AVO for one- and two-fracture set models

Transcription

1 GEOPHYSICS, VOL. 70, NO. 2 (MARCH-APRIL 2005); P. C1 C5, 7 FIGS., 3 TABLES / AVO for one- and two-fracture set models He Chen 1,RaymonL.Brown 2, and John P. Castagna 1 ABSTRACT A theoretical comparison is made of PP and PS angle dependent reflection coefficients at the top of two fractured-reservoir models using exact, general, anisotropic reflection coefficients. The two verticalfracture models are taken to have the same total crack density. The primary issue investigated is determination of the fracture orientation using azimuthal AVO analysis. The first model represents a single-fracture set and the second model has an additional fracture set oblique to the first set at an angle of 60. As expected, the PP-wave anisotropy is reduced when multiple fracture sets are present, making the determination of orientation more difficult than for the case of a singlefracture set. Long offsets are required for identification of dominant fracture orientations using PP-wave AVO. PS-wave AVO, however, is quite sensitive to fracture orientations, even at short offsets. For multiple-fracture sets, PS signals can potentially be used to determine orientations of the individual sets. INTRODUCTION The use of reflected P-wave and P-SV-wave amplitudeversus-offset analysis (AVO) can potentially aid in the characterization of fractured reservoirs (Thomsen, 1988). Cores and well logs offer methods of describing fractures at a very fine scale. The seismic method potentially offers a method of characterizing the reservoir at a larger scale that can be used for predicting reservoir properties. Typically, the estimation of fracture properties, especially those for multiple-fracture sets, requires multiple types of data (e.g., Shen et al., 2002; Grechka et al., 2000). A recent study by DeVault et al. (2002) indicates that S-waves have great potential application for fractured reservoirs. The utility of PS-waves is examined here for the particular problem of fracture-set orientation when multiplefracture sets are present. In this paper, the offset-dependent reflectivity for the top of a fractured reservoir is studied with a view toward identifying those approaches best suited for determining fracture-set orientations within the reservoir. We examine the azimuthal AVO variations of two fractured models using exact anisotropic reflection coefficients (Rokhlin et al., 1986). Model 1 is designed containing a single-fracture set, and model 2 consists of two-fracture sets. The singlefracture-set model exhibits a stronger azimuthal AVO variation. The results of the modeling study illustrate the potential problems and approaches that can be used in the interpretation of multiple-fracture sets. SYNTHETIC FRACTURED-RESERVOIR MODELS Two models of fractured reservoirs are set up for synthetic azimuthal AVO studies in this paper. The models studied are simple and limited to a constant fracture density so that the effects of fracture orientation could be studied. See the paper by Liu et al. (2000) for a discussion of multiple-fracture sets. The matrix material of the reservoirs is assumed to be limestone with 10% porosity, and the overlying seal layer is assumed to be shale. Both the incident shale and background (matrix) for the fractured reservoir layers are assumed to be isotropic. Only the presence of fractures contributes to the anisotropy of the models examined. Table 1 lists the petrophysical parameters for the isotropic portions of the models. All of these parameters are set within the range of the laboratory and empirical relationships between V p, V s,andρ described by Castagna et al. (1993) for the rocks considered. Model 1 is assumed to have one set of vertical fractures whose planes have an azimuth measured from north of 0.The X 2 -axis points north, and the X 1 -axis points east. A positive azimuth angle is measured toward the east from the X 2 -axis. This means that the normals to the first set of fractures are pointed parallel to the X 1 -axis (Figure 1b). Model 2 has two sets of fractures whose planes are at azimuths of 0 and 60 (Figure 1c). The crack density of the fracture set in model 1 is set equal to 0.1. For the purpose of comparison between models, the total crack density in model 2 is also set as 0.1, with the Manuscript received by the Editor August 25, 2002; revised manuscript received August 8, 2004; published online March 22, University of Oklahoma, Institute of Exploration and Development Geosciences, Norman, Oklahoma che@gcn.ou.edu; jcastagna@ou.edu. 2 Oklahoma Geological Survey, 100 E. Boyd Street, Norman, Oklahoma raybrown@ou.edu. c 2005 Society of Exploration Geophysicists. All rights reserved. C1

2 C2 Chen et al. crack density of each fracture set equal to In this way, the total crack density is the same for models 1 and 2, while their anisotropy differs. Table 2 lists the fracture parameters described above. The stiffness matrices (Table 3) are calculated assuming that the excess compliance caused by each fracture set can Table 1. Model matrix information. Reservoir matrix Overlying shale V p (m/s) V s (m/s) Density (g/cm 3 ) Porosity 10% simply be added to find the change in compliance caused by the presence of both fracture sets. This assumption neglects any interaction between the fractures. As a first-order approximation, we use the scalar cracks described by Schoenberg and Sayers (1995) to estimate the compliance for each fracture set. Using scalar cracks simplifies the stiffness tensor for the models, but it is not expected to change the major conclusions for the paper. The reflection-coefficient calculations are made using the method described by Chen (2000) and Rokhlin et al. (1986). First, the horizontal slowness of the incident wave is determined. Next, this horizontal slowness is used to set up two sixth-order polynomials that can be solved to find the reflected and refracted slownesses for the two media across the reflecting boundary. The eigenvectors for each of the reflected and refracted waves are determined next. Finally, the boundary conditions are set up, and the reflection and refraction coefficients are determined. According to Hudson (1980, 1981), one vertical set of fractures can introduce transverse isotropy with a horizontal symmetry axis (HTI), while multiple sets of fractures can cause arbitrary anisotropy. An example of what happens with multiple fracture sets can be examined in two simple models discussed below. The reader is referred to the inversion work by Bakulin et al. (2002) for a study of two orthogonal-fracture sets. An incident P-wave is assumed for each model. The vertical planes of incidence for the P-waves will be described by the azimuths of the planes. These planes will all contain the X 3 -axis, and the azimuth is measured positively in a clockwise movement from north (Figure 1a) (the same direction as the X 2 -axis). The three expected reflections are a quasi-p (PP)- wave, a quasi-in-plane S (PSI)-wave and a quasi-out-of-plane S-wave. The incident phase and/or ray (group) angle (both are the same for incident medium, which is isotropic) range for the study varies from 0 to 45. This angle is measured from the X 3 -axis in the plane of incidence. The variation of reflection amplitudes with angle of incidence is observed at four different azimuth directions: 0, 30, 60,and 90, respectively. In other words, the plane of incidence is varied, although the fracture geometry is the same; i.e., the stiffness tensor remains the same while the azimuthal angle changes. AZIMUTHAL INTERPRETATION OF AVO FROM TOP OF RESERVOIR The first wave mode to be considered is a downgoing P-wave reflected from the reservoir as a P-wave (PP). Figures 2 and 3 show the exact azimuthal PP reflection amplitudes from models 1 (single-fracture set) and 2 (two-fracture Table 2. Model fracture information. Figure 1. (a) Azimuthal direction of incident plane, described by angle φ. (b)x 1 X 2 -plane sketch of fracture orientation in model 1. (c) X 1 X 2 -plane sketch of fracture orientations in model 2. Crack density Azimuthal angle Dip angle Model 1 Fracture set no Model 2 Fracture set no Fracture set no

3 Fractured AVO C3 sets), respectively. First, there are only slight differences on the normal-incidence PP reflection coefficients, showing that the total crack density may be the primary factor related to fractures that influence the zero-offset PP reflections. Secondly, the azimuthal variations of the PP reflection can only be clearly observed within each curve family when the incidence angles exceed 25. This is why long offsets are expected to be required to detect vertical-fracture orientations with P-waves. Note that model 1 (Figure 2), with a single fracture set, shows more azimuthal AVO than model 2 (Figure 3). Note also that, in Figure 3, the azimuth 90 curve is identical to the azimuth 30 curve. For these two situations, the incidence plane happens to be perpendicular to one of the two fracture sets. As a result, the P-wave sees the same reflection response at these azimuths, because the two fracture sets have the same crack density. The next reflected phase to be considered is the incident P-wave, which reflects from the reservoir as an S-wave (PS). The polarization of S-waves for anisotropic media can be expressed in many ways. To simplify the description, we describe Table 3. Stiffness matrix information. C ij (GPa) Isotropic background: Single-fracture set (model 1): Two-fracture sets (model 2): Figure 2. Azimuthal P-wave reflection coefficients for model 1. Figure 3. Azimuthal P-wave reflection coefficients for model 2.

4 C4 Chen et al. the S-wave polarization as in-plane (near-sv) and out-ofplane (near-sh). In this way, the reader gets an intuitive feeling for the polarization without actually plotting the polarization or having to keep track of fracture alignments. Figures 4 and 5 show the out-of-plane shear reflection (or near-sh reflection) amplitudes from models 1 and 2, respectively. This mode is unique to the anisotropic circumstances and is caused by coupling between the in-plane (near-sv) and out-of-plane (near-sh) components of motion at the interface. It can be seen that: 1) The azimuthal variation of the converted PS reflections is much more sensitive to fractures than PP reflections (Figures 2 and 3). Even at small incidence angles, Figures 4 and 5 show a distinct azimuthal AVO response for both models 1 and 2. 2) The normal incidence reflections are always zero for all quasi-ps-waves, because all the fracture sets are vertical. There is no converted shear wave when the P-wave is normally incident upon the reflection surface for the model assumed. 3) In Figure 4, for model 1, the azimuth 90 and 0 AVO curves are zero. With only one set of vertical fractures at azimuth 90, the reservoir model is an HTI medium with a single vertical-symmetry plane perpendicular to the fractures (Tsvankin, 1995, 1996). One of the symmetry planes is the isotropic plane at azimuth 0 (X 2 X 3 plane) and the other is an effective VTI plane at azimuth 90 direction (X 1 X 3 plane) (Tsvankin, 1995, 1996). These models show that the converted shear-wave reflections can be used to find the orientation of the fracture set if only one fracture set exists. 4) In Figure 5, for model 2, a zero-reflection coefficient curve is observed at an azimuth of 60, which equally splits the two fracture systems. The two reflection-coefficient curves for azimuths 90 and 30 show up as mirror images of each other reflected about the azimuth 60 curve. These observations indicate that the azimuth 60 planeactsasa symmetry plane, but that it is not parallel or perpendicular to any fracture sets. In this two-fracture-set model, the 60 azimuth plane can be misinterpreted as an apparent effective orientation of one fracture set. Figure 4. Azimuthal P-SH reflection coefficients for model 1. Figures 6 and 7 show the quasi-in-plane shear reflections (or near-sv) for models 1 and 2, respectively. Once again, as in the out-of-plane S-wave case, the in-plane S-wave reflection curves show strong azimuthal variations for fracture models under small incidence-angle conditions. Even more importantly, the azimuthal AVO variations are larger than those of out-of-plane S-wave curves (compare to Figures 4 and 5). Another observation is that the azimuthal AVO from the singlefracture-set model (model 1) is larger than those of the twofracture-set model (model 2). Figure 5. Azimuthal P-SH reflection coefficients for model 2. Figure 6. Azimuthal P-SV coefficients for model 1.

5 Fractured AVO C5 If the ideal fracture sets contribute equally to fracture permeability, then one of the symmetry planes identified by PS reflections is in the direction of maximum horizontal permeability, while the other represents a minimum direction of horizontal permeability. If there is no PS reflection at normal incidence, the existing fracture sets can be assumed to be normal to the reflection boundary. ACKNOWLEDGMENTS H. Chen received financial support from the OU Integrated Reservoir Characterization Consortium sponsors. Appreciation is expressed to Bill Lamb for his discussions of the topic. H. Chen and R. Brown acknowledge the support of this work by the U.S. Department of Energy through project DE-AC26-99BC Figure 7. Azimuthal P-SV coefficients for model 2. CONCLUSIONS Exact reflection-coefficient versus angle-of-incidence curves for P- and PS-waves were calculated for models with one or two sets of fractures. We find that: 1) The azimuthal variation of converted PS reflections is more sensitive to fractures than PP reflections. Even at small angles of incidence, the PS reflection coefficients show distinct azimuthal AVO variations. The azimuthal variations of the PP reflection caused by fractures can be clearly observed only when the incidence angle is large (greater than 25 for the models in this synthetic study). 2) For the same total crack density, a model containing a single-fracture set exhibits the largest variation of azimuthal AVO. Multiple-fracture sets tend to weaken the azimuthal anisotropic effects (especially for PP-waves). 3) With large-offset data, the azimuthal variation in P-wave reflections may indicate the existence of fracture zones. For larger relative-amplitude variations with azimuth, there is a greater possibility for a single-fracture set or a dominant fracture orientation. 4) The out-of-plane/in-plane PS-wave azimuthal AVOs can be used, when they can be observed, to identify symmetry planes as well as the orientation of individual fracture sets. This offers a powerful tool for understanding the fracture makeup of a reservoir. REFERENCES Bakulin, A., V. Grechka, and I. Tsvankin, 2000, Estimation of fracture parameters from reflection seismic data, Part III: Fractured models with monoclinic symmetry: Geophysics, 65, , 2002, Seismic inversion for the parameters of two orthogonal fracture sets in a VTI background medium: Geophysics, 67, Castagna, J. P., M. L. Batzle, J. E. Daiser, K. M. Tubman, and M. L. Burnett, 1993, Shearwave velocity control, in J. P. Castagna and G. E. Backus, eds., Offset-dependent reflectivity: Theory and practice of AVO analysis: SEG. Chen, H., 2000, Anisotropic effects upon amplitude-vs-offset response in realistic earth models: Ph.D. dissertation, University of Oklahoma. DeVault, B., T. L. Davis, I. Tsvankin, R. Verm, and F. Hilterman, 2002, Multicomponent AVO analysis, Vacuum Field, New Mexico: Geophysics, 67, Grechka, V., P. Contreras, and I. Tsvankin, 2000, Inversion of normal moveout for monoclinic media: Geophysical Prospecting, 48, Hudson, J. A., 1980, Overall properties of a cracked solid: Mathematical Proceedings of the Cambridge Philosophical Society, 88, , 1981, Wave speeds and attenuation of elastic waves in material containing cracks: Geophysical Journal of the Royal Astronomical Society, 64, Liu, E., J. A. Hudson, and T. Pointer, 2000, Equivalent medium representation of fractured rock: Journal of Geophysical Research, 105, Rokhlin, S. I., T. K. Bolland, and L. Adler, 1986, Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media: Journal of the Acoustic Society of America, 79, no. 4, Schoenberg, M., and C. Sayers, 1995, Seismic anisotropy of fractured rock: Geophysics, 60, Shen, F., X. Zhu, and M. N. Toksoz, 2002, Effects of fractures on NMO velocities and P-wave azimuthal AVO response: Geophysics, 67, Thomsen, L., 1988, Reflection seismology over azimuthally anisotropic media: Geophysics, 53, Tsvankin, I., 1995, Body-wave radiation patterns and AVO in transversely isotropic media: Geophysics, 60, , 1996, P-wave signatures and notation for transversely isotropic media: An overview: Geophysics, 61,