Application of Biot-Gassmann Subtitution method in generating synthetic of S-wave sonic log for simultaneous AVO inversion - repository civitas UGM

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Preface

All praises are due to Allah, God Almighty, Who made this annual event of successful. The “3rd

Annual Basic Science International Conference (BaSIC-2013)” is an annual scientific event organized

by the Faculty of Mathematics and Natural Sciences, Brawijaya University. As a basic science conference, it covered a wide range of topics on basic science: physics, biology, chemistry, mathematics and statistics. In 2013, the conference took a theme of “Basic Science Advances in Energy, Health and Environment” as those three aspects of life are hot issues.

The conference in 2013 was the continuation of the preceding conferences initiated in 2011 as the

International Conference on Basic Science (ICBS), where it was a transformation from the similar

national events the faculty had organized since 2004. What also changed in year 2013 was the use of the ISSN for the conference proceedings book, instead of an ISBN used in previous proceedings books. The change was based on the fact that BaSIC is an annual event, and, therefore, the use of ISSN is more appropriate. The proceedings book was also divided into four books: Physics, Biology, Chemistry and Mathematics, each with a different ISSN. The proceedings were also published in electronic forms that can be accessed from BaSIC website. I am glad that for the first time both types of publication can be realized.

This event is aimed to promote scientific research activities by Indonesian scientists, especially those of Brawijaya University, in a hope that they may interact and build up networks and collaborations with fellow overseas counterparts who participated in the conference. This is in line with university vision as a World Class Entrepreneurial University.

I am grateful to all the members of the program committee who contributed for the success in framing the program. I also thank all the delegates who contributed to the success of this conference by accepting our invitation and submitting articles for presentation in the scientific program. I am also indebted to PT Semen Gresik and PT PLN (Persero) for their support in sponsoring this event.

I wish for all of us a grand success in our scientific life. And I do hope that the coming conferences will pick up similar success, and even better.

Malang, April 2013

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Foreword by the Rector of Brawijaya University

First of all I would like to congratulate the Organizing Committee for the success in organizing this amazing event. I believe all dedicated time and efforts will contribute to the advancement of our beloved university.

I would like to welcome all participants, domestic and overseas, especially the distinguished invited speakers, to Malang, to the conference. An international conference is a good means to establish and build relationships and collaborations among participants. So, I hope this conference will facilitate all of you, the academicians and scientists, to setup a network of mutual and beneficial collaboration. As a university with a vision to be “A World Class Entrepreneurial University”, Brawijaya University will support all efforts to realize that dream.

Finally, I do hope that the conference will run smoothly and nicely and is not the last one. I would like to thank all parties who have lent their hands in making this conference happened.

Malang, April 2013

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Program Committee

Patrons

Rector, Universitas Brawijaya

Dean, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya

Advisory Boards

Associate Deans 1, 2 and 3, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya

Chairperson

Johan A.E. Noor, Ph.D.

Deputy-Chair Dr. Suharjono

Secretary

Agus Naba, Ph.D.

Treasurers Mrs. Sri Purworini Mrs. Rustika Adiningrum Mr. Surakhman

Secretariat & Registration Dr. Masruroh

dr. Kusharto Mr. Sugeng Rianto Mr. Gancang Saroja

Conference Web Agus Naba, Ph.D.

Publication & Proceedings Arinto Y.P. Wardoyo, Ph.D. Mr. Wasis

Public Relations & Sponsorship Chomsin S. Widodo, Ph.D. Mr. Moch. Djamil

Mrs. Firdy Yuana

Venue

Mr. Ahmad Hidayat Dr. Ahmad Nadhir Mr. Sunariyadi Mr. Purnomo

Mr. Karyadi Eka Putra

Accommodation & Hospitality Ms. Siti J. Iswarin

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Mrs. Nur Azizah Mr. Robi A. Indrajit Mrs. Trivira Meirany

Master of Ceremony Himafis

Transportation, Excursion & Social Events Djoko Santjojo, Ph.D.

Dr. Sukir Maryanto Mr. Wahyudi Mrs. Arnawati

Workshop, Poster & Scientific Exhibitions Hari Arief Dharmawan, Ph.D.

Mr. Pudji Santoso Mr. Sahri

Mr. Murti Adi Widodo

Documentation

Mauludi A. Pamungkas, Ph.D. Mr. Susilo Purwanto

General Supports Himafis

Scientific Program Dr. rer.nat. M. Nurhuda Dr. Sunaryo

Mr. Agus Prasmono

Local Scientific Committees (Reviewers & Editors) Physics

Dr. rer.nat. Abdurrouf Adi Susilo, Ph.D. Mr. Unggul P. Juswono Dr.-Ing. Setyawan P. Sakti

Biology

Dr. Moch. Sasmito Djati Dr. Muhaimin Rifai Dr. Catur Retnaningdyah

Chemistry Dr. Masruri

Dr. Ahmad Sabarudin Dr. Lukman Hakim

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International Scientific Committee and Editors

A/Prof. Lilibeth dlC. Coo, University of the Philippines, the Philippines

Prof. Dr. Gereon Elbers, FH Aachen, Germany

Prof. S.K. Lai, National Central University, Taiwan

Prof. Kwang-Ryeol Lee, Korean Institute of Science and Technology, Korea

A/Prof. Dann Mallet, Queensland University of Technology, Australia

Prof. Lidia Morawska, Queensland University of Technology, Australia

Prof.Dr. Petr Solich, Charles University, Czech Republic

Dr. Michitaka Suzuki, Nagoya University, Japan

Prof. Hideo Tsuboi, Nagoya University, Japan

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

Abstract— Simultaneous AVO inversion is novel method in reservoir characterization. The

method will produce several physical properties of reservoir such as P-wave Impedance, S-wave Impedance, density, Vp/Vs ratio, Lamda-rho and mu-rho. These physical properties could be used to estimate the type and content of reservoir lithology. Simultaneous AVO inversion needs P-wave sonic log, S-wave sonic log and density as input. S-Wave sonic logs are rarely available due to the expensive cost of data acquisition. We generate synthetic S-wave sonic log by mean Biot-Gassman Substitution method instead of the Castagna or Mudrock line method and compare the results with the original wave sonic log. We use the synthetic S-wave sonic log, P-S-wave sonic log and density log to create the initial model for simultaneous AVO (Amplitude versus offset) inversion. This initial model together with the seismic wavelets which are extracted from 3D seismic data statistically to perform simultaneous AVO inversion that will produce physical property like P-wave Impedance, S-wave Impedance, density and Vp/Vs ratio in a 3D cube.

Index Terms— Simultaneous AVO Inversion, Biot-Gassman substitution, S-wave sonic,

P-wave sonic, Vp/Vs ratio

I. INTRODUCTION

The objectives of this papers are to conduct S-wave estimation by mean Biot-Gassman substitution method for running simultaneous AVO inversion of pre-stack seismic data in order to estimate the elastic parameters of the rock, which will derive pseudo density (Rho/Dn), P-wave ervelocity (VP), S-wave velocity (VS), acoustic impedance (ZP), shear impedance (ZS), and VP/VS ratio volume. Rock properties of reservoir could be derived from these elastic parameters.

II. TEORI P-wave and S-wave Velocity Theory

There are two types of waves that are of great interest to us when analyzing seismic data, i.e. the compressional wave or P-wave, and the transverse wave or S-wave. Unlike density, seismic velocity involves the deformation of a rock as a function of time. As shown in Figure II.4, a cube of rock can be compressed, which changes its volume and shape or can be sheared, which changes its shape but not its volume.

Fig. 1. A rock may be deformed by compression and shear wave

The simplest forms of the P and S-wave velocities are derived for non-porous, isotropic rocks. These are the equations for velocity written using the Lamé coefficients:

Another important parameter is the Poisson's Ratio. A change in this ratio can indicate a change in the pore fluid. Poisson's Ratio can be defined in terms of P and S wave

Note that there are several values of Poisson’s ratio and S P

V V

ratio that are important to

remember.

Sudarmaji, B.E. Nurcahya and Sismanto are with Lab. Geofisika, Jurusan Fisika FMIPA, Universitas Gadjah Mada, Sekip Utara Po. Box Bls 21 Yogyakarta 55281, Fax: +62-0274-545185, Telp: +62-0274-522214 (E-mail:

ajisaroji@yahoo.com; budiekanurcahya@yahoo.com;sismanto@ugm.ac.id

If

Castagna et al (1985) derived simple empirical relationship between P-wave and S-wave velocity, which can be written:

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This is simply that the equation is a straight line, so VP and VS are linearly related. This line is also legendary called as the Mudrock Line

The Biot-Gassmann Equations

The basic use of the Biot-Gassmann equations is to “substitute” or replace the fluids in a set of target layers with another set of fluids.

Independently, Gassmann (1951) and Biot (1956), developed a more complete theory of wave propagation in fluid saturated rocks, by deriving expressions for the saturated bulk and shear moduli, and substituting into the regular equations for P and S-wave velocity:

sat

Note thatsatis found using the volume average equation described earlier

Pre-stack Simultaneous AVO Inversion.

The purpose of simultaneous AVO inversion is to invert pre-stack CDP gathers (PP and optionally PS angle gathers) to obtain reliable estimates of compression impedance (ZP), Shear impedance (ZS), and density () from which to predict the fluid and lithology properties of the subsurface of the earth.

Post-stack inversion ignores the fact that, in wet clastic rocks, ZP and ZS should be related. VP and VS should be linearly related (as shown from Castagna's equation) when there are no complicated factors, such as the presence of hydrocarbons. Also, density should relate to VP through some form of Gardner's equation.

Therefore, simultaneous (or joint) inversion would include some form of coupling between the variables. This should add stability to a problem that is sensitive to noise and usually produces non-unique solutions, so simultaneous inversion solves the Fatti’s equation.

The Aki-Richards equation (Russell, 2005) is a linearized version of the Zoeppritz equations. The Aki-Richards equation was re-expressed by Fatti (1994) as:

Workflow of S-wave velocity estimation using Biot-Gassman Substitution could be seen in figure 2. Input for this process are petrophysics data log, such as: density, P-wave velocity, porosity, water saturation and the composite of hydrocarbon in the reservoir. Some rock physic parameters, such as: balk or shear modulus of oil, gas and water could be determined based empirical data from previous study. Final product of this work are estimated S-wave velocity.

Figure 3. show the wave velocity comparison among original wave velocity, S-wave velocity estimated using Castagna and Biot-Gassman method. S-S-wave velocity estimated Biot-Gassman method have more similar shape with original S-wave velocity than S-wave velocity estimated using Castagna method.

Fig. 2. Workflow of S-wave velocity estimation using Biot-Gassman Substitution Application of Biot-Gassman Substitution Method in

Generating Synthetic of S-Wave Sonic Log for Simultaneous AVO Inversion

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Fig. 3. S-wave velocity comparison among original S-wave velocity , S-wave velocity estimated using Castagna and Biot-Gassman method

From estimated S-wave velocity and P-wave velocity, P-Impedance  Z_P and

S-Impedance(ZS)could be could be calculated with multiplying velocity of P-wave (VP)

and S-wave (VS) with density (). The value of S P

V V

could estimated from estimated

S-wave and P-S-wave velocity too.

It is needed to make cross-plot analysis or sensitivity analysis in order to correlate between elastic parameters log that have been generated with Gamma ray log as sand-shale indicator. Figure 4 show Cross-plot V_Pvs VS log as function Gamma Ray log certain

depth interval around gas reservoir. Rocks that composited by sand, shale, coal, sand saturated with gas from different reservoir could be seen from the cross plot. Therefore, sand reservoir saturated with gas could be delineated with certain value ofV_Pvs V_S.

Fig. 4. Cross plot V_Pvs V_Sas function Gamma Ray from certain depth interval around gas reservoir

IV. SIMULTANEOUS AVO INVERSION

The final product of simultaneous AVO inversion is to invert pre-stack CDP gathers (PP and optionally PS angle gathers) to obtain reliable estimates of P-wave velocity (VP) and

S-wave velocity (VS) and ratio of

properties of the subsurface of the earth.

Figure 5 to figure 7 show map of P-wave velocity (V_P) , map of S-wave velocity (

estimated S-wave velocity from the Biot-Gassman substitution method. Good sand reservoir of hydrocarbon saturated with gas are shown by middle value of P-wave and

S-wave velocity and low value of ratio S P

V V

. The reservoir sand saturated with gas have value

of P-wave velocity around 2300 m/s - 3600 m/s, S-wave velocity around 1800ms - 2800

ms and ratio

Fig. 5. Map of P-wave velocity (V_P)overlaid with time structure from certain layer that contains gas reservoir

Fig. 6. Map of S-wave velocity (VS) overlaid with time structure from certain layer that contains gas reservoir

Fig. 7. Map of ratio

S P

V V

overlaid with time structure from certain layer that contains gas reservoir

ACKNOWLEDGMENT

We would like to say thanks to Geophysics Laboratory of Gadjah Mada University with their support of hardware, software and data so this research could be conducted.

REFERENCES

[1] B. H. Russell, et al., “Joint simultaneous inversion of PP and PS angle gathers”, CREWES Research Report, Volume 17, 2005.

[2] C.H.P.Veeken, Seismic Stratighraphy, Basin analysis and Reservoir Characterization, Amsterdam: Elsevier,2007.

[3] D.P.Hampson, B.H. Russell, and B. Bankhead, “Simultaneous inversion of pre-stack

seismic data”, Ann. Mtg. Abstracts, SEG2005, p. 1633-1637

[4] G.P. Allen and J.L.C. Chambers, “Sedimentation in the Modern and Miocene Mahakam Delta”, Indonesian Petroleum Association, 1998.

[5] G.Mavko , et al,”Fluid substitution: Estimating changes in VP without knowing VS”, Geophysics, Nov-Dec. 1995,

[6] J.P.Castagna, M.L. Batzle, and R.L.Eastwood, ”Relationship between

compressional-wave and shear-compressional-wave velocities in clastic silicate rocks”, Geophysics, Vol. 50, 1985,p.

571-581.

[7] Per Avseth, et al, “Quantitative Seismic Interpretation”, Cambridge University Press, 2005P.F. Anderson and L.R. Lines, “A comparison of inversion techniques for estimating Vp/Vs

from 3D seismic data”, CREWES Research Report - Volume 20, 2008.

[8] R.T.Shuey,”A Simplification of The Zoeppritz Equations”, Geophisycs 50, 1985,p. 609-614.

[9] S.Rutherford, and R.William, , Amplitude versus offset variation in gas sands, Geophysics 54, 1989, p. 680-688.

[10] W.J.Ostrander, “Plane-Wave Reflection Coefficients for Gas Sands at Non Normal

Angles of Incidence”, Geophysics 49, 1984, p.1637-1648.

Application of Biot-Gassmann Subtitution method in generating synthetic of S-wave sonic log for simultaneous AVO inversion - repository civitas UGM

Preface

Foreword by the Rector of Brawijaya University

Table of Contents

Program Committee