I) Data Conditioning
The pre-conditioning processes are the processes that used to prepare the input data to the subsequent rock physics modeling. The well log Conditioning and predictions of the missing logs are the two most processes that are strongly recommended before any colored inversion analysis.
Well Data Conditioning
However, there are some critical logs that did not record in some of the used wells in the study area (Figure 5). These missing logs are crucial for constructing the colored inversion and seismic spectral blueing. In this step, the available logs are employed to predict the missing logs of other wells. We test three methods: published numerous empirical relationships, Customized Equations, and neural network methods to determine the most effective technique for prediction.
Editing and Replacement Methods
a. Empirical Equation
We use the Reversed Gardner’s Equation to predict the missing of P-wave velocity log:
b. Customized Equation
Alternatively, P-wave velocity can be predicted using a customized equation based on the relationship between density and the P-wave velocity. In this case, a 3rd order relationship was found, which exhibited a correlation coefficient 0.66 and matched the background trend (Figure 6).
c. Neural Network Approach
Neural network approach was employed to predict P-wave and S-wave velocities. Density, resistivity, and neutron porosity logs were utilized jointly to accomplish the prediction process. It is crucial to mention that the utilized logs were utilized in a non-linear manner in order to predict the P-wave velocity. Afterward, the S-wave velocity was predicted utilizing the same logs in a non-linear manner. The selection of the neural network approach was driven by its ability to learn and process vast amounts of data, as well as its non-linear capabilities. The logs played a crucial role in providing the required information to train the neural network and generate the predictions. By leveraging the insights from these logs, the neural network was trained to make accurate predictions regarding P-wave and S-wave velocities.
The correlation coefficients obtained from the comparison of actual and predicted logs are presented in Figure 7. The neural network method yielded correlation coefficients of 0.75 for the P-wave velocity and 0.88 for the S-wave velocity. These values are indicative of a strong agreement between the predicted and actual logs, which demonstrates the effectiveness of the neural network approach. The comparison between different methods is depicted in Figure 8. The neural network method stands out from other methods with the highest correlation coefficients and the closest match to the actual logs. This demonstrates that the neural network approach is the most effective method for estimating logs in this study.
The final result of estimated logs using the neural network method is shown in Figure 9. The estimated logs closely match the actual logs, indicating a high level of accuracy and precision in the neural network approach. Overall, the results obtained from the correlation coefficients and comparison among methods highlight the superiority of the neural network method in estimating logs. The high correlation coefficients and close match to the actual logs indicate that the neural network approach provides the best results in terms of accuracy and precision.
Seismic Data QC and Conditioning
The quality control yardstick to assess the quality of seismic angle stacks and determine their suitability for the colored inversion and seismic spectral blueing process involves comparing them to the inversion synthetic at the well location. Figure 10 displays the seismic angle before conditioning.
The workflow for conditioning seismic angle stacks is depicted in Figure 11. It consists of three main steps: frequency filtering, events alignment (trim statics), and amplitude balancing.
1. Frequency Filtering: The objective of this process is to unify the frequency content of the three angle stacks. This can be done by designing low pass filter for the overlapping amplitude spectra of the three angle. The rationale for frequency filtering is based on a very important reason. The subsequent events alignment process, is based on window-based cross-correlation between the near, mid, and far traces for each CDP. For the high frequency events on the nears and mid, interference can occur on the far either constructively or destructively. This interference can result in time shifts that cycle-skip the events, thereby destroying the Amplitude Versus Offset (AVO) character. By filtering out these high frequency events, we can ensure that the time shifts necessary for obtaining the highest cross-correlation values do not interfere with the AVO character.
2. Events Alignment (Trim Statics): The trim statics process utilizes a cross-correlation technique between the near, mid, and far traces of each CDP. By analyzing this function, one can find the optimal time shift or lag that yields the highest correlation value. Once this time shift is identified, it is applied directly to the data.
The trim statics process involves a time-window-based operation, allowing multiple values of the time window to be tested. During this process, the time shifts required for achieving the maximum correlation may exceed the dominant period time. As a result, the near traces may be correlated with shallower or deeper events on the mid or far traces, a phenomenon known as cycle-skipping. To constrain the time shifts, a maximum allowable time shift can be postulated in the trim statics process.
In this study, a time-variant trim statics method is applied, where the calculation is performed over a series of small, overlapping windows. The duration of each window is 80 milliseconds, and the calculated shifts are interpolated no farther than 20 milliseconds (Figure 12). This approach allows for a more accurate and precise estimation of the time shifts.
3. Amplitude Balancing: Amplitude balancing adjusts the amplitudes of the seismic angle stacks to ensure a consistent representation throughout the entire dataset. This step is important for ensuring accurate inversion results and preserving the amplitude variations within the seismic data.
By following these steps, the quality control yardstick ensures that the seismic angle stacks are of good quality and can be used directly for the colored inversion and seismic spectral blueing processes.
II) Wavelet Extraction
The wavelet that gives an optimum tie of a well log to a seismic section has a characteristic length, shape, and timing. However, estimating this wavelet accurately can be challenging. The statistical wavelet extraction process typically relies on auto-correlation and assumes a user defined constant phase. Additionally, the seismic data is typically processed using a zero phase technique, which is achieved by convolving the seismic data with an inverse filter that converts the estimated wavelet in the data to a zero phase equivalent.
In this study, four statistical wavelets were extracted from the full-stack seismic data to represent the main stratigraphic intervals (Figure 13). These wavelets were extracted using the auto-correlation method and a user defined constant phase. The wavelets were then compared to seismic data, and an example of synthetic to seismic match is presented in Figure (14).
By extracting statistical wavelets from the seismic data, it is possible to obtain detailed information about the stratigraphic intervals. This information can be valuable for well log correlation and seismic interpretation. The wavelet extraction process provides a quantitative approach to tie well logs to seismic sections, allowing for more accurate and reliable interpretations.
III) Seismic Colored Inversion
The primary goal of the inversion process is to estimate the physical properties of rocks by combining seismic and well-log data. Common physical parameters of interest include impedance, velocity, and density (Pendral, 2006). Inversion-based attributes can also be utilized to improve seismic section interpretation. These attributes provide additional information about the rock properties, which can enhance our understanding of the subsurface. By analyzing these attributes, interpreters can gain valuable insights into the geology and potential hydrocarbon reservoirs (Pendral, 2006). To achieve inversion, a mathematical relationship is established between a set of model parameters and the earth's response. This relationship is typically characterized by some form of forward modeling. For instance, if we use the elastic wave equation and a model with known parameters (velocity and density), we can generate a synthetic seismogram. During the inversion process, various parameters may be adjusted or optimized. By iteratively adjusting the parameters, the model can be refined to match the actual seismic data, providing insights into the rock and fluid properties of a given area (Russell and Hampson, 1991). Figure (15) provides an example of a Seismic Colored Inversion Operator main window with the default charts rearranged in five columns. However, the figure demonstrates an alternative layout that is optimized for displaying the inversion results.
To avoid unnecessary introduction of harmful frequencies into the seismic data, it is crucial to exercise extreme caution when utilizing the seismic colored inversion (CI) operator. Incorrect application of the operator can lead to the unintended addition of noise, which can subsequently distort the analysis. To address the issue of accuracy, we conducted extensive testing to verify whether the results we obtained from the CI operator aligned with the well data. By exploring various trails, we were able to determine the most suitable parameters to employ while limiting the influx of noise into the seismic data. Additionally, the test results confirmed that the outcomes obtained from the operator were consistent with what was seen in the wells, thereby reinforcing the reliability of our analysis.
The seismic wedge models presented in Figure (16) suggest that the application of colored inversion wavelets leads to an increase in the vertical resolution of the full-stack seismic data, from 31 meters to 23 meters. This improvement in seismic resolution is advantageous for analyzing the subsurface structure and identifying geological features. Additionally, the seismic data reveals a good resolution for smaller geologic features both in the vicinity of the well location and away from it. This improvement aids in identifying subtle structures and enhances the overall quality of the seismic interpretation. When comparing the seismic data before and after the CI process depicted in Figure (16), it is evident that the seismic resolution has been enhanced.
IV) Seismic Spectral Blueing
Spectral Blueing is a technique that shapes the mean seismic spectrum to follow the well-derived reflectivity trend and optimize the vertical resolution without boosting noise to an unacceptable level (Blache-Fraser and Neep, 2004). The spectrum is reshaped to match the real trend of the reflectivity obtained from wells. Shaping the seismic spectrum to follow the Blue reflectivity is referred to as the spectral Blueing which enhances seismic resolution and outputs more geological details. Spectral Blueing technique recovers higher frequency data while it does not go beyond the seismic bandwidth. But the spectrum still need to be broadened in order to get result that is much more consistent with well reflectivity spectrum. So, before proceeding with the SSB workflow, it is necessary to enhance the frequency content in seismic data.
One of the key advantages of the SSB algorithm is its ability to bridge the gap between seismic and well data, enabling a geologically (well-log) driven optimization of the frequency spectrum. The theoretical justification for the SSB algorithm lies in its ability to compensate for the inherent limitations in seismic data. Seismic data are typically not optimized for the frequency content, which is an important aspect of seismic imaging. By incorporating well data, specifically density and P-wave sonic logs, into the optimization process, the SSB algorithm can overcome these shortcomings.
The Seismic Spectral Blueing (SSB) algorithm was originally proposed by Velzeboer (1981) and later refined by Walden and Hosken (1985). The practical application of the SSB algorithm has been demonstrated by Blache-Fraser and Neep (2004). they demonstrate the effectiveness of the method in boosting the seismic spectra to a level controlled by the well-derived reflectivity spectrum. This enhancement is achieved by adjusting the gain or amplification of seismic frequencies based on their corresponding values in the well data. The algorithm primarily focuses on recovering attenuated frequencies within the band, which can improve seismic resolution. By focusing within the seismic band, the SSB algorithm avoids introducing noise or other artifacts that may be present outside the frequency band of interest.
In the process of seismic signal analysis, a common practice is to assume that the seismic data spectrum remains unchanged within the analysis time window. However, this assumption can be far from reality, particularly for larger windows. To overcome this problem, Neep (2007) introduced a series of time variant seismic signal analysis operators that are based on log properties at the corresponding time. This step aims to address the problem of the limitation of the seismic vertical resolution by enhancing the seismic high frequency. One of the key aspects of this design is the use of a "mean seismic spectrum" and "mean reflectivity spectrum" within the seismic frequency band. The mean seismic spectrum is calculated from 40 seismic traces in both the inline and crossline directions from the whole 3D seismic cube around the well location within a specific time window. This window, typically 750 ms, is selected to provide sufficient data to capture the high-frequency component of the seismic signal. By matching the mean seismic spectrum to the mean reflectivity spectrum within the seismic frequency band, this design aims to compensate for the attenuation effects that can occur over time (Figure 17). This helps in improving the seismic vertical resolution, as high-frequency information is preserved more effectively. As a result, the seismic image of the well and surrounding area is enhanced, providing a more accurate understanding of the geological structure.
Identify a time gate for the interval in which the operator will operate within the zone of interest (target). Ideally, seismic traces and well data (log traces) should be guided by an interpreted horizon within the target zone. In this way, the various gated log traces should have sample values over similar geology. However, in our case, we utilize a window interval as a training exercise instead of a horizon.
After applying the designed operator to the seismic data, the amplitude spectrum was extracted and compared to the amplitude spectrum of the original (pre-SSB) seismic data set. This comparison revealed that the SSB has significantly increased the usable seismic bandwidth (as shown in Figure (18).
Seismic wedge models indicate that the vertical resolution of the full-stack seismic data has been significantly improved by applying the "blued" seismic wavelet (Figure 18). Examination of the seismic data reveals a noticeable enhancement in the seismic reflector continuity and the resolution of small-scale geologic features near the well location as well as away from it. The comparison of the seismic data before and after the SSB process clearly demonstrates a distinct improvement in the seismic resolution (Figure 18).
V) Spectral Decomposition Attribute Extractions (SDAE)
As the full spectrum of frequency can be broken down into different band passes by decomposing the frequency spectrum of the CI and SSB volumes which allows for more resolution and accurate analysis of the data. Then the RGB display is generated by combining the decomposed spectral into an RGB volume (Guo et al., 2009) for CI and SSB volumes respectively. The decomposed spectral is pointed out into color axis that represents the red, green and blue element into the 3D color volume to extract the reservoir polygon for gross rock volume (GRV) calculation.
By using the discrete fast Fourier transform (DFFT), spectral decomposition enables imaging and mapping temporal bed thickness and geologic discontinuities over large 3D seismic surveys by decomposing seismic data into different frequency cubes. To delineate stratigraphic settings like sand bars and structural settings with complex fault systems using 3D seismic data (Brown, 2011), this signal analysis technology has been successfully used. All data within a seismic volume is displayed simultaneously during the seismic volume rendering process. In order to identify hidden structural or depositional features, a seismic volume can be rendered and opacified to make it partially opaque (high amplitudes) and partially transparent (crossover amplitudes). Henderson et al. (2008) recommend the red-green-blue (RGB) blending method because it blends seismic attributes and allows for better visualization of geological features using its opacity scales. It is possible to outline a 3D object using seismic volume rendering or RGB blending, and then input the outline into the calculation of volumetrics (Chaves et al., 2011; Li et al., 2013; Torrado et al., 2014; Cao et al., 2015; Haris et al., 2017; Okiongbo and Ombu, 2019).
In order to display RGB multi-color data, the amplitude spectrum of the data was analyzed; three dominant frequencies were identified. We selected three frequencies to represent the seismic bandwidth's low (5 Hz), middle (15 Hz), and high (30 Hz) frequencies. The three frequencies were then blended into one full color image based on their RGB blends. It is important to note that mixing outputs from different frequencies allows the analysis of geological features related to various geometrical scales simultaneously, i.e., higher frequencies reveal more detailed features, and lower frequencies those with a coarser character. Three frequencies (5, 15 and 30 Hz) were mixed into a 3D color volume to create RGB color blended maps in this study (Figure 19).
Each frequency's RGB color blending is shown in figure (19). By time slicing the colored volume, a set of RGB color blendings for Sand reservoir SD-3 units have been created. A spectral decomposition attribute extraction is also performed for conventional seismic as well as CI and SSB cubes. According to the SDAE results for different cubes, it's obvious that there is more detail in the SSB cube than in the other cubes. In addition, the SDAE results for CI cubes also show a better level of detail than what is shown in conventional seismic SDAE cubes (Figure 19).