Reservoir characterization covers the essential components of seismic data interpretation. It combines various kinds of results to minimize the uncertainties and to enhance the complete understanding of the subsurface structures [1,2,3]. Generally, conventional interpretation techniques are used to delineate the large-scale structural traps that do not provide much success when dealing with thin interbedded reservoirs which are below the seismic resolution limit . Amplitude reflections from alternating thin layers often face tuning thickness problem due to low seismic resolution [5,6,7]. Therefore, amplitude anomalies are considered and analyzed with the help of different techniques such as amplitude versus offset (AVO) or amplitude versus angle  and spectral decomposition [9,10].
The AVO technique is widely used to differentiate the lithological properties and the fluid content within the target zone [11,12,13]. AVO attempts to use the offset-dependent variation of P-wave reflection coefficients to estimate lithological changes along with the interface. The fundamental principle of AVO analysis is the Knott–Zoeppritz equation, which depicts how transmission and reflection coefficients fluctuate with angle . However, AVO response is affected by different parameters such as pore fluid, lithology, reservoir thickness, and offset-dependent factors [11,15,16,17,18,19].
Out of these factors, reservoir thickness plays a crucial role in the validity of AVO results [4,20]. Primarily this is because, when a thin layer (with a thickness less that 1/4 of the wavelength) is interbedded between two closely spaced layers, then reflections from the top and bottom interfaces will go for constructive interference. Due to this, a single event of high amplitude can be observed on seismic data, on which, the effect of thin beds cannot be recognized via commonly used two-layer (single interface) AVO modeling . The bed thickness at which two events become indistinguishable in the time domain is called tuning thickness, and the effect of thin beds on seismic amplitude can be analyzed with the help of three-layer (double interface) wedge modeling [6,22].
In recent years, AVO modeling has drawn reasonable attention to sort out the thin-bed problems . The reflection coefficient method and the time delay theory are considered to be potential techniques to illustrate the AVO response from thin beds in the time domain [6,23,24]. In this context, various studies have attempted to resolve the problem caused by thin beds on seismic AVO data [25,26,27,28]. For example, Chung and Lawton  developed the relationship between reflection coefficient and bed thickness.
AVO interpretation can be facilitated by cross-plotting the AVO attributes such as intercept and gradient, which is helpful to understand AVO responses in an intuitive way . The intercept/gradient technique is not only a valuable indicator to classify the AVO anomalies but also used as a suitable tool to analyze the thin-bed reservoirs. Rutherford and Williams  classified different AVO trends with varying incident angles from the top of gas-saturated reservoirs based on intercept/gradient method. AVO anomalies are further classified into four main classes by several authors based on the intercept/gradient method [29,30,31].
The objective of this study is to analyze the effect of reservoir thickness on amplitude anomalies in the Huizhou sub-basin of Pearl River Mouth Basin (PRMB; Figure 1). For this purpose, we have utilized the petrophysical-based wedge modeling and AVO analysis using wire line log data. The Huizhou sub-basin contains a complete petroleum system and is famous for hydrocarbon exploration . In this area, Zhujiang Formation of Miocene age and Zhuhai Formation of Oligocene age are the primary reservoir rocks . The Zhujiang Formation mainly contains carbonate sediments, which are probably derived from the Dongsha uplift . The Zhujiang Formation contains thin beds of limestone which act as reservoir rocks in the Huizhou sub-basin. However, delineation of these thin beds through seismic data is not possible due to low seismic resolution . Therefore, in order to solve this problem, we have performed petrophysical-based wedge modeling and AVO analysis on the Zhujiang Formation as a case study.
2 Geological setting
During the opening of the South China Sea (SCS), several basins in the northern margin of SCS such as PRMB, Beibu Gulf Basin, and Yinggehai Basin started to develop in the Cenozoic era [35,36,37]. The hydrocarbon-bearing Huizhou sub-basin is situated on the north side of the PRMB as shown in Figure 1. Structures related to normal faulting developed predominantly in NE, NNE, and EW directions in the Huizhou sub-basin with spatial distribution of the fault strikes showing certain regularity . The overall structure of the Huizhou sub-basin shows an en-echelon arrangement which consists of Hubei, Huinan, Luxi, Huidong and Huixi half grabens along with Huidong and Huizhong low uplifts controlled by two NS trending main faults (Figure 1).
The seismic sections of syn-rift strata indicate that the extensive faulting activity occurred during Paleogene. Wenchang and Enping Formations in this sub-basin have experienced uplifting, sagging, and initial faulting of a large area at the initial phase of sedimentation [38,39]. In response to these structural events, the depositional environment changed from fluvial to deep lakes, shallow lakes, and then fluvial–deltaic . During the post-rifting stage, NE-SW- and NW-SE-oriented faults are developed along with some tenso-shear EW-oriented faults. These faults show minor throw as shown in Figure 2 and reflect that the faulting activity remained quiet after 32 Ma in Late Oligocene-Early Mid Miocene. However, the activity again started at 10.5 Ma . These active faults facilitated the migration process of hydrocarbons from Paleogene to Neogene.
The Huizhou sub-basin contains seven formations. Some of them are formed during the syn-rift stage (Enping and Wenchang), whereas Hanjiang, Yuehai, Zhujiang, Zhuhao, and Wanshan Formations are deposited during the post-rift stage. The boundary between the syn-rift and the post-rift stage can be marked by an unconformity as shown in Figure 2 (T70). The Enping and Wenchang Formations of Eocene–Oligocene and Eocene ages, respectively, are proven source rocks . The Miocene Zhujiang and the Oligocene Zhuhai Formations are primary hydrocarbon reservoirs in the Huizhou sub-basin, whereas Wenchang and Enping Formations are considered as secondary reservoirs. The considerable porosity and high permeability in the Zhuhai Formation made it one of the potential reservoirs within this basin. The overlying alternative marine carbonate and mudstone strata of Neogene age provides a seal to the hydrocarbon migration.
The Huizhou sub-basin is famous for hydrocarbon resources [32,33]. The Zhujiang Formation of Miocene age contains thin beds of carbonates which are proven reservoir intervals [33,43]. However, these thin intervals cannot be accurately interpreted through conventional seismic interpretation due to the tuning effect. In this study, an integrated study based on AVO modeling is performed to solve this problem. The study is completed as follows.
3.1 Petrophysical analysis/evaluation of reservoir properties
Petrophysical analysis transforms the well log measurements into reservoir properties . These reservoir properties can be successfully used for litho-fluid identification and to determine the accurate thickness of the hydrocarbon bearing zones [3,45,46]. For this study, well (X) from the study area is selected and petrophysical analyses are performed in order to identify the productive zones along with their corresponding thicknesses. The petrophysical analyses are completed through the following steps.
The first step in formation evaluation is to properly estimate the volume of shale, which is calculated by using the gamma ray (GR) log. For this purpose, the Stieber  method is used as it works well in the study area, with relation given as follows:
In the next step, density porosity (φd) is calculated with the help of density log which is combined with neutron porosity (φn) obtained from neutron porosity log in order to eliminate the effect of gas on reservoir porosity using the following equation:
3.2 Wedge modeling
Well log analyses clearly indicate that the Zhujiang Formation of Miocene age contains thin reservoir intervals (Figure 3); therefore, wedge modeling is carried out to estimate the seismic response with reference to thickness variation. A three-layer wedge model is developed in which a layer of limestone is embedded between two shale layers. The elastic values used to develop the double interference wedge model are given in Table 1.
The elastic parameters used to develop the three-layer wedge model for the selected interval
|Layers||Vp (m/s)||Vs (m/s)||Density (g/cm3)|
The tuning thickness is determined by using the following equation :
3.3 AVO analysis
The theory of AVO is based on the Zoeppritz equations, which give the plane wave reflection and transmission coefficients as a function of the angle of incidence and elastic parameters. The changes in elastic properties are useful indicators to infer the litho-fluid changes from one layer to another. In this study, exact Zoeppritz equations are used to analyze the variation in reflection coefficient concerning the incidence angle from the top and bottom of the target interval. The used exact Zoeppritz equations are given below .
Although the Zoeppritz equation deals with the angle of incidence, in this study, we are more concerned to analyze the variations in thickness and their consequent effect on AVO response. In order to analyze the effect of thickness, we convolved the reflection coefficients obtained from the Zoeppritz equation with Ricker (source) wavelet. For convolving coefficients, we considered the two-way travel time because the change in thickness of the layer also effects the travel time values.
Finally, we have used Shuey’s  equation to estimate the value of intercept and gradient at different thicknesses. Then, these attributes are cross plotted to analyze the effect of thickness on AVO attributes. The used Shuey’s  equation can be expressed as follows:
R(0) is the reflection coefficients at the normal angle of incidence, also known as AVO intercept. B represents the AVO gradient and explains the variation in reflection amplitudes at an intermediate angle of incidence. The third term C is denoted as curvature and explains the behavior of reflection coefficients at far angles of incidence, sometimes close to the critical angle . If we assume that the angle of incidence is less than 30°, Shuey’s equation is reduced to the two-term equation written as:
On the basis of the petrophysical analysis, different hydrocarbon-bearing zones are identified, as shown in Figure 3. In these zones, the crossover between density and neutron porosity logs, decrease in volume of shale (less than 15%), water saturation (less than 50%), and increase in effective porosity (porosity values vary from 15 to 25%) suggest that these clean and porous zones are favorable for the accumulation of hydrocarbons. The thickness of these hydrocarbon bearing zones varies from 5 to 24 m (Figure 3). Hence, the petrophysical analysis clearly depicts that the Zhujiang Formation of Miocene age contains thin hydrocarbon-bearing beds that have been embedded between shale beds.
Since the thickness of the hydrocarbon intervals is below seismic resolution, it is not possible to accurately demarcate these thin intervals on seismic data. In the presence of thin beds, seismic waves from closely spaced boundaries exhibit single event of high amplitude, and consequently, these reflected waves will not reveal the actual response of the subsurface geology. The amplitude of seismic reflections also changes with the change in thickness of the bed . Therefore, based on petrophysical analysis, we have chosen a reservoir interval, which has 15 m thickness favorable for hydrocarbon accumulation. A three-layer wedge model is constructed keeping in view the thickness of the reservoir zone, in which the carbonate layer is embedded between two shale layers (Figure 4a). The parameters used to construct the wedge model are listed in Table 1. The wedge model has a maximum thickness of 50 m. A zero-phase Ricker wavelet of 35 Hz frequency is convolved with the reflection coefficient in order to generate the synthetic traces (Figure 4b). The top of the wedge shows a positive impedance contrast, whereas the bottom shows a negative impedance contrast. Figure 4c indicates that the amplitude increases with the increase in thickness up to 19 m and then shows a decrease in amplitude up to 42 m thickness. However, when the thickness increases from 42 m, amplitude response becomes flat, which indicates that seismic reflections from the top and base of the wedge are not interfering.
From the above analysis, it is clear that the peak of seismic amplitudes can be observed at 19 m thickness, which means that at 35 Hz frequency, beds having a thickness of 19 m or above can be easily resolved on seismic data. A similar procedure is adapted for 40 and 45 Hz frequencies in order to analyze the variation in tuning thickness due to change in frequency values (Figures 5 and 6). Wedge model results illustrate that at 40 and 45 Hz frequencies carbonate beds having a thickness of 17 and 15 m can be easily resolved through seismic data, respectively.
In the above discussion, we have analyzed the synthetic gathers at zero offset. Furthermore, synthetic angle gathers are examined in order to understand the effect of thin bed tuning on angle-dependent reflectivity. Angle-dependent reflectivities (amplitudes) along the top and bottom interfaces (Figure 7a and b) are estimated with the help of convolved and exact Zoeppritz equations considering the 19 m bed thickness (Figure 7c and d). The Zoeppritz equation explains the reflection of plane waves coming from a single interface, which does not contain potential information about the reflection responses of thin layers . Therefore, we have also considered the convolved amplitudes to understand the reflection response of thin layers. Figure 7c (upper interface) shows that at zero angle, the value of convolved amplitudes is much higher than the Zoeppritz, and both values gradually decrease with the increase in the angle of incidence. However, the value of convolved amplitudes decreases more rapidly than the Zoeppritz amplitudes crossing its reflectivities at an angle of 32 degrees. After that angle, the convolved amplitudes become smaller than the Zoeppritz reflectivity, which may indicate a destructive interference. On the other hand, the reflectivities along the lower interface are the converse of the top interface (Figure 7d). The gap between these amplitudes curves also decreases with the increase in the angle of incidence; however, these two reflectivity curves (convolved and Zoeppritz) do not intersect each other.
To further analyze the behavior of angle-dependent reflectivity, we have computed the reflectivity responses for 14 and 24 m thicknesses (considering 5 m above and below the tuning thickness), keeping the other parameters same as used for Figure 7. The computed results are shown in Figures 8 and 9, respectively. The obtained results depict that at 14 m thickness (Figure 8b) top and bottom interfaces do not pass through the center of the peak and trough of the synthetic, respectively. It means that at this thickness, the maximum values of amplitudes (reflectivity) cannot be obtained. Figure 8c and d also show a decrease in convolved amplitudes as compared to Figure 7c and d. However, reflectivity values computed from the exact Zoeppritz equation do not show any change. Hence, at 14 m thickness, the obtained reflectivity values are lower than those values which we have obtained at 19 m thickness. So, at 14 m thickness (at a frequency of 35 Hz) AVO results cannot accurately interpret the tuning phenomena. Similarly, results obtained at 24 m thickness also show a decrease in convolved amplitude values, but in this case, top and bottom interfaces move apart from each other (Figure 9). So from the above discussion, it is obvious that at 35 Hz frequency AVO analysis provides more reliable results for 19 m thin bed.
Similarly, we have performed AVO analysis for 17 and 15 m thicknesses considering the 40 and 45 Hz frequencies, respectively. The obtained results are shown in Figures 10 and 11. From these results (Figures 10 and 11), it is quite clear that reflectivity responses obtained along the top and bottom interfaces are identical to those reflectivities which we have obtained for 19 m thickness at 35 Hz frequency (Figure 7). We also have computed reflectivity response considering the thickness values 5 m above and below the tuning thickness values, i.e., at 12 and 22 m, (for 40 Hz frequency), 10 and 20 m (for 45 Hz frequency). The obtained results are shown in Figures 12–15, respectively. Again, it is evident that the AVO responses obtained for 12 and 10 m thicknesses (Figures 12 and 14) are identical to what we have observed in Figure 8 and the AVO responses obtained for 22 and 20 m thicknesses (Figures 13 and 15) are identical to Figure 9. It means that the AVO response at different tuning thicknesses (19, 17, and 15 m) does not change, provided that the other parameters remain same except frequency.
AVO attributes (intercept and gradient) are considered a powerful tool to analyze the thin bed tuning. The values of intercept and gradient are calculated for the top interface with the help of Shuey’s two-term equation (equation (9)) considering different thickness values. Values of intercept increase with the increase in thickness and attain their peak values at 15, 17, and 19 m thickness for 45, 40, and 35 Hz frequencies, respectively (Figure 16a). After that, intercept values gradually decrease with the increase in bed thickness and become almost flat after 35 m thickness. A mirror image of Figure 16a is obtained for a cross plot of gradient versus thickness with a negative increase in gradient values (Figure 16b). It means that the values of intercept and gradient attain their peak value at λ/4, which represents tuning thickness at their respective frequencies and also cross validate the results obtained with the help of equation (6).
In this work, the quantitative seismic response of thin limestone beds of the Zhujiang Formation is studied by integrating petrophysics, wedge modeling, and three-layer AVO modeling. The petrophysical analysis depicts that the Zhujiang Formation of Miocene age contains thin (5–24 m) hydrocarbon-rich limestone intervals. Through wedge modeling, it is observed that the beds having a thickness of 19, 17, and 15 m can be resolved if the acquired seismic data have a dominant frequency of 35, 40, and 45 Hz, respectively. AVO results show that convolved amplitudes show clear variations in AVO response at different thickness values, whereas Zoeppritz results remain unchanged. Convolved amplitudes provide maximum values at tuning thickness (at a particular frequency), whereas the value of convolved amplitudes decrease above and below the tuning thickness. Furthermore, AVO attributes also validate the wedge modeling results and show the decreasing trend after the tuning thickness.
The authors would like to acknowledge the National Natural Science Foundation of China for substantial support of general projects (41374116 and 41674113), Chinese National Offshore Oil Company for providing well log data used in this research, and Chinese Scholarship Council. We would also be thankful to Mat Hall for providing open-access python script and for valuable guidance for this work.
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