1 University of Edinburgh, 2 British Geological Survey, 3 China University of Petroleum

Transcription

1 Estimation of fluid mobility from frequency deendent azimuthal AVO a synthetic model study Yingrui Ren 1*, Xiaoyang Wu 2, Mark Chaman 1 and Xiangyang Li 2,3 1 University of Edinburgh, 2 British Geological Survey, 3 China University of Petroleum Summary Azimuthal amlitude-versus-offset (AVOZ) data can contain abundant information on fracture roerties, lithology and fluid saturation, but rocedures for interretation in terms of such roerties remain relatively oorly develoed, articularly considering the frequency deendent content. In our numerical model, we develoed recently develoed rock hysics model based inverse schemes with a articular emhasis on accounting for the frequency-deendence of anisotroy, which is believed to be imortant in fractured reservoirs. Frequency-deendent anisotroy is exected to be influenced by fluid mobility, and determining this arameter from seismic data would be advantageous. In this aer we build a frequency deendent anisotroic synthetic model and show the variations of AVO resonse due to frequency effects. We resent a new method to analyse the synthetic waveform data, and demonstrate that it is caable of detecting variations in fluid mobility. Further testing and alication to field data are lanned.

2 Introduction Azimuthal variations of AVO data (AVOZ) have been widely used to detect fractures for some time. While the link to fractures is clear, additional arameters (orosity, fluid content and lithology) also are known theoretically to have an imortant influence. Qualitative interretation of AVOZ, by contrast, tyically relies on simle techniques (ellise fitting of attributes), justified by simlified anisotroic rock hysics models. There is an indeed need to involve more detailed rock hysics models in the quantitative interretation of AVOZ data. Motivated by the work of Reide et al. (2005), Varela et al. (2009) introduced a rock hysics model based method for the estimation of fracture density from AVOZ. Maultzsch et al. (2003) demonstrated a number of examles of frequency-deendent anisotroy in fractured reservoirs which lead us to target other roerties. Ren et al. (2013) extend the Varela et al. (2009) method to the case of fluid mobility which is considered to lay an imortant role in controlling frequency-deendent roerties (Batzle et al., 2006) and whose determination would clearly be very imortant. In this aer, we build a synthetic model within a HTI layer derived by Chaman (2003) frequency deendent rock hysics model. Sectral decomosition and balancing technique are alied to obtain frequency content of amlitudes. We use SVD to analyze the amlitudes. The frequency deendent fluid mobility of HTI layer () can be quantitatively interreted. We argue that in certain cases it may be ossible to obtain fluid mobility information from AVOZ data. Building synthetic model Figure 1a shows the layout and geometry of the model (in the XZ lane). From to to bottom there are four layers, which are two isotroic, anisotroic and isotroic in order. The P- and S-wave velocities, density and thickness of each layer are embedded within relating layers. The material of the anisotroic layer is a set of vertical fractures with fracture density of 0.1. In this study, I will analyse the reflection from 2 nd interface between the isotroic layer 2 and the underlying HTI layer 3. The seismic amlitude of 2 nd interface is calculated by using Chaman (2003) fluid induced frequency deendent anisotroic rock hysics model. In this model, a relaxation timescale arameter τ which deends on fluid viscosity and ermeability was introduced to control the frequency range over which the attenuation and disersion occurs. The focus on this aer is determining τ from waveform data. Figure 1b shows the seismic rofile containing only Z-comonent of this synthetic model. The 1 st and 2 nd P-wave reflections which we are interested are highlighted. The S-wave, PS-wave and some noise can be removed during rocessing. NMO correction is alied on these two reflections and the result is illustrated in Figure 2. The waveform data can be created with a set of τ and azimuth angles. However, to obtain frequency deendent reflection coefficients, Sectral decomosition technique is desired. Sectral decomosition and balancing Sectral decomosition is a technique for deriving the frequency content of a signal. Fourier transform can give the overall frequency behavior of a signal, however it is inadequate for analyzing a non-stationary signal (Seismic signals are non-stationary due to absortion and attenuation of energy). Cohen (1995) introduced short-time Fourier transform (STFT) by taking short segments of the signal and then erforming the Fourier transform on the windowed data to obtain local frequency information. The signal, f(t), can be transformed by a time-shifted window function, φ(t), as STFT(ω, t 0 ) = f(t)φ (t t 0 )e iωt dt Where t 0 is the translation time, ω is the frequency. STFT is widely used in seismic interretation. In Figure 3, we can see that the sectral amlitudes of the first reflection with different frequency domain have significant difference which is not suosed to haen when it is elastic, because the sectral amlitudes have an overrint from the source wavelet (Partyka et al., 1999). Wilson et al. (2009) derived a method to remove the effect of the source wavelet by a weight function, w(f), making the amlitudes at different frequencies comarable. When working with synthetic data, the to two layers are elastic so that the 1 st reflection is elastic. These elastic reflections are used to (1)

3 derive weights that automatically balance deeer sectral amlitudes. Note that, considering the trace deendent NMO stretch, I calculated the weights trace by trace. Wilson s equation can be derived as B(t, n, f) = S(t, n, f)w(n, f) (2) Balanced sectral amlitudes are dislayed in Figure 4, in which we can see the similar resonse of the 1 st interface but difference of the 2 nd reflection by frequency. Singular value decomosition (SVD) In our synthetic model, we study the lane wave amlitude at second reflection. The lower layer is assumed to be anisotroic and to have frequency deendent roerties. The balanced sectral amlitude, considering as reflection coefficient, can be constructed into a matrix varying with a discrete number of incidence angles (θ), azimuths (φ), relaxation timescale arameters (τ) and frequencies (f). Alternatively, considering a single frequency we can write: Rθ τ φ Rθ θ τ φ Rθ θ τ φ R q 1 θ1τ qφ Rθ θ2τ 1φ R= R θ τ φ Rθ τ φ (3) Rθ τ φ Rθnτ φ R θnτ φ Rθnτ φ R θnτ φ R n q 1 θnτ qφ Singular value decomosition (SVD) can be alied to this matrix in the usual way giving a reresentation: R = FDV T = FW (4) Alying SVD and multilying the decomosed matrices allows us to obtain the aroximation to the reflection coefficient as: R(θ, φ, τ) C 1 (φ, τ)f 1 (θ) + C 2 (φ, τ)f 2 (θ) + (5) where the basis functions F i (θ) are given by the columns of matrix F, the coefficients C i (ω, τ) are given by the columns of the weight matrix W, size of which is corresonding to the singular value of matrix D. Usually we only need to consider two or three terms of aroximation in ractice with small error (Riede et al., 2005). Results In synthetic model we find that the reflection coefficient is well aroximated with the use of only the 1st order basis function. The reflection coefficient can therefore be aroximated from Equation 5 as: R(θ, φ, τ) = C 1 (φ, τ)f 1 (θ) (6) The coefficients C i (ω, τ) variation with φ and τ can be resented in Figure 5. In order to obtain the aroximation attributes of the coefficients C i (ω, τ), a cosine fitting is alied on these datasets (Figure 5), which is assumed to follow the equation: y = C + αcos(φ) + βcos(2φ) + γcos(3φ) (7) There are four attributes C, α, β and γ, in which according to this model, all attributes deend on frequency. The second attribute α has the most direct deendence on τ. We also notice that, comared with the value of C and α, β and γ can be neglect. We can cross-lot C and α resectively for each frequency, and aly olynomial fitting method to the result (Figure 6). Cross-lotting these attributes for each frequency gives rise to a temlate which allows us to see clearly the effect of changing values of the frequency or τ (Figure 6). Conclusions This aer has carried out a synthetic model in which we found that fluid-mobility does have an imact on azimuthal AVO, articularly if we consider variations with frequency. To obtain aroriate seismic amlitudes, sectral decomosition and sectral balancing technique are alied. To analyze the amlitudes variations, link to all deendent arameters, we alied our numerical

4 method. From the synthetic model study, we have successfully validated we can derived a temlate showing the variation of fluid mobility from waveform data. Further testing and alication on field data will be carried out. References Batzle, M.L., Han, D.-H. and Hofmann, R. [2006] Fluid mobility and frequency-deendent seismic velocity, direct measurements. Geohysics, 71, N1-N9. Chaman, M., [2003] Frequency-deendent anisotroy due to meso-scale fractures in the resence of equant orosity. Geohysical Prosecting, 51, Cohen, L., [1995] Time Frequency Analysis. Prentice Hall Inc., New York, USA. Maultzsch, S., Chaman, M., Liu, E. and Li, X.-Y. [2003] Modelling frequency-deendent seismic anisotroy in fluid-saturated rock with aligned fractures: imlication of fracture size estimation from anisotroic measurements. Geohysical Prosecting, 51(5), Partyka, G., Gridley, J. and Loez, J., [1999] Interretational alications of sectral decomosition in reservoir characterization. The Leading Edge, 18, Ren, Y., Chaman, M., Wu, X., Guo, Z., Li, X.-Y. [2013] Estimation of fluid mobility from frequency deendent azimuthal AVO-A modelling study. 83rd SEG Annual Meeting, Extended Abstracts, Riede, M., Causse, E. van Wijngaarden, A. J., Buland, A., Dutzer, J. F. and Fillon, R. [2005] Otimized AVO analysis by using an otimal linear aroximation. 75th SEG Annual Meeting, Extended Abstracts, Wilson, A., Chaman, M. and Li, X.-Y. [2009] Frequency-deendent AVO inversion. 79th SEG Annual Meeting, Extended Abstracts, Varela, I., Maultzsch, S., Chaman, M. and Li, X.-Y. [2009] Fracture density inversion from a hysical geological model using azimuthal AVO with otimal basis functions. 79th SEG Annual Meeting, Extended Abstracts, L1: Isotroic 0.5km ρ = 2.35g/cm 3, V = 3.3km/s, V s = 1.1km/s 1st L2: Isotroic 0.5km ρ = 2.4g/cm 3, V = 3.6km/s, V s = 1.8km/s 2nd L3: HTI 0.5km ρ = 2.4g/cm 3, fd = 0.1, k f = 0.4 3rd L4: Isotroic Halfsace ρ = 2.49g/cm 3, V = 4.2km/s, V s = 2.1km/s st nd 1 reflection - P-wave 2 reflection - P-wave Figure 1 a. Four layers synthetic model. The rock roerties are embedded within the geometry. b. Seismic rofile of this model. The 1 st and 2 nd P-wave reflections are highlighted in the figure. Figure 2 NMO corrections of the to two reflections when τ = 2e 4. a. P-wave roagates erendicular to the direction of fractures (φ = 0 o ). b. P-wave roagates arallel to the direction of fractures (φ = 90 o ). For the 2 nd interface, amlitude at far offsets of φ = 0 o are larger than that of φ = 90 o illustrate more significant anisotroy.

5 Figure 3 Sectral decomosition slices of the to two reflections when τ = 2e 4, φ = 0 o. a and b are sectral decomosition; c and d are sectral balancing. a. 10Hz slice. b. 50Hz slice. There is significant difference of the 1 st reflection between different frequency which is not suosed to be. These two slices are incomarable unless rocessed with sectral balancing. Figure 4 Sectral balanced amlitude from sectral decomosition (Figure 3). a. 10Hz slice. b. 50Hz slice. The 1 st reflections of difference frequency are similar but significant difference at 2 nd reflections due to fluid induced anisotroy (Chaman, 2003). τ=18e-4 τ=14e-4 τ=10e-4 τ=6e-4 τ=2e-4 f=50hz f=40hz f=10hz f=20hz f=30hz Figure 5 Weights variation with azimuth angle and τ. * shows data calculated from study model. Solid line is cosine fitting curve. Color relates to different τ. Figure 6 Frequency deendent fluid roerty τ temlate. The sots are derived from the cross-lot of two attributes. The colored solid lines illustrate frequency variation. The colored dash lines refers to different τ.