SEG/San Antonio 2007 Annual Meeting. γ Q in terms of complex-valued weaknesses that relates

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1 Chichinina* G Ronquillo-Jarillo abinin nstituto Mexicano del etróleo; Obolentseva L Gik and B Bobrov nstitute of etroleum Geology and Geophysics of iberian Branch of Russian Academy of ciences ummary We perform an ultrasonic experiment on anisotropy of wave propagation in the model constructed from plexiglas plates with oil saturation and without any saturation We determine the directional dependencies of - and -waves attenuations and velocities and estimate homsen-style parameters for attenuation ε and γ as well as homsen s velocity parameters We develop a theory that predicts certain relationship between anisotropies of - H- and -wave attenuation and velocity in transversely isotropic () media due to aligned fracture set aking into account the interplay of the velocity and attenuation anisotropies we develop the effective model of the attenuative fractured medium fitted to the experimental data We derive formulas for the parameters ε and γ in terms of complex-valued weaknesses that relates these parameters to fractured medium parameters We found out that the ratio of the symmetry-axis - and -wave attenuations / and the parameter are interlinked and strongly dependent of the fluid type in cracks that is confirmed by the experiment he value of is much greater for dry-crack medium than for wet-crack medium that is correlated with the / -ratio which is on the contrary larger in wet-crack medium and smaller in drycrack medium his is in accordance with laboratory measurements at ultrasonic frequencies of - and -wave quality factors ntroduction owadays reliable seismic data on -anisotropy is in very short supply; there are only few recent works eg asconselos & Jenner (005) Maultzsch et al (005) and arela et al (006) As for ultrasonic laboratory data there are some petrophysical experiments on -anisotropy where attenuation of - and -waves is measured at two orthogonal directions (eg Yin and ur 99; rasad and ur 003; Best 994) n order to obtain the reliable estimates of -anisotropy for attenuative medium one needs to know the values of - - and H-wave attenuations in the full interval of incidence angles i e from 0 to 90 with the symmetry axis here are few ultrasonic experiments with artificial plate models on - wave attenuation anisotropy for wide range of propagation angles (eg Hosten et al 987; Zhu et al 007) Ultrasonic experiments on -anisotropy for all three types of waves and H in the full interval of wave incidence angles in medium are close to be absent n the presented experiment we get attenuations and velocities for - and H-waves Joint analysis of the data for - - and H-wave attenuations and velocities provides the information for the proper reconstruction of the attenuation-anisotropy properties of the model Joint inversion of all the attenuations and velocities enables estimating homsen-style (homsen 986) parameters for attenuation ε and γ which were introduced by Zhu & svankin (006) We derive formulas for the directionally dependent attenuation and the attenuation parameters in terms of complex-valued weaknesses that relate these parameters to fractured-medium properties (Chichinina et al 004; 005; 006a; 006b) We are going to reveal the new sense of the parameter which is close to be meaningful for fracture characterization in seismic exploration heoretical background o describe anisotropy in attenuative medium (due to a single set of fractures) we introduce complex-valued stiffness matrix We rewrite the elastic stiffness matrix { C ij } given in the form of choenberg and ayers (995 p 07) and get the following complex-valued stiffness matrix { C ij } for medium with vertical symmetry axis (): L K ( ); ( ); K λ ξ λ K L J C ij L M ( ξ ); µ ( ); J M ( ); R µ R where () are complex-valued weaknesses which and were generated from the real-valued weaknesses in the following manner: and i i () see also (MacBeth 999) n equation () λ µ are the Lame s constants in the background rock M λ + µ ξ λ M g and g is defined as g µ /( λ + µ ) ( / ) where and are -wave and -wave velocities in the background rock n equation () and are the normal and tangential weaknesses (Bakulin et al 000) which weaken the isotropic background rock due to the presence of fractures ( 0 < < 0 < < ) EG/an Antonio 007 Annual Meeting 49

2 We describe the anisotropy of attenuation by the matrix of the inverse quality factor that is { ij } which can be expressed (Carcione 000) as mc ij ij (3) ReCij where { C ij } is the complex-valued stiffness matrix given by equation () hen the matrix { ij } for the attenuative medium can be written as ξ L K J K ; ξ K L J ξ L ; J J J ξ ij J ; ; (4) Following choenberg and Douma (988) we express the -wave velocity (α ) as ( ) ( [ sin ] sin α g α g α ) (5) the -wave velocity (α ) as ( ( g )sin α ) (6) and the H-wave velocity H (α ) as H ( cos α) (7) where α is measured relatively the symmetry axis z We define attenuation (Carcione 000) as m( ) Re( ) (8) where is complex-valued phase velocity and then can be written as Re( ) + i m( ) Within equations (5)-(7) we replace the weaknesses and with the complex-valued weaknesses and following equation () o we get complex-valued ( α ) H and ( ) hen we separate the imaginary and real parts m( ) and Re( ) and derive the attenuation following equation (8) By this manner we get the - - and H-wave attenuation as ( [ g sin α ] + g sin α α ) [ g sin α ] g sin α (9) + ( g )sin α ( g )sin α (0) cos α ( α ) () cos α H Experiment versus theory he model is constructed from rectangular plexiglas plates each mm thick which were held on together by compressing uniaxial pressure Ma here is periodic variability of plate thickness (from 00 to 03 mm) with the spatial period of 0 mmt is assumed that attenuation is due to linear slip interfaces between the plates he ultrasonic experiment was performed for two models with oil saturation and without any saturation ( dry model ) he experimental data on the - - and H-wave velocity and attenuation is presented in Figure (marked by symbols) for the dry model (a c) and the oil-saturated model (b d) he angle α is measured relatively the symmetry axis z ote that only the restricted α -angle range from 45 to 90 is available in the experiment (see details in Gik & Bobrov (996)) heory-predicted attenuation and velocity Figure (a-b) shows phase velocities (α ) (α ) and H (α ) calculated from equations (5)-(7) with the model-input parameters ( and ) from able Figure (c-d) shows the corresponding curves for attenuation ( α ) ( α ) and ( α ) calculated from equations (9)-() H with the model-input parameters ( and ) given in ables - homsen-style approximation curves are shown by dotted line o describe the shear-wave attenuation and ( α H ) observed in the experiment we have to introduce the O isotropic attenuation ( ) hen equations (0) and () for and ( α H ) should be corrected as O ( α ) ( α ) + ( ) () O H ( α ) H + ( ) (3) O where ( ) in the oil-saturated model and ( ) O 003 in the dry model able Model-input parameters for velocity ε γ We found out certain theory-predicted interrelationships between the - and -wave velocities and attenuations in terms of the weaknesses that enabled us Oil Dry n Oil-saturated and Dry models the host-rock velocities 680 m/s 340 m/s and g ( ) 0 5 able Model-input parameters for attenuation γ ε Oil Dry EG/an Antonio 007 Annual Meeting 50

3 Figure Experimental data (marked by symbols) and theoretical curves for the - - and H-wave velocity (α ) (a b) and attenuation (c d); for the dry model (a c) and the oil-saturated model (b d) he angle α is measured relatively the symmetry axis For - and H-wave attenuation is calculated from equations (9) () and (3) elocity (α ) is calculated from equations (5) (6) and (7) (solid line) Model-input parameters are given in ables homsen-style approximation for and (α ) is marked by dotted line with the anisotropy parameters given in ables to get the corrected (mutually compatible) values of the - and -wave symmetry-axis velocities and attenuations from the experimental data (Because of the lack of data at the angles α from 0 to 45 the straightforward estimation of the symmetry-axis velocities was unavailable) Following the theory we have substantially corrected the velocities especially the H-wave velocity H (α ) in the case of the dry-crack model; that is why it occurred to be not wellsuited to the experimental data as it is shown in Figure (a) for the dry model he same takes place in the case of the attenuation curves shown in Figure (d) for the oilsaturated models homsen-style parameters for attenuation Following Zhu & svankin (006) we write homsenstyle anisotropy parameters for attenuation as ε γ H 05 d ( α ) dα α 0 where the symbol marks the direction of wave propagation normal to fracture planes (that is the symmetry-axis direction) and the symbol marks the direction parallel to fracture planes (that is the isotropyplane direction) n terms of the matrix { ij } and H 66 For the -wave attenuation homsen-style approximation can be written (Zhu and svankin 006) as 4 [ + sin α + ( ε )sin α] (4) We found out that ε is independent of the attenuation: ε ( ) ) (5) On the contrary the parameter does depend on the attenuation: EG/an Antonio 007 Annual Meeting 5

4 4 (6) Following approximations of Zhu and svankin (006) we define the H-wave attenuation as ( + γ sin α) (7) H where the γ -value is given in able he -wave attenuation is ( + σ sin α ) (8) 4 where the parameter σ was estimated as 55 for the dry model and σ -6 for the oil-saturated model Following the sign of σ (plus or minus) the -wave attenuation curve shown in Figure (c) turns its pattern from the convex (for the dry model) to the concave (for the oil-saturated model) Figure (d)) Unfortunately to corroborate this we have not got any reliable experimental data for -wave attenuation in the case of the dry model ote that in equations (7) and (8) the -value given in able should be corrected for the isotropic attenuation O ( ) following equations () (3) -anisotropy in the oil-saturated and dry models We found out that neither ε no γ can serve for distinguishing dry cracks from oil-saturated Moreover the velocity parameter ε is much more sensitive to the fluidfill type in cracks than the attenuation parameter ε Besides we found out the essential difference in the symmetry-axis - and -wave attenuations and in the oil-saturated and dry models Actually after oil saturation the -wave attenuation increases: OL ( ) ( ) 4 6 but at the same time the -wave attenuation decreases: OL ( ) ( ) 0 34 his resulted in the essential contrast in -values for the oil-saturated and dry models that is OL 7 Actually it follows from equation (6) that can be defined by the relative difference between - and -wave attenuations and : ( ) (9) if assumed / 0 5 in equation (6) hus the essential difference in -values for the oilsaturated and dry models is caused by the great change in the / -value for the oil-saturated and dry models ( ) OL ( ) 4 hus we found out that the symmetry-axis- -ratio is much larger in a wet-crack medium than in a dry-crack medium ( ) WE ( ) >> his is in accordance to laboratory measurements at ultrasonic frequencies of - and -wave quality factors (oksöz et al 979) as well as attenuation data from sonic logs (Klimentos 995) that WE show ( ) ( ) / > / (ote that / / ) n particular they have observed / > for wet rocks (with water or brine) and / < for dry (or gassaturated) rocks Conclusions he experimental data was used as an illustration material for the theory application We managed with the lack of data at the angles from 0 to 45 to the symmetry axis this situation is similar to that which takes place in the case of seismic reflection data in frames of H model he behavior of - - and H-wave attenuation as a function of the wave-propagation direction is similar in common to the well known directional dependences for the velocities in medium he attenuation curves are alike the velocity curves according to the principle the maximum of velocity curve corresponds to the minimum of attenuation curve and vice versa Attenuation anisotropy is much stronger than velocity anisotropy For example in the oil-saturated model the - wave velocity anisotropy is 4% but the anisotropy of attenuation is much greater 5% n real seismic data the -wave velocity anisotropy caused by liquid-saturated cracks is very small and hardly can be used for seismic exploration However the -wave attenuation anisotropy is rather strong and can be used in fracture characterization for estimation of fracture direction in reservoir rocks from azimuthally varying Examples are in asconselos & Jenner (005) Maultzsch et al (005) arela et al (006) and Chichinina et al ( a 006b) We found out that the ratio of the symmetry-axis - and - wave attenuations / and the parameter are interlinked and strongly dependent of the fluid type in cracks that is confirmed by our ultrasonic experiment herefore we believe that analysis of -anisotropy may get potential use for seismic exploration for example the analysis of versus offset (O) in seismic reflection data he value of estimated by means of the O analysis may serve as an indicator of the crack-fill fluid due to its link to the parameter / An estimate of / ( / < or / >) may provide an additional information for fracture-reservoir characterization (oksöz et al (979) Klimentos (995) Winkler (979) iwari and McMechan (003) and Batzle et al (005)) EG/an Antonio 007 Annual Meeting 5

5 EDED REFERECE ote: his reference list is a copy-edited version of the reference list submitted by the author Reference lists for the 007 EG echnical rogram Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web REFERECE Bakulin A Grechka and svankin 000 Estimation of fracture parameters from reflection seismic data art : H model due to a single fracture set: Geophysics Batzle M R Hofmann M rasad G Kumar L Duranti and H De-Hua 005 eismic attenuation: Observations and mechanisms: 75th Annual nternational Meeting EG Expanded Abstracts Best A 994 eismic attenuation anisotropy in reservoir sedimentary rocks: 64th Annual nternational Meeting EG Expanded Abstracts 8 85 Carcione J M 000 A model for seismic velocity and attenuation in petroleum source rocks: Geophysics Chichinina abinin and G Ronquillo-Jarillo 004 -wave attenuation anisotropy in fracture characterization: umerical modeling for reflection data: 74th Annual nternational Meeting EG Expanded Abstracts OA analysis as an instrument for fracture characterization: 75th Annual nternational Meeting EG Expanded Abstracts a OA analysis: -wave attenuation anisotropy for fracture characterization: Geophysics 7 no 3 C37 C48 Chichinina abinin G Ronquillo-Jarillo R Obolentseva 006b Azimuthal O analysis applied to oil and gas exploration: Russian Geology and Geophysics Gik L D and B A Bobrov 996 Experimental laboratory study of anisotropy for thin-layered media: Russian Geology and Geophysics Hosten B M Deschamps and B R ittmann 987 nhomogeneous wave generation and propagation in lossy anisotropic solids: Application to the characterization of viscoelastic composite materials: Journal of the Acoustical ociety of America Klimentos 995 Attenuation of - and -waves as a method of distinguishing gas and condensate from oil and water: Geophysics Macbeth C 999 Azimuthal variation in -wave signatures due to fluid flow: Geophysics Maultzsch M Chapman E Liu and X Y Li 005 Observation and modeling of anisotropic attenuation in data: 75th Annual nternational Meeting EG Expanded Abstracts 3 34 rasad M and A ur 003 elocity and attenuation anisotropy in reservoir rocks: 73rd Annual nternational Meeting EG Expanded Abstracts choenberg M and J Douma 988 Elastic wave propagation in media with parallel fractures and aligned cracks: Geophysical rospecting choenberg M and C M ayers 995 eismic anisotropy of fractured rock: Geophysics homsen L 986 Weak elastic anisotropy: Geophysics iwari U K and G A McMechan 003 Estimation of water/gas saturation and effective pressure from seismic velocities and quality factors as function of frequency: redictions of an empirical model: Journal of eismic Exploration oksöz M D H Jounston and A imur 979 Attenuation of seismic waves in dry and saturated rocks: Laboratory and measurements: Geophysics arela M asser M Chapman and E Liu 006 Anisotropic azimuthal attenuation as an indicator of fracture properties a case study on time-lapse walkaround data: 68th Annual Conference and Exhibition EAGE 46 asconcelos and E Jenner 005 Estimation of azimuthally varying attenuation from wide-azimuth -wave data: 75th Annual nternational Meeting EG Expanded Abstracts 3 6 Winkler K W 979 he effects of pore fluids and frictional sliding on seismic attenuation: hd thesis tanford University Yin H and A ur 99 tress-induced ultrasonic velocity and attenuation anisotropy of rocks: 6nd Annual nternational Meeting EG Expanded Abstracts Zhu Y and svankin 006 lane-wave propagation in attenuative transversely isotropic media: Geophysics 7 no 7 30 Zhu Y svankin Dewangan and K van Wijk 007 hysical modeling and analysis of -wave attenuation anisotropy in transversely isotropic media: Geophysics 7 no D D7 EG/an Antonio 007 Annual Meeting 53