Amplitude Variation With Offset Gradient Research Articles

Anisotropy in shale and its impact on AVO modelling and prospect de-risk: a case study of a Central North Sea field

The inherent anisotropy in shale is an attribute associated with its clay minerals platelets alignment and layering and very common with transversely isotropic (TI) medium. This implies that velocity is fastest along the horizontal axis and slowest along the vertical axis, which could affect velocity signature from sonic tools measurements in deviated wells. This may lead to wrong amplitude variation with offset (AVO) signature, inaccurate depth conversions, seismic-to-well tie difficulty etc. Nineteen (19) wells in Forties field andthirteen (13) in Huntington field were investigated and interpreted for the presence of anisotropy effect within the caprock over the reservoir Forties sands of the Sele (shales) Formation. In order to analyse the Thomsen weak anisotropy parameters (ϵ, γ and δ) per field, wells with closer Sele depth range were considered. The well inclinations ( θ ), average compressional (α) and shear (β) velocities per well were utilised for forward and inverse modelling of Thomsen anisotropy equations. The estimated anisotropy (VTI) parameters and the P-wave ( α o ) and S-wave velocities (βo ) at zero inclinations in Sele Formation for the studied wells are: α o = 2448 ± 15.9 m/s, β o = 1003 ± 34.8 m/s, ϵ = 0.15 ± 0.02, γ = 0.33 ± 0.10, δ = 0.030 ± 0.015 in the Forties field Sele, while α o = 2775 ± 23.6 m/s, β o = 1306 ± 47.9 m/s, ϵ = 0.22 ± 0.02, γ = 0.43 ± 0.14, δ = 0.022 ± 0.018 in the Huntington field. AVO responses were compared, assuming both isotropic and anisotropic P–P reflectivity models. Result shows an increase in AVO gradient for all anisotropic case in both fields. AVO signatures were either completely or averagely masked in both fields using the isotropic assumptions. There is also an increase in AVO gradient for all anisotropic cases in both fields. Velocity decreases of about 1.2% and 3.5% were observed in the Sele Formation for the Forties and Huntington fields respectively for anisotropy. The corrected two-way traveltime (TWT) should in principle allow for a better seismic-to-well tie estimation. Similarly, using the faster deviated velocity (i.e. uncorrected velocity) in any depth conversion would result in under estimation of the actual depth across the field.

Bayesian joint residual moveout and amplitude-variation-with-offset inversion

Residual moveout (RMO) can have a severe impact on seismic amplitude-variation-with-offset (AVO) analysis. It is, therefore, common practice to quality control and correct the processed seismic data for RMO before AVO analysis. However, a complicating factor is that AVO effects and tuning may result in up- or down-dipping events that are easily mistaken for events with RMO, e.g., AVO Class 2p response. Flattening these events will lead to an incorrect AVO estimation. We present a new Bayesian joint RMO and AVO inversion to estimate the RMO time shifts and the AVO intercept and gradient. The joint inversion corrects the seismic data based on the RMO and AVO prior models rather than explicitly assuming that the data should be flattened. The prior models will typically guide toward flat gathers but will also allow for up- and down-dipping events when these are possible within the prior model. The method is illustrated on synthetic and real seismic data. For cases wherein flat events are correct, the results are similar to sequential methods with RMO correction before AVO analysis, but in situations wherein dipping seismic reflectors may be misinterpreted as events with RMO, the joint inversion provides better results by evaluating RMO and AVO simultaneously. The inversion results include the posterior covariance matrix, which represents uncertainties for the AVO intercept and gradient, the RMO time shifts, and the correlations between these at all samples. The uncertainty of the RMO time shift varies within seismic gathers and depends on the seismic quality and how clear and well determined the seismic events are. The uncertainty of the RMO is lower for clear and continuous events but increases in the zones with weaker and noisy events. The uncertainty of the RMO time shifts has a low impact on the uncertainty of the AVO intercept but increases the uncertainty of the AVO gradient significantly.

Estimation of net-to-gross ratio and net pay from seismic amplitude variation with offset using Bayesian inversion

Net-to-gross ratio and net pay are essential properties for characterizing turbidite reservoirs. We present a Bayesian inversion that estimates the probability density distributions of the reservoir properties from the amplitude-variation-with-offset (AVO) attributes intercept and gradient, which are measured at the top of the reservoir. The method is adapted to the region-specific characteristics of the sand-shale interbedding as observed from well data. The likelihood function is estimated by a Monte Carlo simulation, which involves generating pseudo-wells, seismic modeling using the reflectivity method, picking the amplitudes at the top of the reservoir, and estimating the AVO intercept and gradient. In a North Sea oil field case example, the AVO gradient is most sensitive to variations in the net-to-gross ratio, while the AVO intercept is most sensitive to the type of pore fluid. The inversion was successfully tested on pseudo-wells and synthetic seismic AVO from well data. We show that the inversion can be applied to AVO maps to produce maps of the most likely estimates of the net-to-gross ratio and the net pay-to-net ratio, the resulting net pay, and the uncertainty.

Anisotropic three-term amplitude-variation-with-offset projections: A case study

A seismic amplitude-variation-with-offset (AVO) analysis is an important element in seismic reservoir characterization and has been successfully applied in many fields. Traditionally, AVO studies are based on AVO intercept ([Formula: see text]) and gradient ([Formula: see text]) only; curvature ([Formula: see text]) is neglected because it is very sensitive to noise and avoiding noisy [Formula: see text] is very difficult in practice. The recently introduced concept of three-term (3T) AVO projections, combined with continuous improvements in seismic data acquisition and processing, allows interpreters to effectively use [Formula: see text] by optimizing projection angles based not only on rock physics but also on seismic noise. The effectiveness of the 3T AVO projection, in which [Formula: see text], [Formula: see text], and [Formula: see text] are used as the triplet of reflectivities that are summed in the projection, and the impact of random noise on the 3T AVO projection have been investigated using data from an offshore Western Australian field. The 3T AVO projection is used in the framework of the extended elastic impedance. Because the study area is known to have nonnegligible differences in anisotropy parameters between the various lithologies, its impact on [Formula: see text] and [Formula: see text] is taken into account. First, the 3T projection angle targeting lithology fraction logs is optimized using well-log data. Analyses using synthetic seismograms are then performed to investigate the impact of seismic noise. Finally, the method is applied to field data. The results find that (1) [Formula: see text] is an important component of seismic reservoir characterization even if it appears unusable and (2) seismic noise must be taken into account when optimizing the projection angle.

Numerical modeling of seismic responses from fractured reservoirs in 4D monitoring — Part 1: Seismic responses from fractured reservoirs in carbonate and shale formations

One of the most urgent problems of oil and gas reservoir monitoring is the assessment of fractured reservoir infill type — with fluid-filled, gas-filled, or closed (no-reservoir situation) fractures, which is of significant value for time-lapse seismic technology. We used the grid-characteristic method for numerical modeling of seismic responses from fractured periodic elastoacoustic structures. We consider every single fracture individually (without using the effective medium approach), and we set explicit boundary conditions on fracture surfaces. We assume realistic height-to-thickness ratios — fracture opening (aperture) — equaling three to five orders of magnitude. These techniques make our models as close to real fractured reservoirs as possible. Analyzing the simulated seismic responses, we solve the problem of assessing the fractured reservoir infill type. As a result, previously unknown properties of seismic responses from fractured reservoirs were revealed. We use amplitude variation with offset (AVO) as the main tool for the analysis of the fracture infill type effect on the seismic response in three frequency ranges. Three out of four models exhibit a stable positive AVO gradient regardless of the rock type and frequency range. The analysis of linearized Zoeppritz equations confirms such AVO behavior. We have developed quantitative criteria (indicators) for recognition of a fracture infill type. Amplitude-frequency analysis is shown to expand the capabilities of the infill type recognition. Thus, a method for determining the fractured reservoir infill type is established for carbonate and shale formations, which could become the basis for a new direction in time-lapse technology.

Application of AVO attributes for gas channels identification, West offshore Nile Delta, Egypt

The offshore part of the Nile Delta is considered one of the most prolific provinces for gas production and for future petroleum exploration. Amplitude Variation with Offset (AVO) analysis supported by composite logs considered as one of the best-advanced techniques enables the interpreter to understand the seismic data. It is used to generate a new view of the output results, especially for the identification of gas zones as gas channels by using pre-stack AVO attributes that based on the intercept product gradient (A*B) and the Scaled Poisson’s Ratio Change. Free gas, regardless of the percentage show obvious AVO anomaly. Well log data, including gamma-ray, resistivity, and Vp sonic logs are used in the seismic data to well tie and in the generation of the synthetic seismogram. Seismic data conditioning processes with check-shot correction is performed to improve the resolution of the reflection events and signal to noise ratio. AVO attributes technique, as a direct hydrocarbon indicator, including AVO gradient analysis and AVO crossplot separate the gas levels in the sand-shale sequences. The identified gas-bearing zones consistent with well log data responses. As the main conclusion, we show the visual evidence for the gas-bearing zones by interpreting different AVO responses due to the changes in fluid and rock types.

A physical modelling study of the reservoir scale effect on amplitude variation with incidence angle

Abstract The 3D pre-stack seismic data from a physical modeling experiment were employed to investigate the effect of reservoir scales on AVO (amplitude variation with offset or incidence angle). Eight cuboid samples simulating cavernous reservoirs with different widths and the same thickness and elastic parameters were set within a 3D model. 3D seismic data acquisition and processing were conducted. To get the AVO responses of the samples with different widths, trough amplitudes corresponding to the sample tops at different incidence angles were extracted from the pre-stack angle gathers. Amplitude calibration for transducer radiation patterns was conducted on the extracted amplitudes at different angles. AVO analysis was conducted to quantitatively demonstrate the effect of sample scales on AVO characteristics. The effect of sample width was weak when the width was less than 60 m, which was 3/5 of the wavelength. When the width was larger than 60 m, both AVO intercept and gradient gradually increased with the sample width. The AVO gradient peaked at 150 m, which was 1.5 times the wavelength. Cross-plot analysis of AVO intercept and gradient showed the samples were aligned in a straight line when the sample width was less than twice the seismic wavelength. The result in this study partially verified the conclusions of reservoir scale effect on AVO responses drawn from previous numerical modelling studies. For a heterogeneous rectangular reservoir, the effect of reservoir scales on AVO responses could potentially be used to quantitatively estimate reservoir scale.

The Shuey-Radon transform

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.

Characterization of naturally fractured Arbuckle Group in the Wellington Field, Kansas, using S-wave amplitude variation with offset

S-wave amplitude variation with offset (AVO) analysis is sensitive to the presence of fractures and can provide a high-resolution seismic-based fracture characterization as compared with traditionally used traveltime-based methods. To determine viable attributes for estimation of properties such as spatial density and fluid fill of fractures, S-wave AVO modeling and analysis is carried out in the Wellington Field, Kansas, where 9C-2D seismic data have been acquired. Analysis is performed on the Ordovician fractured-carbonate interval called the Arbuckle Group, which is being considered for [Formula: see text] sequestration. AVO modeling of the Arbuckle interval indicates that differences in AVO intercepts of different S-wave polarizations can estimate S-wave anisotropy parameter [Formula: see text], which gives an estimate of fracture density. In addition, modeling suggests that AVO gradients of [Formula: see text] and [Formula: see text] waves can be used to derive a seismic attribute to discriminate fluid fill in fractures, provided good-quality S-wave gathers are available. The intercept anisotropy (IA) attribute obtained from AVO intercepts of S-waves provides fracture density estimates within the Arbuckle Group. These estimates are consistent with the field-wide, low-frequency observations from seismic velocities and spatially limited, high-frequency estimates obtained from drill cores and sonic and borehole-image logs. The IA attribute highlights possible high-permeability zones in the Upper and Lower Arbuckle suitable for [Formula: see text] injection. The Middle Arbuckle indicates low fracture density, potentially acting as a baffle to vertical flow and providing a seal for the Lower Arbuckle. The gradient anisotropy attribute obtained from the AVO gradient of S-waves suggests that most fractures in the Arbuckle are brine saturated. This attribute has a potential application in monitoring the movement of a [Formula: see text] plume in the Arbuckle Group when time-lapse data become available. These results demonstrate that S-wave AVO attributes can supplement the P-wave derived subsurface properties and significantly reduce uncertainties in subsurface fracture characterization.

Amplitude variation with offset analysis of time-lapse land seismic data in a gas field, Thrace Basin, Turkey

The Thrace Basin that is located in northwestern Turkey contains sandstone and carbonate reservoirs of Eocene and Oligocene age. Production and exploration activities are still underway. Mapping undrained sweet spots from seismic data is currently a challenge, so time lapse (4D) seismic is used to reduce the risk for new production and development drilling. We have evaluated the normalization and amplitude variation with offset (AVO) analysis of 3D-4D land seismic data in a gas producing field from which baseline and monitor surveys were acquired in 2002 and 2011, respectively. Through AVO analysis, intercept (A) and gradient (B) analysis was conducted, and fluid factor (FF) attribute maps were generated for the assessment of the remaining potential areas. Synthetic gathers were created for simulation of the AVO response, drained and undrained stages and compared with the corresponding 4D seismic data. The drainage of gas from the reservoir interval is evident from the difference maps between 2002 and 2011 seismic data. Both data sets were processed using an amplitude friendly processing sequence. This parallel processing was followed a mild data conditioning and crossequalization for reliable 4D interpretation. The 4D seismic data, especially land data, has low repeatability and requires conditioning to reduce the 4D noise. The 4D noise can be described as nonrepeatable noise, and any difference outside the reservoir zone is not related to production. A so-called crossequalization was applied to the base and the monitor data to bring out similarities so that they cancel out when differences of seismic data and its attributes indicated only the production results over the reservoir zones. As the available 4D data crossequalization software was implemented for stack data only, we created angle band stacks and crossequalized each angle band stack from the base and the monitor data cubes. Five angle band stacks from the base and the monitor prestack data cubes 0°–55° (0°–15°, 15°–25°, 25°–35°, 35°–45°, and 45°–55°) were crossequalized individually. The crossequalized angle band stacks were used in AVO analysis and AVO inversion to generate pore fill identifiers such as FF to map possible undrained zones after 10 years of production.

Stochastic inversion of seismic PP and PS data for reservoir parameter estimation

We have investigated the value of isotropic seismic converted-wave (i.e., PS) data for reservoir parameter estimation using stochastic approaches based on a floating-grain rock-physics model. We first performed statistical analysis on a simple two-layer model built on actual borehole logs and compared the relative value of PS data versus amplitude-variation-with-offset (AVO) gradient data for estimating the floating-grain fraction. We found that PS data were significantly more informative than AVO gradient data in terms of likelihood functions, and the combination of PS and AVO gradient data together with PP data provided the maximal value for the reservoir parameter estimation. To evaluate the value of PS data under complex situations, we developed a hierarchical Bayesian model to combine seismic PP and PS data and their associated time registration. We extended a model-based Bayesian method developed previously for inverting seismic PP data only, by including PS responses and time registration as additional data and PS traveltime and reflectivity as additional variables. We applied the method to a synthetic six-layer model that closely mimics real field scenarios. We found that PS data provided more information than AVO gradient data for estimating the floating-grain fraction, porosity, net-to-gross, and layer thicknesses when their corresponding priors were weak.

Estimation of pressure-saturation changes for unconsolidated reservoir rocks with highVP/VSratio

We find that conventional time-lapse seismic pressure-saturation discrimination methods become unstable for high [Formula: see text] ratios. Using first-order approximations in the amplitude variation with offset (AVO) gradient and intercept changes and in the rock-physics models increase the inaccuracy in pressure-saturation changes estimates. We propose a new method, based on a stepwise linear approximation to the intercept and gradient reflectivity changes, to estimate pressure and saturation changes. The applicability of the new method is tested on synthetic data over a range of 0%–50% gas saturation and 0–3.5 MPa pore-pressure changes. The new method is more consistent and provides better estimates compared with conventional methods. In the presence of random noise (up to 15%), the estimates are reasonably better for the new method. We use this new method to investigate the feasibility of pressure-saturation discrimination for a shallow unconsolidated sand reservoir in which an underground blowout occurred in 1989. We analyze a sand layer at 490-m depth that was charged by gas due to the blowout. Because of the shallow depth, the [Formula: see text] is expected to be higher than 2 before the blowout. Near- and far-offset time-lapse seismic data sets from 1988 and 1990 are used as input to estimate changes in AVO intercept and gradient and then changes in pressure and saturation. We find that the new method estimates more realistic pressure-saturation changes compared to the conventional one.

AVO-sensitive semblance analysis for wide-azimuth data

Conventional semblance-based moveout analysis models prestack reflection data with events that have hyperbolic move-out and no amplitude variation with offset (AVO). Substantial amplitude variation and even phase change with offset do not significantly compromise the semblance operator. However, polarity reversal associated with a change in the sign of the reflection coefficient may cause conventional semblance to fail. An existing modification of the semblance operator that takes amplitude variations into account (so-called AK semblance) is limited to narrow-azimuth data and cannot handle nonhyperbolic moveout at large offsets. We employ a 3D nonhyperbolic moveout inversion algorithm to extend the AK semblance method to wide-azimuth data recorded on long spreads. To preserve velocity resolu-tion, the ratio [Formula: see text] of the AVO gradient and intercept is kept constant within each semblance window. In the presence of azimuthal anisotropy, however, the parameter [Formula: see text] has to be azimuthally dependent. Synthetic tests confirm that distortions in moveout analysis caused by polarity reversals become more common for long-offset data. Conventional semblance produces substantial errors in the NMO ellipse and azimuthally varying anellipticity parameter [Formula: see text] not just for class 2 AVO response but also for some models with class 1 AVO. In contrast, the AK semblance algorithm gives accurate estimates of the moveout parameters even when the position of the polarity reversal varies with azimuth. The AK method not only helps to flatten wide-azimuth reflection events prior to stacking and azimuthal AVO analysis but also provides input parameters for the anisotropic geometrical-spreading correction.

Amplitude analysis with an optimal model-based linear AVO approximation: Part II — Field data example

AVO analysis can be conducted by estimating amplitude variation with offset (AVO) attributes from seismic prestack data and by characterizing the measured amplitude responses by the position of their projection in the attribute space. The most common AVO attributes are the intercept (zero-offset reflectivity) and AVO gradient. We have constructed an optimized, model-based linear AVO equation that is more accurate than usual AVO approximations. The parameters of this equation represent new AVO attributes that are more directly related to the information contained in seismic reflection amplitudes. We use these new AVO attributes to classify reflector responses from field data. Five seismic facies are defined that are characterized by differentdistributions of seismic parameters. Nine reflector classes are formed by associating appropriate pairs of facies. The expected locations of the different reflector classes in the space of optimized attributes are found by modeling and are used to derive a classification scheme. This scheme is applied to sections of optimized attributes calculated from the prestack data, leading to a vertical section showing the distribution of most probable facies in an area containing a sand reservoir. We compare the new approach to classification with intercept and gradient. The new method is more robust and less sensitive to the number of attributes (two or three) used for classification. It offers an optimal, flexible, and robust way of extracting the information contained in reflection amplitudes by simple linear AVO equations.

Fracture-porosity inversion from P-wave AVOA data along 2D seismic lines: An example from the Austin Chalk of southeast Texas

Vertical aligned fractures can significantly enhance the horizontal permeability of a tight reservoir. Therefore, it is important to know the fracture porosity and direction in order to develop the reservoir efficiently. P-wave AVOA (amplitude variation with offset and azimuth) can be used to determine these fracture parameters. In this study, I present a method for inverting the fracture porosity from 2D P-wave seismic data. The method is based on a modeling result that shows that the anisotropic AVO (amplitude variation with offset) gradient is negative and linearly dependent on the fracture porosity in a gas-saturated reservoir, whereas the gradient is positive and linearly dependent on the fracture porosity in a liquid-saturated reservoir. This assumption is accurate as long as the crack aspect ratio is less than 0.1 and the ratio of the P-wave velocity to the S-wave velocity is greater than 1.8 — two conditions that are satisfied in most naturally fractured reservoirs. The inversion then uses the fracture strike, the crack aspect ratio, and the ratio of the P-wave velocity to the S-wave velocity to invert the fracture porosity from the anisotropic AVO gradient after inferring the fluid type from the sign of the anisotropic AVO gradient. When I applied this method to a seismic line from the oil-saturated zone of the fractured Austin Chalk of southeast Texas, I found that the inversion gave a median fracture porosity of 0.21%, which is within the fracture-porosity range commonly measured in cores from the Austin Chalk.

Factors facilitating or limiting the use of AVO for coal-bed methane

There are similarities and differences in employing amplitude variation with offset (AVO) to explore for gas-sand reservoirs, as opposed to coal-bed methane (CBM) reservoirs. The main similarity is that large Poisson’s ratio contrasts, resulting in AVO gradient anomalies, are expected for both kinds of reservoirs. The main difference is that cleating and fracturing raise the Poisson’s ratio of a coal seam as it improves its reservoir potential for CBM, while gas always lowers the Poisson’s ratio of a sandstone reservoir. The top of gas sands usually has a negative AVO gradient, leading to a class one, two, or three anomaly depending on the impedance contrast with the overlying caprock. On the other hand, the top of a CBM reservoir has a positive AVO gradient, leading to a class four anomaly. Three environmental factors may limit the usage of AVO for CBM reservoirs: the smaller contrast in Poisson’s ratio between a CBM reservoir and its surrounding rock, variations in the caprock of a specific CBM reservoir, and the fact that CBM is not always free to collect at structurally high points in the reservoir. However, other factors work in favor of using AVO. The strikingly high reflection amplitude of coal improves signal/noise ratio and hence the reliability of AVO measurements. The relatively simple characteristics of AVO anomalies make them easy to interpret. Because faults are known to improve the quality of CBM reservoirs, faults accompanied by AVO anomalies would be especially convincing. A 3D-AVO example offered in this paper shows that AVO might be helpful to delineate methane-rich sweet spots within coal seams.

Coherence methods in mapping AVO anomalies and predicting P‐wave and S‐wave impedances

ABSTRACTFilters for migrated offset substacks are designed by partial coherence analysis to predict ‘normal’ amplitude variation with offset (AVO) in an anomaly free area. The same prediction filters generate localized prediction errors when applied in an AVO‐anomalous interval. These prediction errors are quantitatively related to the AVO gradient anomalies in a background that is related to the minimum AVO anomaly detectable from the data. The prediction‐error section is thus used to define a reliability threshold for the identification of AVO anomalies. Coherence analysis also enables quality control of AVO analysis and inversion. For example, predictions that are non‐localized and/or do not show structural conformity may indicate spatial variations in amplitude–offset scaling, seismic wavelet or signal‐to‐noise (S/N) ratio content. Scaling and waveform variations can be identified from inspection of the prediction filters and their frequency responses. S/N ratios can be estimated via multiple coherence analysis.AVO inversion of seismic data is unstable if not constrained. However, the use of a constraint on the estimated parameters has the undesirable effect of introducing biases into the inverted results: an additional bias‐correction step is then needed to retrieve unbiased results. An alternative form of AVO inversion that avoids additional corrections is proposed. This inversion is also fast as it inverts only AVO anomalies. A spectral coherence matching technique is employed to transform a zero‐offset extrapolation or near‐offset substack into P‐wave impedance. The same technique is applied to the prediction‐error section obtained by means of partial coherence, in order to estimate S‐wave velocity to P‐wave velocity (VS/VP) ratios. Both techniques assume that accurate well ties, reliable density measurements and P‐wave and S‐wave velocity logs are available, and that impedance contrasts are not too strong. A full Zoeppritz inversion is required when impedance contrasts that are too high are encountered. An added assumption is made for the inversion to the VS/VP ratio, i.e. the Gassmann fluid‐substitution theory is valid within the reservoir area. One synthetic example and one real North Sea in‐line survey illustrate the application of the two coherence methods.

Modeling offset‐dependent reflectivity for time‐lapse monitoring of water‐flood production in thin‐layered reservoirs

The objective of this case study is to predict whether 5 years of water‐flood production from a thinly layered Gulf of Mexico reservoir will change its seismic amplitude‐variation‐with‐offset (AVO) response in a detectable manner. Density and velocity profiles were computed from in situ wireline logs for 100% oil, gas, and brine saturations and for a 5‐year prediction that was based on a fluid‐flow and production simulation. Analytical AVO curves for simple half‐space models did not match AVO curves extracted from synthetic seismograms computed with a full‐waveform layer‐stack algorithm. Several different amplitude corrections were tried to reduce the AVO curves from the synthetic data to the analytical ones, but, ultimately, none was deemed satisfactory. Instead, AVO change attributes based on relative changes, polarity changes, or ratios were used. Attributes based on the change of AVO gradient were perceived to be most diagnostic of the water flood, but they were also overly sensitive to interference noise and amplitude correction errors. For field data from the study area, a large decrease in intercept magnitude may be the best indicator of the waterfront.

AVO polarization and hodograms: AVO strength and polarization product

An alternative approach to identifying amplitude‐variation‐with offset (AVO) anomalies is to consider the AVO polarization in the AVO intercept–AVO gradient (A‐B) plane. This method does not require deviations or separations from a background trend exhibited in traditional crossplots such as intercept‐gradient (A‐B) or near trace–far trace (N‐F). A benefit of the hodogram or polarization method is that the wavelet is taken into consideration. Crossplotted intercept and gradient are polarized along a “background trend” for nonanomalous events and at angles different from the “background trend” for anomalous events. This allows recognition of anomalous behavior otherwise buried in a background.Attributes resulting from this methodology include (1) the polarization angle, (2) the polarization angle difference, (3) the AVO strength, (4) the polarization product, and (5) the linear‐correlation coefficient. These different attributes can then be used to enhance AVO interpretation. Synthetic modeling for a succession of gas and brine layers encased in shale units indicates that the method can potentially be an effective hydrocarbon indicator. Application of the method to a real seismic dataset shows polarization anomalies associated with hydrocarbons.

Velocity analysis in the presence of amplitude variation

Conventional semblance velocity analysis is equivalent to modeling prestack seismic data with events that have hyperbolic moveout but no amplitude variation with offset (AVO). As a result of its assumption that amplitude is independent of offset, this method might be expected to perform poorly for events with strong AVO—especially for events with polarity reversals at large offset, such as reflections from tops of some class 1 and class 2 sands. We find that substantial amplitude variation and even phase change with offset do not compromise the conventional semblance measure greatly. Polarity reversal, however, causes conventional semblance to fail. The semblance method can be extended to take into account data with events that have amplitude variation, expressed by AVO intercept and gradient (i.e., the Shuey approximation). However, because of the extra degrees of freedom introduced in AVO‐sensitive semblance, resolution of the estimated velocities is decreased. This is because the data can be modeled acceptably with a range of combined erroneous velocity and AVO behavior. To address this problem, in addition to using the Shuey equation to describe the amplitude variation, we constrain the AVO parameters (intercept and gradient) to be related linearly within each semblance window. With this constraint we can preserve velocity resolution and improve the quality of velocity analysis in the presence of amplitude and even polarity variation with offset. Results from numerical tests suggest that the modified semblance is accurate in the presence of polarity reversals. Tests also indicate, however, that in the presence of noise, the signal peak in conventional semblance has better standout than does that in the modified semblance measures.