TY - JOUR
AU - Guangzhi,, Zhang
AB - Abstract Previous work has demonstrated that seismic velocity dispersion is often related to a hydrocarbon-saturated reservoir with a high value of attenuation. The velocity dispersion properties can be used as new hydrocarbon indicators if they can be estimated quantitatively from seismic data. In this context, based on the assumption that the reflection coefficient of the interface between dispersive media varies with frequency, we propose an approximation of the reflection coefficient which involves the dispersion-dependent attributes indicating the level and gradient of P-wave velocity dispersion. We develop a new generalization of an AVO inversion scheme to extract the dispersion-dependent attributes from multi-frequency prestack seismic data obtained by the Morlet wavelet decomposition method. The method test and real application show that the dispersion-dependent attributes have the potential to be useful in the discrimination of hydrocarbon accumulation. However, the hydrocarbon detection quality of the dispersion-dependent attributes can be degraded by the inverse Q-filtering procedure which compensates the high-frequency amplitudes. dispersion, attenuation, prestack inversion, hydrocarbon detection 1 Introduction Since the 1970s, the amplitude-dependent technology of reservoir prediction and hydrocarbon detection has been the focus area for oil exploration and production, such as the poststack-based ‘bright spot’ technology, prestack-based amplitude-variation-with-offset analysis technology and so on (Smith and Gidlow 1987, Hampson 1991, Russell et al2003). These technologies have made great contribution to the early oil and gas exploration. However, with the exploration of lithologic reservoirs and deepwater reservoirs, the amplitude-dependent only technology cannot meet the demand for more accurate seismic prediction of fluid-saturated properties and distribution in the reservoir. Therefore, new techniques, which can highlight prospects missed by conventional methods, are urgent for reservoir prediction and hydrocarbon detection. In the last 20 years, with the help of spectral decomposition, it has been found that frequency-dependent anomalies can be successfully used for the accurate delineation of the reservoir even in cases of a deep reservoir (Bath 1974, Mitchell et al1996, Quan and Harrisy 1997, Goloshubin and Korneev 2000, Goloshubin et al2002, Lichman and Goloshubin 2003, Castagna et al2003, Korneev et al2004, Holzner et al2005). There are numerous laboratory and field cases where different reservoir types have different frequency-dependent characteristics and the low-frequency component can relate to the hydrocarbon reservoir directly. Nevertheless, the mechanism of frequency anomaly is still ambiguous; therefore, it is uncertain whether these frequency-dependent abnormal observations are induced by the true hydrocarbon reservoir or man-made processing (Ebrom 2004). Although the mechanisms of reservoir-related frequency anomaly are uncertain, an ample amount of evidence suggests that the wave attenuation can indeed cause frequency anomaly when a seismic wave travels through the hydrocarbon-saturated reservoir. Therefore, the quantitative attributes related to the attenuation properties can be used as hydrocarbon indicators, such as quality factor (Q). Hydrocarbon-saturated zones associated with anomalously strong attenuation often show low values of quality factor (Castagna et al1995, Klimentos 1995, Dasgupta and Clark 1998, Dasios et al2001, Maultzsch et al2003, Rapoport et al2004). However, the low Q zones can also be associated with fracturing (Worthington and Hudson 2000). In view of the Kramers–Kronig relations and laboratory results, we know that strong attenuation of the seismic wave can be associated with significant velocity dispersion in a seismic frequency band. Similar to the hydrocarbon indication ability of attenuation properties, the level of dispersion can also be quantitatively represented as a hydrocarbon indicator (Batzle et al2001, Chapman et al2006). Some work has been carried out on the estimation of dispersion attribute, but it shows that the robust estimation method has proven elusive. Some authors estimate the P-wave dispersion through the velocity analysis from prestack seismic gather (Cobos and Han 2006). Some authors focus the effect of dispersion on the reflection coefficients in a dispersive medium (Cooper 1967, Krebes 1984, Nechtschein and Hron 1997, Ursin and Stovas 2002, Sidler and Carcione 2007). Considering the velocity dispersion, Ren et al (2009) divide the variation of normal incidence magnitude into three general classes, which provides insight into frequency-dependent seismic interpretation. In general, the research works mentioned above are mainly theoretical modelling and instruction, which are complicated and limit the practical application in field data. Wilson et al (2009) propose a method called frequency-dependent AVO inversion from the synthetic data test; it shows that dispersion-dependent properties can be estimated which may be used as hydrocarbon indicators. In this study, following the Shuey approximation (Shuey 1985), we propose a reflection coefficient approximation equation which includes two dispersion-dependent attributes representing the level of P-wave dispersion and the gradient of dispersion level variation with offsets. With the help of Morlet wavelet decomposition (Mallat 1999), the two dispersion-dependent attributes can be estimated through the multiple-frequency prestack seismic inversion method. The method tests and real field example illustrate the applicability of the dispersion-dependent attributes inversion method. We show the advantage of dispersion-dependent attributes for the hydrocarbon accumulation detection through the comparison with other frequency-dependent direct hydrocarbon indicators (DHI), such as a low-frequency shadow. We also conduct an investigation to test the hydrocarbon detection quality of the dispersion-dependent attributes, even after the compensation of high-frequency information. 2 Dispersion-dependent attributes inversion 2.1 Equation derivation Shuey (1985) rearranged the Aki–Richard P–P reflection coefficient approximation equation (Aki and Richards 1980) and first proposed the concept of AVO intercept and AVO gradient, which are useful in conventional AVO analysis. In the case when incidence angle is less than 30°, the Shuey approximation equation can be expressed in two terms as follows: 1 where RPP is the P–P reflection coefficient, θ is the average of the incident and refracted angles, P is the P-wave normal incidence reflection coefficient, called AVO intercept; G is related to the Poisson ratio, called the AVO gradient. We can rearrange the intercept term of equation (1) and obtain a new approximation expression: 2 where is the relative P-wave velocity contrast and is the relative density contrast. In equation (2), the velocity is P-wave group velocity (velocity of wave envelope). However, when the seismic wave passes through the layers, attenuation makes the velocity (phase velocity) change from frequency to frequency due to the velocity–frequency or modulus–frequency dispersion. Following the arguments of Chapman et al (2005), we can assume that the reflectivity varies with frequency due to the difference of the elastic properties on each side of the interface, and the changes between the interfaces are mainly due to P-wave phase velocity varying with frequency, not the density. Using a similar way of derivation proposed by Wilson et al (2009), the Shuey approximation equation can be extended to be frequency dependent as a function of angle and frequency, as follows: 3 where θ is the average of the incident and refracted angles and f is the frequency. If we make the first-order Taylor expansion of the above equation with frequency, we can obtain the equation 4 With the assumption that f0 is the dominant frequency of the seismic frequency band, the equation can be simplified as 5 With and ⁠, we can obtain the final reflection coefficient equation including dispersion-dependent attributes as follows: 6 Here, represents the level of P-wave velocity dispersion and, similar to the AVO gradient, DG can be used as the gradient which represents the dispersion level variation with offset. Both the parameters and DG are dispersion-dependent attributes which can be used as hydrocarbon indicators. 2.2 Inversion methodology Multi-frequency seismic amplitude information is needed in the dispersion-dependent inversion, which is different from frequency-dependent AVO inversion proposed by Wilson et al (2009). The data used in the method here are amplitude information instead of balanced spectral information. Because the Morlet wavelet can properly represent the energy absorption and phase distortion of real seismic wavelets during the propagation in the porous media, we employ the Morlet wavelet transform to decompose the original seismic gather into multi-frequency volumes (Mallat 1999). With the help of seismic time–frequency spectral analysis, we choose suitable scales of the real Morlet wavelet and realize the decomposition calculation. After the scale-frequency transform (Sinha et al2005, 2009), we can obtain the multi-frequency seismic amplitude information which is used to invert the dispersion-dependent attributes. In the construction of the inversion equation, we first rearrange equation (6) and obtain the equation 7 where ΔR(θ, f) = RPP(θ, f) - RPP(θ, f0). We consider a situation when there are two offsets (indicated by incidence angle θ1 and θ2), two depth samples (indicated by subscripts 1 and 2) and two frequencies (f1 and f2) to simplify the inversion problem. Equation (7) can be expressed by the matrix 8 where represent the forward operator of the ith sample in the offset of θi. Similar to the matrix construction above, when there are m offsets, n samples and l frequencies, the forward model matrix can be expressed by the blocky matrix 9 where ΔRiii  (i = 1, 2, …, l; ii = 1, 2, …, m) represent the column vector of the ith offset, fii frequency data, which consists of n samples, ΔFi (i = 1, 2, …, l) is the diagonal matrix of difference between frequency fi and f0, Aiii (i = 1, 2, …, l; ii = 1, 2, …, m) is the diagonal matrix composed of the forward coefficient of the ith offset and frequency fii; and DG are the dispersion-dependent attributes column vectors which represent the level of P-wave dispersion and the gradient of the dispersion level with offset, respectively. Based on the linear nature of wavelet transform, the multi-frequency wavelet matrix can be constructed using the basic wavelet and original wavelet. Put the multi-frequency wavelet matrix into the inversion process, we can obtain the equation 10 where Diii (i = 1, 2, …, l; ii = 1, 2, …, m) is the column vector of the ith offset, the difference data between fi andf0; Wi (i = 1, 2, …, l) is the rebuilt wavelet matrix of frequency fi. It should be noted that the rebuilt wavelets of different frequencies are different. Set up vectors D and G as below: 11 Then we can obtain the equation as follows: 12 We find the least-squares solution of equation (12), the dispersion-dependent attributes and DG of each sample can be estimated as 13 3 Methodology test 3.1 1D methodology test We use one CMP gather of real data to verify the feasibility of this inversion method and test the ability of dispersion-dependent attributes to discriminate different pore-fluid types. According to the interpretation results of nearby drilling well, we know that there are two reservoirs in the time gate 2.47–2.60 s (as shown in figure 1, where the blocky well is the interpretation result, green represents gas sand, red represents oil sand and white represents shale). We make the time–frequency analysis of a seismic trace to know the dominant frequency band of the seismic data, and make the dispersion-dependent inversion using five multi-frequency bands data (10, 15, 20, 30 and 40 Hz) to estimate the dispersion-dependent attributes which represent the level of P-wave dispersion and the gradient of the dispersion level variation with offset. Figures 1(a)–(d) display the band-pass SP log, P-velocity log and inverted dispersion-dependent attributes and DG, respectively. Figures 1(a) and (b) reveal that the SP log can discriminate the different reservoir types, while P-wave velocity cannot. As shown in the red ellipse, both these two dispersion-dependent attributes show significant anomalies at the interfaces of the hydrocarbon reservoir, which are expected to be caused by the strong attenuation and significant velocity dispersion in the hydrocarbon deposits. Due to the significant variation of the P-wave velocity contrast with frequency in the interfaces of hydrocarbon deposits, the level of P-wave dispersion can be used to indicate the hydrocarbon anomalies quantitatively and the gradient of the dispersion level with the offset can also be used as the hydrocarbon indicator with the increase of the incidence angle and travelling path. Figure 1 Open in new tabDownload slide Comparison of the band-pass SP log, P-velocity log and dispersion-dependent attributes DVp and DG. (a) The curve of SP well log; (b) curve of P-wave velocity; (c) curve of normalized dispersion-dependent attributes DVp; (d) curve of normalized dispersion-dependent attributes DG (the red ellipses indicate the top and base interfaces of the hydrocarbon-bearing reservoir). Figure 1 Open in new tabDownload slide Comparison of the band-pass SP log, P-velocity log and dispersion-dependent attributes DVp and DG. (a) The curve of SP well log; (b) curve of P-wave velocity; (c) curve of normalized dispersion-dependent attributes DVp; (d) curve of normalized dispersion-dependent attributes DG (the red ellipses indicate the top and base interfaces of the hydrocarbon-bearing reservoir). As shown in figure 1(b), the P-wave velocity of the reservoir increases with depth, which makes the relative contrast of P-wave velocity all positive in the interfaces. However, the velocity increases with frequency caused by attenuation and dispersion, which makes a positive anomaly in the top interfaces of the hydrocarbon-saturated layer and a negative anomaly in the bottom interfaces. It is consistent with the fact that the relative P-wave velocity increases with frequency in the top interface, while decreases with frequency in the bottom interface. And due to the increase in the incidence angle and travelling path, the energy attenuation makes the frequency band of the seismic trace narrower and the level of velocity dispersion weaker, which conduct negative anomalies of DG in the interfaces of the hydrocarbon reservoir, as shown in figure 1(c). And we can see that the absolute value of dispersion-dependent attribute of the gas reservoir is higher than the oil reservoir, which is consistent with some literature that the attenuation of the gas reservoir is stronger than that of the oil reservoir. The real seismic data test shows that the dispersion-dependent attributes can be estimated from the dispersion-dependent inversion method, which can be used as hydrocarbon indicators for a strong attenuation hydrocarbon reservoir such as the gas reservoir. 3.2 2D methodology test In order to test the validation and practicability of the dispersion-dependent inversion method further, we make the inversion of the 2D test data similar to the real application situation. We use the 2D prestack test gather from Hampson–Russell software; we choose 100 CMP including 8 traces per CMP and the offset is from 70 to 560 m. Figure 2 is the 2D test gather, and the black circle indicates the location of a known gas reservoir which is the typical ‘bright spot’ reservoir. After obtaining the multi-frequency band seismic data, we estimate the dispersion-dependent attributes using the inversion method above. Figures 3(a) and (b) display the normalized DVp and DG attribute section, respectively, and the inserted well log is the P-wave velocity log. From the inverted dispersion-dependent attributes, we can see that both DVp and DG attributes show anomalies in the interfaces of the gas reservoir, which verifies the hydrocarbon detection potential of the dispersion-dependent attributes. Figure 2 Open in new tabDownload slide Test prestack gather from Hampson-Russell software (the black circle indicates the gas reservoir). Figure 2 Open in new tabDownload slide Test prestack gather from Hampson-Russell software (the black circle indicates the gas reservoir). Figure 3 Open in new tabDownload slide Inverted dispersion-dependent attributes: (a) DVp and (b) DG (the red circle indicates the gas reservoir). Figure 3 Open in new tabDownload slide Inverted dispersion-dependent attributes: (a) DVp and (b) DG (the red circle indicates the gas reservoir). 4 Application We apply the dispersion-dependent inversion approach to discriminate the hydrocarbon accumulation in a real seismic data example. We know where the target reservoir is and the target reservoir is delta front sheet sand including two gas sand layers. The amplitude of the target overlying gas sand is relatively weak, which limits the reservoir quality of the conventional AVO attributes. Figure 4 is a gradient attribute section estimated from AVO analysis. The inserted curve is the band-pass resistivity log and the anomalously high value indicates the two gas reservoirs (red circles) between 2.55 and 2.65 s in time. We can see that the discrimination quality and resolution is very poor in the hydrocarbon accumulation. What we expect to see here is the hydrocarbon detection ability of the dispersion-dependent attributes in the location of the gas reservoir. And considering the complicated mechanism causing the velocity dispersion, we try to investigate whether the dispersion-dependent attributes still work if the inversion method is applied on the Q-compensated prestack seismic data. Figure 4 Open in new tabDownload slide AVO gradient section (the red circle indicates the gas reservoir). Figure 4 Open in new tabDownload slide AVO gradient section (the red circle indicates the gas reservoir). After prestack data conditioning process, we inverse-Q filter the prestack seismic data. The poststack seismic sections without and with Q-compensation are shown in figures 5(a) and (b), respectively. As pointed out by Wang (2002, 2006), the inverse-Q filtering compensates for the amplitude dissipation of high-frequency plane waves and corrects the phase distortion resulting from frequency dispersion. From the two figures, we can see that the inverse-Q filtering techniques improve the seismic resolution and reflection continuity, which leads to a clearer appearance of the subsurface structure. Figure 5 Open in new tabDownload slide Poststack seismic section: (a) the section without Q-compensation and (b) the section with Q-compensation (the blue circle indicates the gas reservoir). Figure 5 Open in new tabDownload slide Poststack seismic section: (a) the section without Q-compensation and (b) the section with Q-compensation (the blue circle indicates the gas reservoir). In order to compare the dispersion-dependent attributes with low-frequency shadows underneath the gas reservoir, we obtain the iso-frequency data using the match pursuit time–frequency decomposition method (Wang 2007). Figure 6 shows the iso-frequency sections (10, 20, 30 and 40 Hz) obtained from poststack seismic data without Q-compensation. We can see that the low-frequency shadows, underneath the gas reservoirs, are obvious at 10 and 20 Hz. The strong energy associated with low-frequency shadows beneath the gas reservoirs gradually disappears with increasing frequency. However, the target gas reservoirs show strong energy right at the top of the reservoir in 40 Hz which may be caused by the thin bed tuning. From the iso-frequency sections, we can see that the low-frequency shadow can be used to indicate the gas reservoir, but the resolution of the iso-frequency volume is so poor that it cannot delineate the detail of the reservoirs. Figure 6 Open in new tabDownload slide Iso-frequency sections: (a) 10 Hz, (b) 20 Hz, (c) 30 Hz and (d) 40 Hz (the red circle indicates the gas reservoir). Figure 6 Open in new tabDownload slide Iso-frequency sections: (a) 10 Hz, (b) 20 Hz, (c) 30 Hz and (d) 40 Hz (the red circle indicates the gas reservoir). Figure 7 shows the inverted dispersion-dependent attributes sections from prestack seismic gather without Q-compensation. Figures 7(a) and (b) are the normalized DVp and DG attributes, respectively, and the inserted curve is the band-pass resistivity log. We can see that the anomaly zone of the two attributes shows good correlation at the hydrocarbon accumulation (red circle). And the vertical resolution of the subsurface attributes is higher than the iso-frequency anomalies because of the removal of the band-pass filter effect of the wavelet in the inversion methodology, which is better for reservoir prediction. Considering the drilling well and geological information, we think that the dispersion anomalies of the two attributes in the downdip area are caused by thin bed tuning and not by the dispersion anomalies of a hydrocarbon. Figure 7 Open in new tabDownload slide Inverted dispersion-dependent attribute sections from prestack data without Q-compensation: (a) DVp section and (b) DG section (the red circle indicates the gas reservoir). Figure 7 Open in new tabDownload slide Inverted dispersion-dependent attribute sections from prestack data without Q-compensation: (a) DVp section and (b) DG section (the red circle indicates the gas reservoir). Figures 8(a) and (b) show the normalized DVp and DG sections inverted from inverse-Q filtered prestack seismic gather, respectively. The inverse-Q filtering will, in general, remove the Q-effect to produce high-resolution seismic data (Wang 2002, 2006, 2007). However, from the comparison between figures 7(a) and (b), we can see the hydrocarbon detection quality of the dispersion-dependent attributes is affected by the Q-compensated procedure. Figure 8(a) shows that the anomalies of DVp still appear in the target hydrocarbon accumulation, but even so, the anomalous value in non-hydrocarbon bearing layers conflict the drilling and geological information. Meanwhile, figure 8(b) shows DG has no anomalies in the target hydrocarbon accumulation. It suggests that the dispersion anomalies related to the hydrocarbon accumulation with strong attenuation can be affected by compensation of the high-frequency amplitudes. Figure 8 Open in new tabDownload slide Inverted dispersion-dependent attribute sections from prestack data with Q-compensation: (a) DVp section and (b) DG section (the red circle indicates the gas reservoir). Figure 8 Open in new tabDownload slide Inverted dispersion-dependent attribute sections from prestack data with Q-compensation: (a) DVp section and (b) DG section (the red circle indicates the gas reservoir). In this application, we have known the existence of the gas reservoir and then see the dispersion anomalies in the dispersion-dependent attributes. The dispersion-dependent inversion technique has shown the useful potential for hydrocarbon detection. However, it is possible that the dispersion-dependent anomalies are not only caused by strong attenuation effect, but also caused by wave interference of thin bed tuning and so on. In real applications, the dispersion-dependent anomalies should be verified and integrated by other methods to diminish the ambiguity of reservoir characterization. 5 Conclusion Based on the assumption that strong attenuation caused by the hydrocarbon is associated with significant velocity dispersion, the dispersion-dependent attribute can be used as a hydrocarbon indicator. We have presented a technique to invert the quantitative dispersion-dependent attributes indicating the level and gradient of P-wave velocity dispersion, which is essentially an extension of conventional AVO analysis to multi-frequency AVO inversion. The method test and real data application show that the dispersion-dependent attributes have the potential to improve the ability to identify hydrocarbon accumulation using seismic data. However, considering the factors corrupting the technique, it is crucial to integrate the other technologies and information to verify the dispersion anomalies for a reliable reservoir prediction and hydrocarbon detection in the real application. Nevertheless, we believe that the proposed technique may be useful in detecting hydrocarbon-related dispersion, which is helpful in reservoir hydrocarbon detection. Acknowledgments This research is supported by National 973 program (no 2007CB209605). We thank CGGVeritas for permission to use the test data in Hampson-Russell software. We are grateful to anonymous reviewers for their constructive comments. 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TI - Dispersion-dependent attribute and application in hydrocarbon detection
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/8/4/002
DA - 2011-12-01
UR - https://www.deepdyve.com/lp/oxford-university-press/dispersion-dependent-attribute-and-application-in-hydrocarbon-Iz0TfvUCl1
SP - 498
VL - 8
IS - 4
DP - DeepDyve
ER -