TY - JOUR
AU - Azbel,, Kostia
AB - Abstract Reservoir characterization is a crucial prerequisite to predict the economic potential of a hydrocarbon reservoir or to examine different production scenarios. Unfortunately, it is impossible to determine the exact reservoir properties at the required scale. The most abundant seismic data have a resolution of around 30 m. Wells resolve the reservoir down to the centimetre scale, but only at some points in the vertical direction. This paper presents a method, referred to as frequency bandwidth enhancement (FBE), for enhancing the frequency bandwidth and restoring high frequencies. The method increases the resolution of seismic data by padding the frequency spectrum of seismic wavelets, thus pushing the notch corresponding to the time limit of resolution to a higher part of the spectrum. This approach (patent pending) results in sharper wavelets capable of identifying thinner beds. A by-product of extending the frequency spectrum is the elimination of the tuning effect of beds thinner than the new limit of resolution. When tuning curves before and after the process are compared, it is observed that although different, the differences are minuscule and insignificant compared to the benefits coming from being able to resolve thinner beds. The procedure enunciated here is robust and helps define trends better, leading to more confident interpretations. Such applications could redefine prospects, which in some cases may have been declared unsuccessful on the basis of interpretation of seismic data with the original bandwidth. The reservoir characterization is realized with the aid of coherence cube processing, which is an extremely powerful tool to efficiently exploit the wealth of structural and stratigraphic information encapsulated in the seismic waveforms of 3D seismic data volumes. reservoir characterization, frequency bandwidth enhancement, coherence cube processing 1 Introduction Reservoir characterization comprises determining reservoir architecture, establishing fluid-flow trends, constructing reservoir models and identifying reserve growth potential. However, geophysicists are often frustrated at their inability to extract and understand the subtle stratigraphic detail contained in 3D seismic volumes. Seismically, stratigraphic bodies with definitive shapes show up if they are encased in rocks with contrasting velocity. Low-porosity carbonate bodies associated with thin shales and encased in shaly carbonate rocks having a narrow frequency bandwidth may not be seen on seismic data. Often we come across examples where the initially processed 3D seismic volume results in interpretations that sometimes are geologically suspect, e.g., cases involving complex faulted patterns or subtle stratigraphic plays. Similarly, post-mortem analysis may cite small fault displacements or obscure seismic data as reasons for dry wells. In such cases, the usual practice is to create a new version of the 3D volume with some target-oriented processing to improve imaging in the zone of interest that will, in turn, lead to a more accurate interpretation. In some cases this helps, but in others some questions still remain unresolved. In the latter, more often than not, more accurate stratigraphic interpretation is needed but the available bandwidth of the seismic data is inadequate to image or resolve the thickness of many of the thin targets seen in the wells. This problem can be addressed by having data of reasonable quality and augmenting it by some frequency restoration procedure that would improve the vertical resolution (Wang 2002, 2003). Frequency restoration is necessary because seismic waves propagating in the subsurface are attenuated and this phenomenon is frequency dependent—higher frequencies are absorbed more rapidly than lower frequencies. Consequently, the highest frequency recovered on most seismic data is usually about 80–100 Hz. This enables confident mapping of subsurface horizons of interest, clarifies detailed geological settings and eventually leads to more profitable seismic exploration programmes. The coherence cube analysis (Bahorich and Farmer 1995, Marfurt et al1998, 1999) provides accurate maps of the spatial change in the seismic waveform that can readily be related to geologic features and depositional environments. Faults and fracture systems can be spatially imaged and directly mapped from the coherence cube without the tedious task of drawing faults on each vertical section and proceeding blindly without the knowledge of their spatial position in the early crucial phase of the interpretation. Stratigraphic features can be readily detected in the volume, relieving the interpreter of the tedious task of locating them, thus saving time for detailed analysis (Maione 1999). 2 Frequency bandwidth extension We are aware that seismic waves propagating in the subsurface get attenuated. Since this loss is frequency dependent, seismic signals with higher frequencies are absorbed more rapidly than those of lower frequencies (Wang and Guo 2004). Attempts are usually made to determine the subsurface attenuation in terms of the attenuation constant α or the quality factor Q (Wang 2004). The conventional methods used for their determination from surface seismic data not only have their limitations but also have a certain level of uncertainty. The frequency bandwidth enhancement (FBE) approach to enhance the frequency bandwidth results in sharper wavelets capable of identifying thinner beds. Resolving thin beds from seismic data implies identifying individual reflections from the top and bottom of a bed, and the limit of resolution is defined as the smallest bed separation that can be identified as two distinct events in seismic data. Ricker (1953), Widess (1973) and Kallweit and Wood (1981) studied the limit of resolution more than two decades ago by convolving wavelets of known characteristics with two spikes, the distance (time interval) between the spikes representing the top and bottom of the structure under study. Through their analysis they quantified the thinnest bed to be resolved as a function of the wavelet's characteristics (breadth or frequency information). The interference between wavelets as beds become thinner (wedge model) results in thickness and amplitude deviations from the real ones. These differences are graphically displayed and analysed using tuning curves where apparent versus real thickness and amplitudes are compared. Ricker (1953), Widess (1973) and Kallweit and Wood (1981) quantified the time limit of resolution, but gave no insight into the possible ramifications of doing it in the spectral domain. Our method described below deals with the expression of a thin bed in the frequency domain and a methodology for extending the relevant part of the spectrum and, as a consequence, decreases the limit of resolution. Moreover, we show that the expression, in the frequency domain, of two spikes convolved with a wavelet is a notch in the amplitude spectrum at a frequency that is a function of the spikes' separation (in time) and events' polarity. Furthermore, the notch is present in the spectrum for beds thinner than the time limit of resolution, implying that conducting the analysis in the frequency domain will allow us to push the limit of resolution to a higher degree, i.e. we can resolve smaller thickness of beds. The basic technique described below increases the limit of resolution (thinner beds in the time domain) by extending the frequency spectrum of the wavelet such that the (frequency) value of the highest identifiable frequency notch corresponds to the limit of resolution of the extended spectrum. The resultant seismic data are of much higher frequency and allow us up to a 30% increase in resolution. The effect of padding the frequency spectrum where no seismic information is recorded in the first place is also analysed. We will use a Kallweit and Wood (1981) resolution criteria to illustrate the technique since they used a broadband wavelet, similar to that used in our analysis, to quantify resolution. The analysis, done for spikes of the same polarity and amplitude, can be easily extended to include spikes of different polarities and amplitudes. It is stated without proof that such an analysis would result in conclusions similar to those observed in the test case. The practical time limit of resolution, as defined by Kallweit and Wood (1981), for a broadband wavelet with a maximum frequency fU and a white spectrum occurs at a one-quarter-wavelength condition and approximates TR = 1/(1.4fU), provided that the wavelet's band ratio exceeds two octaves. The frequency representation of two spikes of the same polarity separated at a time interval Δt corresponds to a notch at frequency fN = 1/(2Δt). The thinner the bed being analysed, the larger the value of fN. The notch in the frequency spectrum for the time limit of resolution will fall at a frequency fR = 1/(2TR) or fR = 0.7fU; that is, the notch falls at 70% of the maximum frequency. As the bed thickness decreases, the representation in time is an increase in the amplitude of the wavelet where upper and lower limits cannot be distinguished (the events are in tune). The representation in the frequency (spectral) domain corresponds to a notch in the amplitude spectrum at frequencies higher than fR (0.7fU) and up to nearly fU. The technique presented here is based on the fact that thinner beds can be better resolved in the frequency domain than in the time domain. Based on Kallweit's model, the time limit of resolution can be reduced by 30% by extending the wavelet's maximum frequency to a value such that the notch at the highest usable frequency (close to fU) before extension corresponds to 1/(1.4fUE) where fUE corresponds to the new (extended) maximum frequency. In practice, the extension of the frequency bandwidth by padding is imperfect and results in wavelets that are not white and, for this reason, do not honour Kallweitt's time limit of resolution; nevertheless, the time limit of resolution is still reduced by 30% by making fUE larger than 1.4fU. By padding amplitudes between fU and fUE, where there is no seismic signal, the wavelet becomes sharper with the resultant decrease in the limit of resolution. Since no real signal exists from fU to fUE, it will be impossible to see the effect of beds thinner than TRN on the extended spectrum and the resultant tuning curves will have different characteristics than those observed in the usual case. Namely, amplitudes will not increase for wavelets convolved with thinner beds than the new limit of resolution. 3 Coherence cube processing We have used several coherence formulations (Bahorich and Farmer 1995, Marfurt et al1998, 1999) within this research project. These algorithms are based on the following basic mathematical solutions: correlation (C1), semblance (C2) and eigen-decomposition (C3). Numerous hybrids of these algorithms have been developed and some will be discussed here. The correlation algorithm (C1). The basic correlation approach has been around since the early days of digital signal processing. When applied to two seismic traces it can be defined as the degree of linear relationship between them, a measure of how much they look alike or the extent to which one can be considered a linear function of the other. It is interesting to note that the frequency domain equivalent of correlation, in the time domain, is coherence. The semblance algorithm (C2). The introduction of the semblance algorithm by Barhorich and Farmer (1995) to the coherence cube methodology added a significant contribution, especially for revealing detailed stratigraphic features. This is made possible in part due to the shorter temporal apertures which can now be employed. Semblance is the energy of a summed trace divided by the mean energy of the components of the sum which is the energy of the stacked trace normalized by the energy of the components of the stack. It is this technique which forms the basis of the C2 algorithm. The eigen-decomposition algorithm (C3). This is a multi-trace eigen-decomposition process that is more robust with higher resolution than previous algorithms. Consider two seismic traces whose amplitudes are crossplotted sample by sample on the Cartesian coordinate system. The distribution of the general shape of the plotted points can be represented by an ellipse and the pattern formed by these points is governed by the coherence of the two input traces plotted. The ellipsoidal shape is not a measure of the individual samples but more a measure of the overall waveform shape being input. The coherence algorithms used are typically referred to as C1, C2 and C3. The methodology originally patented by Bahorich and Farmer (1995) describes a correlation technique as a part of the approach for providing the numerical similarity of a cube of seismic traces. This resulted in the C1 algorithm. Further work performed by Bahorich and Farmer (1998, 2000) produced the superior C2-based semblance algorithm. In 1996 Marfurt et al announced the eigen structure algorithm (C3) with, in most cases, a significant response improvement over the semblance-based formulation. The eigen solution (C3) has proved to be highly successful, with increased robustness, in revealing both subtle faults and stratigraphy in one execution. These results are far superior to the correlation (C1) and semblance (C2) solutions used in the past and available on workstations. An additional improvement was made which gives an option to remove the structural effect from the technique caused by the instability of the zero crossing on the seismic trace. This is achieved by a higher fidelity dip/azimuth search. Recently, a major breakthrough was accomplished by introducing an eigen gradient term which produces a significant lift in the sensitivity resulting in higher resolution. This capability, called high-resolution eigen, makes even the most subtle waveform changes visible to the eye with both faulting and stratigraphic detail. The ability to measure three-dimensional spatial variations in the seismic waveform with full dip and azimuth comprehension is extremely powerful in exploiting 3D data volumes. The basic seismic waveform contains a measure of time, amplitude, frequency, phase and absorption. Spatial variations in these measurements are the seismic response to lateral variations in the physical and geometric properties and characteristic of the rocks. Measuring these combined changes in the seismic response allows the interpreter to physically locate and map these changes in space and time thus giving a better understanding of the subsurface model. The coherence cube methodology as applied here is an attempt to capture these changes. 3D seismic coherence is computed by measuring waveform similarity within an aperture which includes traces and time samples within a user-specified space and time window control. The waveform similarity is measured along all possible planes within the dips specified. Faults can be identified by their low similarity measurement when the aperture is straddling the fault location. Subtle changes in the seismic waveform which show the extent and internal details of stratigraphic features can also be identified by using the technique. Results here indicate that the illumination of the subsurface is a function of offset. The imaging of fault and fraction systems is clearly visible using the coherence cube. 4 Real data examples The frequency restoration procedure described above has been run on a 3D seismic data set from an onshore oilfield in southwest China, and convincing and promising results have been obtained. Figures 1 and 2 show the application of FBE on the migrated 3D seismic data using the approach discussed above (padding the frequency spectrum of seismic wavelets to push the notch corresponding to the time limit of resolution to a higher part of the spectrum). The FBE process has increased their bandwidth from 40 Hz or less to over 100 Hz (figures 3 and 4) using this patent-pending new technique. Geologists can redefine thin beds, pinchout, small faults, and new prospects using these high frequency seismic sections with higher confidence. Figure 1 Open in new tabDownload slide Stacked section before (left) and after (right) FBE processing. Many detailed subtle stratigraphic features can be seen on the FBE data (the green line interpretation). Figure 1 Open in new tabDownload slide Stacked section before (left) and after (right) FBE processing. Many detailed subtle stratigraphic features can be seen on the FBE data (the green line interpretation). Figure 2 Open in new tabDownload slide Direct merge of the seismic section before (right) and after (left) FBE processing. Additional small reflectors can be identified in the red circled areas on the FBE data. Figure 2 Open in new tabDownload slide Direct merge of the seismic section before (right) and after (left) FBE processing. Additional small reflectors can be identified in the red circled areas on the FBE data. Figure 3 Open in new tabDownload slide Amplitude spectra of the seismic data before FBE processing. The peak frequency is about 35 Hz with bandwidth from 10 Hz to 80 Hz. Figure 3 Open in new tabDownload slide Amplitude spectra of the seismic data before FBE processing. The peak frequency is about 35 Hz with bandwidth from 10 Hz to 80 Hz. Figure 4 Open in new tabDownload slide Amplitude spectra of the seismic data after FBE processing. The peak frequency is about 70 Hz with bandwidth from 10 Hz to 130 Hz. Figure 4 Open in new tabDownload slide Amplitude spectra of the seismic data after FBE processing. The peak frequency is about 70 Hz with bandwidth from 10 Hz to 130 Hz. Figures 3 and 4 show the frequency bandwidth of the 3D seismic data before and after the FBE processing. The cascaded dipole differentiation filters (e.g. 1, -1) of various orders have been used during the FBE processing, which can shift and increase the dominant frequency of zero phase seismic trace data. Higher orders (and strengths) of filters can be obtained by convolving (cascading) lower order filters with one another. The process is most effective on zero phase data. Figure 5 compares the FBE processing result from the 500 ms to 2000 ms section. The FBE processing has significantly increased the frequency bandwidth, sharpened the wavelet and enhanced the reflection image for much easier and more confident interpretation. Figure 6 shows the time slide at 1000 ms with significant high frequency features and great detail after FBE processing. Figure 5 Open in new tabDownload slide Comparison of a seismic section from 500 ms to 2000 ms before (left) and after (right) FBE processing. Figure 5 Open in new tabDownload slide Comparison of a seismic section from 500 ms to 2000 ms before (left) and after (right) FBE processing. Figure 6 Open in new tabDownload slide Time slide (1000 ms) of seismic data before (left) and after (right) FBE processing. Figure 6 Open in new tabDownload slide Time slide (1000 ms) of seismic data before (left) and after (right) FBE processing. Figure 7 shows the time slide (1680 ms) of coherence processing results using the C2 semblance method (left) and C3 eigen method (right). The eigen-decomposition method gives much higher resolution, more clear, detailed and sharp features than that of the C2 method on the same seismic data, which will provide detailed structure interpretation and reservoir characterization. Figure 7 Open in new tabDownload slide Time slide of coherence processing results comparison of C2 (semblance algorithm, left) and C3 (eigen-decomposition solution, right) methods. Figure 7 Open in new tabDownload slide Time slide of coherence processing results comparison of C2 (semblance algorithm, left) and C3 (eigen-decomposition solution, right) methods. Figure 8 shows a comparison of the time slide (1680 ms) of seismic data (left) and the coherence data (light) using the adaptive high resolution eigen method. There are fracturing zones on the top of the structure and small faults developed along the major fault zone on the coherence cube time slide, which cannot be identified from the time slide seismic data. Figure 8 Open in new tabDownload slide Comparison of a time slide (1680 ms) of seismic data (left) and coherence cube data (right). Figure 8 Open in new tabDownload slide Comparison of a time slide (1680 ms) of seismic data (left) and coherence cube data (right). Figure 9 shows a comparison of the coherence cube time slide (1680 ms) before (left) and after (right) FBE processing. FBE processing has significantly improved and increased the resolution of the seismic data. Much more detailed geological features can be identified and interpreted (the area outlined in red) from the coherence data after FBE processing. Figure 10 shows the coherence results using the adaptive eigen method before (left) and after (right) FBE processing. Figure 9 Open in new tabDownload slide Time slide (1680 ms) of the coherence cube data before (left) and after (right) FBE processing. Figure 9 Open in new tabDownload slide Time slide (1680 ms) of the coherence cube data before (left) and after (right) FBE processing. Figure 10 Open in new tabDownload slide Time slide of adaptive eigen: comparison before (left) and after (right) FBE processing. Figure 10 Open in new tabDownload slide Time slide of adaptive eigen: comparison before (left) and after (right) FBE processing. The bright spot technique and relief-enhanced eigen method are displayed in figures 11 and 12. The ‘bright spot’ volume was created by running the coherence technique on seismic inversion data and numerically merging the inversion volume with the coherence volume. The relief-enhanced eigen solution provides a very novel product which enhances both structural and stratigraphic features to be highlighted. These plots have significantly helped geologists and reservoir engineers to understand and interpret fluid distribution, special reservoir structure, and conduct reservoir characterization with greater confidence. Figure 11 Open in new tabDownload slide Time slide (1680 ms) of bright spot volume display before (left) and after (right) FBE processing. Figure 11 Open in new tabDownload slide Time slide (1680 ms) of bright spot volume display before (left) and after (right) FBE processing. Figure 12 Open in new tabDownload slide Time slide of relief-enhanced eigen: comparison before (left) and after (right) FBE (right) processing. Figure 12 Open in new tabDownload slide Time slide of relief-enhanced eigen: comparison before (left) and after (right) FBE (right) processing. 5 Conclusions The FBE method described in this paper differs from conventional industry methods. It reduces the limit of resolution of seismic data by padding the frequency spectrum of seismic wavelets, thus pushing the notch corresponding to the time limit of resolution to a higher part of the spectrum. These result in sharper wavelets capable of identifying thinner beds. A by-product of extending the frequency spectrum is the elimination of the tuning effect of beds thinner than the new limit of resolution (TRN). When tuning curves before and after the process are compared, it is observed that although different, the differences are minuscule and insignificant compared to the benefits of being able to resolve thinner beds. The procedure enunciated here is robust and helps define trends better, leading to more confident interpretations. Such applications could redefine prospects, which in some cases may have been declared unsuccessful on the basis of interpretation of seismic data with poor bandwidth. Running the coherence cube technique on seismic data shows that improved stratigraphic results can be achieved on good quality seismic data. Acknowledgments This project was made possible by the dedication and effort of many professionals at the Southern E&P Company of SINOPEC, and Paradigm Geophysical. The support of SINOPEC and Southern E&P Company management in facilitating the whole project is specifically acknowledged. We also acknowledge the Southern E&P Company of SINOPEC and Paradigm Geophysical's permission to publish this work. 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TI - Reservoir characterization using seismic data after frequency bandwidth enhancement
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/2/3/005
DA - 2005-09-01
UR - https://www.deepdyve.com/lp/oxford-university-press/reservoir-characterization-using-seismic-data-after-frequency-8h4EXi2mFB
SP - 213
VL - 2
IS - 3
DP - DeepDyve
ER -