned because the dimension of the data is less than the overall di-mension of the quantities you seek to determine. We have learned as an industry to be dubious in the latter single-trace, solve-for-two-functions-of-depth case. We look skeptically at those who would model-match and pull all kinds of arcane cost functions and generalized inverses together, using differ-ent norms and constraints and full-wave predictions of that single trace that can be model-matched with amplitude and


R o u n d t a b l e

phase so that we can call that model-matching scheme full-waveform inversion. Why cant we solve for density and ve-locity uniquely from a single trace, because we can certainly model the single trace from knowing the velocity and density as a function of depth? Thats a beginning and an example of thinking that solving a forward problem in an inverse sense is in some way actually solving the inverse problem. What came along in that earlier time, as a response to this question, were direct acoustic inversion methods that said that inverting for velocity and density as functions of depth from a single trace is impossible, or at least that it is impossible to pro-vide the unique and actual velocity and density as a function of depth. That direct-inversion framework convinced many (hopefully most) people that the one-trace-in, two-functions-out approach is not a question or an issue of which indirect algorithm or LP cost function you are using. It is more ba-sic and stands above algorithm; its an inadequate-data issue. No algorithm with that single-trace data input should call itself inversion, even if that single trace was model-matched and iteratively updated and computed with amplitude and phase and, with too much self-regard, labels itself as full-wave inversion. We learned to stop running that single trace through search algorithms for velocity and densityand that lesson was absorbed within our collective psyches in our in-dustryfor whatever the cost function and local or global minimum you employed. Using the wrong and fundamental-ly inadequate data closes the book and constitutes the end of

the story. Thus, we learned to look for and respect dimension between the data and the sought-after parameters we want to identify. That is a good thing, but it turns out that its not a good-enough thing. In fact, direct acoustic wavefield inver-sion for a 1D Earth requires all the traces for a given shot record in order to determine one or more parameters (e.g., VP and density) as a function of depth.

This article will show (in a similar way) that the fact that you can solve the forward Zoeppritz equations (or a linear approxi-mate) for a PP reflection coefficient as a function of incident angle and the changes in , , and across the reflector does not imply that you can solve for changes in , , and in terms of the PP reflection coefficient as a function of angle. A direct in-verse for the changes in , , and demands all multicomponent sources and receivers, or, equivalently, PP, PS, SP, and SS data.

These conditions on data requirements hold for any pro-cessing/inverse problem in which the reference or background medium is elastice.g., for all amplitude analysis, including AVO and so-called FWI and all ISS multiple removal and imaging with ocean-bottom or onshore acquisition. See Li et al. (2011), Liang et al. (2010), Matson (1997), Matson and Weglein (1998), Weglein et al. (2003), and H. Zhang (2006).

Inadequate data means something much more basic and fundamental than limitations due to sampling, aperture, and bandwidth. That is, indirect solutions can (and often do) in-put data that are fundamentally inadequate from a basic and direct inverse perspective and understanding. The indirect

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R o u n d t a b l e

methods then search locally and globally around error surfaces with Frechet derivatives and conjugate gradients, and they keep hordes of math, physics, geophysics, and computer scientists busy using giant and super-fast computers looking at outputs and 3D color displays, and being convinced that with all the brainpower and resources that are invested, they are on track and are on their way to solving the problem. Whats wrong with linear iterative updating? Whats wrong begins with un-derstanding the meaning of a linear inverse. Even in cases in which the data are adequatee.g., cases with P-wave data and an acoustic inverse modelthe algorithms that a direct inverse provides for explicit linear and each nonlinear estimate of changes in P-wave velocity and density, will differ at the first nonlinear step and at every subsequent step, with the nonlinear iterative linear estimate of these changes in physical properties. The linear, quadratic, cubic, estimates of physical properties from a direct inverse method are explicit and unique (a gener-alized Taylor/geometric series) and order-by-order in the data and will not agree with an iterative linear update. Hence, al-though the iterative linear updating is nonlinear in the data, it does not represent a direct inverse solution. Further, the terms in the direct solution are analytically determined in terms of the first term, whereas iterative linear updating requires gener-alized inverses, SVD, cost functions, and numerical solutions. They could not be more different. If you had an alternative to the solution of the quadratic equation and it produced differ-ent roots from those produced by the direct quadratic formula, (Equation 2), would you call it an inverse solution for the roots? Thats the issue, and its that simple.

For the elastic inverse case, the difference is yet more se-rious. A direct inverse solution for the P-velocity, VP, shear velocity, VS, and density, , and a linear iterative method, will already differ at the linear step, and that difference and result-ing gap grow at each nonlinear step and estimate.

When it comes to directly inverting for changes in elastic properties and density, there are direct and explicit formulas for the linear and nonlinear estimates. The same single un-changed direct inverse ISS set of equations that derived the al-gorithms for free-surface and internal-multiple removaland have demonstrated standalone capability (see, e.g., Ferreira, 2011; Luo et al., 2011; and Weglein et al., 2003, 2011)have also provided the ISS depth imaging (Weglein et al. 2011, 2012) and direct inversion for Earth mechanical properties. In Zhang (2006), we find the first direct nonlinear equations for estimating the changes in elastic properties for a 1D Earth.

The mathematical origin of linear inverse theory (and lin-ear iterative inversion) begins with a Taylor series of the re-corded data, D(m), from the actual Earth. Those data depend on the Earth properties characterized by the label m and the synthetic data D(m0) from an estimate or reference value of those properties that we label, m0. To relate D(m) and D(m0 ), we introduce a Taylor series

, (7)

in which the derivatives are Frechet derivatives. A linearized form of Equation 7 is considered

, (8)

where the Frechet derivative,

(9)

is approximated by a finite-difference approximation involv-ing data at m0 and data at a nearby model, m0+m. m1

1 means the first linear estimate of m, with the subscript standing for linear and the superscript for the first estimate. The matrix inversion of Equation 8 for m1

1 leads to a new approximate m0+m1

1, and

. (10)

The process is repeated and is the basis of iterative linear inversion. Properties of that process related to convergence to m are spelled out in Blum (1972), page 536, with issues where the constants such as M that appear in the convergence criteria are unknown.

Another starting point for this type of perturbative ap-proach is from scattering theory, where D(m) relates to the actual Greens function, G, and D(m0 ) relates to the reference Greens function, G0 , and V = mm0. The identity among G, G0, and V is called the Lippmann-Schwinger or Scattering Equation (see, e.g., Taylor 1972)

(11)

and an expansion of Equation 11 for G in terms of G0 and V produces

. (12)

Keys and Weglein (1983) provide the formal association between D(m0)m and G0VG0. Equation 7 is a Taylor series in m, and as such that series does not have an available in-verse series. However, because Equation 12 (which follows from the scattering Equation 11) is a geometric series in r = VG0 and a = G0 , then a geometric series for S = GG0 in terms of a and rS = ar/(1r)has an inverse series r = (S/a)/(1+S/a) with terms

... .

A unique expansion of VG0 in orders of measurement val-ues of (G-G0 ) is

(13)


R o u n d t a b l e

The scattering-theory equation allows that forward series form the opportunity to find a direct inverse solution. Sub-stituting Equation 13 into Equation 12 and setting the terms of equal order in the data to be equal, we have D = G0V1G0 , where the higher order terms are V2, V3, . . . , as given in We-glein et al. (2003) page R33 Equations 714.

For the elastic equation, V is a matrix and the relationship between the data and V1 is

where V1, V2 are linear, quadratic contributions to V in terms of the data,

.The changes in elastic properties and density are con-

tained in , and that leads to direct and explicit

solutions for the changes in mechanical properties in orders

of the data, ,

The ability of the forward series to have a direct inverse se-ries derives from (1) the identity among G, G0, V provided by the scattering equation and then (2) the recognition that the forward solution can be viewed as a geometric series for the data, D, in terms of VG0. The latter derives the direct inverse series for VG0 in terms of the data.

Viewing the forward problem and series as the Taylor series (Equation 7) in terms of m does not offer a direct inverse series, and hence there is no choice but to solve the forward series in an inverse sense. It is that fact that results in all current AVO and FWI methods being modeling meth-ods that are solved in an inverse sense. Among references that solve a forward problem in an inverse sense in P-wave AVO are Beylkin and Burridge (1990), Boyse and Keller (1986),

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R o u n d t a b l e

Burridge et al. (1998), Castagna and Smith (1994), Clay-ton and Stolt (1981), Foster et al. (2010), Goodway (2010), Goodway et al. (1997), Shuey (1985), Smith and Gidlow (2000), Stolt (1992), and Stolt and Weglein (1985). The in-tervention of the explicit relationship among G, G0, and V (the scattering equation) in a Taylor series-like form produces a geometric series and a direct inverse solution.

The linear equations are:

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

and

(22)

where a(1), a

(1), and a

(1) are the linear estimates of the changes

in bulk modulus, shear modulus, and density, respectively. The direct quadratic nonlinear equations are

(23)

(24)

(25)

(26)

(27)

Because relates to , relates to , and so on, the four components of the data will be coupled in the nonlin-ear elastic inversion. We cannot perform the direct nonlinear inversion without knowing all components of the data. Thus, the direct nonlinear solution determines the data needed for a direct inverse. That, in turn, defines what a linear estimate means. That is, a linear estimate of a parameter is an estimate of a parameter that is linear in data that can directly invert for that parameter. Because DPP, DPS, DSP, and DSS are needed to determine a

, a

, and a

directly, a linear estimate for any one

of these quantities requires simultaneously solving Equations 1922. See, e.g., Weglein et al. (2009) for further detail.

Those direct nonlinear formulas are like the direct solution for the quadratic equation mentioned above and solve directly and nonlinearly for changes in VP, VS, and density in a 1D elastic Earth. Stolt and Weglein (2012), present the linear equations for a 3D Earth that generalize Equations 19-22. Those formulas prescribe precisely what data you need as input, and they dic-tate how to compute those sought-after mechanical properties, given the necessary data. There is no search or cost function, and the unambiguous and unequivocal data needed are full mul-ticomponent dataPP, PS, SP, and SSfor all traces in each of the P and S shot records. The direct algorithm determines first the data needed and then the appropriate algorithms for using those data to directly compute the sought-after changes in the Earths mechanical properties. Hence, any method that calls itself inversion (let alone full-wave inversion) for determining changes in elastic properties, and in particular the P-wave veloc-ity, VP, and that inputs only P-data, is more off base, misguided, and lost than the methods that sought two or more functions of depth from a single trace. You can model-match P-data until the cows come home, and that takes a lot of computational effort and people with advanced degrees in math and physics com-puting Frechet derivatives, and requires sophisticated LP norm cost functions and local or global search engines, so it must be reasonable, scientific, and worthwhile. Why cant we use just PP data to invert for changes in VP, VS, and density, because Zoeppritz says that we can model PP from those quantities, and because we have, using PP-data with angle variation, enough dimension? As stated above, data dimension is good, but not good enough for a direct inversion of those elastic properties.

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R o u n d t a b l e

The evidence to succeed is now in your hands

GeoTeric empowers your interpretation to reduce uncertainty, explore alternative scenarios and accelerate decisions.

Whether you seek a more accurate representation of intra-reservoir faulting, reservoir morphology, or potential hydrocarbon migration pathways GeoTeric puts a wealth of geological details directly into your hands.

Based on a best-in-class approach at every stage, GeoTerics robust and reliable Geological Expression workflows empower you to decide and succeed sooner.

Make contact now: email [email protected] or visit www.GeoTeric.com


R o u n d t a b l e

Figure 1. Synthetic well log A-52. Figure 2. The baseline, monitor, and input reflection coefficients.

Figure 3. Comparison of actual changes in shear modulus, P-impedance, and velocity ratio VP / VS . The baseline is the log data in 1986 and the monitor is the log data in 2001.

Figure 4. Comparison of first- and second-order approximations of relative change in shear modulus. The baseline is the log data in 1986 and the monitor is the log data in 2001.

Figure 5. Comparison of first- and second-order approximations of relative change in VP / VS . The baseline is the log data in 1986 and the monitor is the log data in 2001.

Figure 6. Zoomed-in comparison of first- and second-order approximations of relative change in VP / VS. The baseline is the log data in 1986 and the monitor is the log data in 2001.

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R o u n d t a b l e

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NEOS has acquired airborne geophysical data gravity, magnetic, radiometric, electromagnetic, and hyperspectral over a 1,000

square mile area of Colorados Sand Wash Basin. These datasets are being integrated with existing seismic and well information and

simultaneously interpreted to provide an improved, basement-to-surface understanding of the Sand Wash Basin. Data licensees would

strengthen their insights into the drivers of well productivity and Niobrara sweet spots, including basement topography, faulting and

lineament patterns, hydrothermal fluid movements, and other factors affecting deposition, rock quality, thermal maturity, and fluid flow.

Data processing and multi-measurement interpretation is now underway, with First Look deliverables expected before the end of the

year. Late underwriting licenses to the data and interpretive products from the Sand Wash neoBASIN survey remain available under

attractive commercial terms until the final results are delivered to the programs underwriters in early 2014.

To learn more about this program, send an email to: [email protected]

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R o u n d t a b l e

The direct inverse is nonlinear. Iterative linear is nonlinear. But iterative linear inversion is not in any way equivalent to a direct nonlinear inversion. The further evidence that iterative linear inverse is not a direct elastic inverse solution, is that you can iteratively linear invert P-wave data. Hence, you can have the fundamentally inadequate data and perform iterative lin-ear updating. Thats not possible with a direct inverse method. The framework, data needs, and algorithms provided by direct inversion all matter. If you iteratively linear invert multicom-ponent data, you would not be performing a direct inversion, and your nonlinear estimates would not agree with the unique nonlinear terms provided by a direct solution. Multicompo-nent data are important, but the direct inverse algorithm of that data is essential. The framework of a direct method helps you understand what will allow things to work in principle, and, equally important, it helps you identify the issue or problem when things dont work. Indirect methods, on the other hand, can never match that definiteness, clarity, and value. When we use just P-wave data with an acoustic or elastic model-matching FWI for shallow-hazard detection or velocity estimation at top salt, and then issues arise, perhaps the framework and require-ments described in this note might be among the issues behind a lack of predictive stability and usefulness.

In Wave theory modeling of P-waves in a heterogeneous elastic medium (Weglein 2012), a single-channel P-wave for-malism is presented as a way to model P-waves in amplitude and phase without needing to model and predict shear waves. This P-only wave-modeling method is intractable as a param-eter-estimation inverse procedure, blocked at the first and lin-ear term. That supports the need for all multicomponent data in a direct inverse for estimating changes in the Earths me-chanical properties. If one somehow remained insistent that P-data were adequate for a direct elastic inverse, one would have to provide a response to that linear, intractable inverse step. Further, those direct and explicit nonlinear formulas are derivable only from the direct inverse machinery of the inverse scattering series (please see the References section).

Using P-wave data with amplitude and phase for an acoustic Earth model flies in the face of 40 years of AVO experience, which says that the elastic Earth is the minimum realistic Earth model for any amplitude-dependent algorithm or processing method. Using P-wave data for an elastic Earth model, with algorithms that utilize amplitude and phase, violates the neces-sary multicomponent data needs prescribed by direct inversion of VP, VS, and density. Having the adequate data (defined by a direct-inversion framework) is better than not having the neces-sary and sufficient data and i

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