AVO inversion based on generalized extreme value distribution with adaptive parameter estimation

It has been more than three years since The Leading Edge last published a special section on amplitude variation with offset (AVO) inversion, and interest in the subject remains strong. This past spring, SEG hosted a joint symposium in Houston, Texas, on the “Resurgence of seismic inversion,” and the body of talks and case studies demonstrated the method's continued relevance to making impactful drilling decisions. Despite this, and despite AVO inversion's position as a mature and well-established technique, there are an abundance of examples in which inaccurate AVO predictions have led to drastic failures at the drill bit. This highlights the challenges that still exist in the successful execution of such investigations and makes the subject occasionally controversial and certainly fraught with data-quality and best-practice considerations. In this vein, the special section presented here offers examples of the broad sweep of considerations and methods relevant to enabling successful AVO inversion and the interpretation of its products, as well as case studies that demonstrate how application of the technique can be impactful all the way through to appraisal and field development programs.

Solutions to the amplitude variation with offset (AVO) inverse problem are inherently nonunique. Thus, estimating the range of potential solutions is crucial. For this reason, uncertainty inversion is more appropriate than deterministic AVO inversion. However, most studies on deep learning (DL)-based inversion focus on deterministic prediction. In general, there are few studies on uncertainty inversion, mainly focused on poststack seismic data. In this study, we propose a DL-based AVO uncertainty inversion method based on an improved variational Bayesian neural network (VBNN) for predicting multiple elastic parameters. Moreover, to mitigate the issue of insufficient labeled data in inversion tasks, we combine the improved VBNN with a semi-supervised learning framework. Synthetic data experiments demonstrate that the proposed method exhibits higher accuracy and robustness to noisy seismic data than the well-known traditional Bayesian linearized inversion (BLI) method. The proposed method also has slightly higher inversion accuracy than the state-of-the-art improved-hybrid-seismic-prior-guided neural network (IHGNN). Moreover, the uncertainty estimation confirms that the proposed method can explore potential solutions to the AVO inverse problem more effectively and reasonably than the comparison methods. Furthermore, field data AVO inverse experiments verify that the proposed method can obtain reasonable predicted results and effectively reveal uncertainty in the inversion results.

In 2008, WesternGeco acquired the 5000 sq/km Keystone multi-client survey located offshore between the giant Io/Jansz and Scarborough gas fields on Australia’s NW shelf, in order to image potential gas reservoir’s at multiple stratigraphic levels within complex geology. Searching for leads and prospects within such a large volume using seismic data alone is traditionally a time-consuming process. An efficient prospect screening tool has been produced in the form of a well log-calibrated gas sand probability cube derived from amplitude variation with offset (AVO) inversion outputs. Using advanced visualisation techniques the data can then be rapidly interrogated highlighting a number of direct hydrocarbon indicators (DHI's) and potential prospects. AVO and quantitative interpretation have played a key role in a number of discoveries in this area, particularly within the Triassic.

Amplitude variation with offset (AVO) inversion is a typical ill-posed inverse problem. To obtain a stable and unique solution, regularization techniques relying on mathematical models from prior information are commonly used in conventional AVO inversion methods (hence the name model-driven methods). Due to the difference between prior information and the actual geology, these methods often have difficulty achieving satisfactory accuracy and resolution. We have developed a novel data-driven inversion method for the AVO inversion problem. This method can effectively extract useful knowledge from well-log data, including sparse dictionaries of elastic parameters and sparse representation of subsurface model parameters. Lateral continuity of subsurface geology allows for the approximation of model parameters for a work area using the learned dictionaries. Instead of particular mathematical models, a sparse representation is used to constrain the inverse problem. Because no assumption is made about the model parameters, we consider this a data-driven method. The general process of the algorithm is as follows: (1) using well-log data as the training samples to learn the sparse dictionary of each elastic parameter, (2) imposing a sparse representation constraint on the objective function, making the elastic parameters be sparsely represented over the learned dictionary, and (3) solving the objective function by applying a coordinate-descent algorithm. Tests on several synthetic examples and field data demonstrate that our algorithm is effective in improving the resolution and accuracy of solutions and is adaptable to various geologies.

Field records for small source-receiver offsets often contain intensive converted PS-waves that may be caused by the influence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) for a horizontal interface separating two transversely isotropic (TI) media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients [Formula: see text] and [Formula: see text] vanish when both half-spaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values that exceed 0.1, even if the anisotropy strength is moderate. To study the influence exerted by the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropyapproximations for the PS-wave reflection coefficients and com-pare them with exact numerical results. In particular, the analytic solutions show that the contributions made by the Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-axis tilt [Formula: see text] to the coefficients [Formula: see text] and [Formula: see text] can be expressed through the first derivative of the P-wave phase velocity at normal incidence. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are influenced primarily by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the [Formula: see text] and [Formula: see text] modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion that is based on the exact reflection coefficients.

SUMMARY In this paper, we investigate the use of artificial neural networks (ANN) for amplitude variation with offset (AVO) analysis. Prospecting using AVO is dependent on the fact that the difference between near-offset and far-offset responses can be a hydrocarbon indicator. Neural networks are good at “learning” and “predicting” such relationships and can thus be trained to learn the relationship between, for example, a near-offset partially stacked trace and a far-offset partially stacked trace for background (non-hydrocarbon bearing rocks). Far traces can then be predicted by this learned relationship and the difference between observed and ANN predicted traces can potentially be used as a hydrocarbon indicator. An advantage of this method over conventional cross-plotting techniques is that it can be made insensitive to incorrect normal moveout corrections.

An improved artificial immune algorithm is proposed for geophysical P-wave amplitude variation with offset (AVO) inversion. In this paper, the algorithm is described and implemented. The orthogonal crossover is used to generate the initial population and the elitist-crossover is adopted to add the good patterns of the population. The hybrid mutation method is presented to increase the ability of local and global optimization. The improved immune algorithm is then applied to earth interface models of Mexican gulf for AVO inversion. The experimental results show that the improved algorithm is of high precision than the traditional immune algorithm.

Seismic shear waves have been used in oil and gas exploration for decades. A 2D seismic shear wave inline was acquired in the Sanhu area, located in the Qaidam Basin in western China. Although the acquired shear wave data showed high resolution and comparable bandwidth to the compressional wave, it was contaminated by various types of noise, including linear noise, single-frequency noise, and especially internal multiples. Internal multiples seriously compromise the primary reflections at both near offset and far offset and are difficult to suppress. This paper presents a case study of noise attenuation for the seismic shear wave. First, single-frequency noise and linear noise are attenuated through filtering methods. Then, two methods (the Radon transform and the frequency-wavenumber (F-K) filtering) are evaluated for their effectiveness in multiple suppression and amplitude preservation. The results indicate that both methods successfully reduce long-period multiples at the far offset, enhancing the signal-to-noise ratio. We show that F-K filtering retains the characteristic ‘strong–weak–strong’ amplitude variation in the SV-SV-wave data gather, making it preferable for subsequent amplitude variation with offset analysis and inversion. Finally, a wave equation-based multiple suppression inversion method is used to suppress near-offset internal multiples. This involves iteratively predicting internal multiples and adaptively subtracting them from the original data. Stacked sections of different offsets are compared to demonstrate the de-multiple result, and the result is also validated by the improvement of well calibration with the seismic shear wave data.

Most existing amplitude variation with offset (AVO) inversion methods are based on the Zoeppritz’s equation or its approximations. These methods assume that the amplitude of seismic data depends only on the reflection coefficients, which means that the wave-propagation effects, such as geometric spreading, attenuation, transmission loss, and multiples, have been fully corrected or attenuated before inversion. However, these requirements are very strict and can hardly be satisfied. Under a 1D assumption, reflectivity-method-based inversions are able to handle transmission losses and internal multiples. Applications of these inversions, however, are still time-consuming and complex in computation of differential seismograms. We have evaluated an inversion methodology based on the vectorized reflectivity method, in which the differential seismograms can be calculated from analytical expressions. It is computationally efficient. A modification is implemented to transform the inversion from the intercept time and ray-parameter domain to the angle-gather domain. AVO inversion is always an ill-posed problem. Following a Bayesian approach, the inversion is stabilized by including the correlation of the P-wave velocity, S-wave velocity, and density. Comparing reflectivity-method-based inversion with Zoeppritz-based inversion on a synthetic data and a real data set, we have concluded that reflectivity-method-based inversion is more accurate when the propagation effects of transmission losses and internal multiples are not corrected. Model testing has revealed that the method is robust at high noise levels.

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.

The amplitude Variations with Offset (AVO) technique is extensively used in hydrocarbon exploration and production for de-risking of the prospect before drilling. The interpretation of AVO results brings more confidence in the presence or absence of hydrocarbon. The AVO and Direct Hydrocarbon Indicator (DHI) analysis have their own inherent limitations. Therefore, to ensure the presence of true AVO in seismic, other attribute supports are crucial. The present prospect in this study was deposited as a channel-levee complex in the shelf-slope of the Krishna-Godavari basin. There is evidence of false AVO within this complex and thus additional attributes were used in this study to support the AVO analysis. The conventional AVO analysis shows the presence of Class-III AVO for a probable reservoir in seismic. However, it is unable to ensure the presence of hydrocarbon in the stacked reservoir unit. The spectral AVO technique was used to check AVO response at low frequencies for laminated and stacked reservoir units. Additionally, seismic attenuation and dispersion attribute studies were incorporated into the de-risking analysis. The drill result showed two distinct reservoir intervals in this prospect, which validated the predrill interpretation. This integrated approach added significant value in de-risking the prospect using AVO and other seismic attributes in complex geologic setups.

Summary There are examples of hydrocarbon accumulations in the Exmouth sub-basin that exhibit anomalous amplitude and AVO behaviour which are related to the presence of hydrocarbons. These include the Scarborough gas field, the Jupiter and Vinck gas discoveries, and the Macedon-Pyrenees oil and gas field. In these cases, the pre-drill recognition of anomalous amplitude behaviour aided the decisions to drill the discovery wells. In the case of the Macedon-Pyrenees oil and gas field, high seismic amplitudes caused by gas were recognised pre-drill within the Windalia Radiolarite unit. This unit overlies the Barrow Group reservoir section at the Macedon-Pyrenees field. The mapping of gas-related seismic 'brightening' of the Windalia Radiolarite unit provided an independent check on the depth conversion of the structure and was a key factor in promoting the structure as a drillable prospect. Since drilling the discovery well, seismic ‘brightening’ of the Windalia Radiolarite has been recognised over a number of other fields. This fact provides an indication that valid structural closure exists at the Barrow Group, and indicates the possibility of the presence of hydrocarbons. Further seismic analysis has concentrated on the recognition of gas-related brightening and amplitude variation with offset (AVO) behaviour of the Barrow Group reservoir sands. This work has been carried out to aid exploration in other parts of the WA-155-P exploration permit and in surrounding areas of the Barrow and Exmouth sub-basins. The results of an acoustic impedance study utilising well data have shown that the Macedon sands sub-unit of the Barrow Group should brighten significantly when charged with gas. AVO modelling using recorded P-wave and S-wave data has shown a change in AVO behaviour between Macedon sands filled with gas, and similar sands filled with brine. Detailed reprocessing of seismic data across the Macedon-Pyrenees field has been carried out to see whether the modelled behaviour of gas-filled Macedon sands could be recognised on the seismic data. Seismic data quality has been improved significantly through reprocessing and a strong relationship can now be seen between seismic brightening and gas-filled Macedon sands.

Amplitude variations with offset (AVO) analysis which is primarily applied to the prestack seismic gathers has been a topic of great interests as it is expected to provide us with more confident indication of hydrocarbon accumulation than simple investigation of the specific anomalies in the stacked seismic section does.AVO analysis was evaluated for potential indicator of gas sand reservoirs on the seismic data of an area onshore East Malaysia of which the stratigraphy is dominated by sand-shale sequence under deltaic environment of Tertiary age. There are two prospects of interests of which one has been confirmed that hydrocarbon be accumulated in a number of sandstone reservoirs and the other remains untested. AVO has been modeled at the tops of three gas reservoirs, which indicates significant increases in amplitude with offset (AVO anomalies) to be expected for all gas reservoirs.Seismic data was processed to be suitable for AVO analysis. Specific data conditioning and enhancement techniques to preserve amplitudes of the data were employed. These techniques include true amplitude FK filtering and time and space variant offset dependent residual amplitude correction.AVO was analyzed by investigating restricted angle stack sections and partially stacked angle traces of the processed data. Significant AVO anomalies were correlated with some of the tops of hydrocarbon reservoirs particularly gas reservoirs which exhibited considerably high amplitudes on stacked section. However, any significant AVO anomalies were not observed in the seismic data acquired on the untested structure.

The removal of multiples without simultaneously distorting primaries is a difficult aspect of demultiple techniques. We present a new demultiple approach based on detecting and estimating localized coherent signals (multiples and primaries) on stacking velocity spectra. The trajectories of localized coherent signals are determined from the velocity and zero‐offset traveltime; amplitude variations with offset (AVO) are modeled from known AVO properties. We estimate primaries and multiples from stacking velocities by polynomial approximation of the amplitude along the hyperbolic path. This procedure lets us predict multiples on near‐offsets using the multiples on other offsets. To further preserve the amplitude of the rebuilt primaries, stronger multiples, which are detected according to a multiple‐to‐primary energy ratio, are estimated and subtracted from the seismic data before estimating the primaries. Because the estimation of primaries and multiples is done locally in the time–space domain, our method is efficient. Comparisons are made between our method and conventional Radon filters. The results of both synthetic and field seismic data show that our method is very promising in practical applications because it can suppress the multiples efficiently while preserving the primary amplitudes well.

Exploration programs in deepwater Tertiary basins (e.g., the Gulf of Mexico) typically rely on bright‐spot and amplitude variation with offset (AVO) technology to help identify oil‐ and gas‐charged sands. The reliance on these attributes, along with the high cost of exploration programs in deepwater environments, has driven the need to examine the limitations of these technologies and to build robust models for the conditions under which AVO is useful as a fluid and/or lithology indicator. We build subregional AVO background trends for both brine‐ and gas‐saturated sands from several wells from the eastern deepwater Gulf of Mexico. These trends are built from the depth dependencies of velocities and densities for both shale and sands (brine saturated). Simple models of AVO gradient and intercept are constructed as a function of depth below the mud line. Sand and shale properties show little velocity contrast, justifying the interpretation of these data in the context of linearized AVO models. In addition to the in‐situ brine response, the response to gas is also calculated. These trend models indicate that the AVO response is suppressed (although still positive) below a depth of approximately 10 000 ft below the mud line. Even optimistic porosity modeling (sand porosity >30°) does not substantially change this conclusion. An important corollary is that the absence of a strong AVO anomaly at these deeper depths cannot be used with confidence when ruling out hydrocarbon presence. This observation also highlights the need to crossplot attributes to best predict hydrocarbon presence. Velocity data collected as part of this study are also used to generate a local shear velocity estimator for sands and shale. These shear estimators are similar in form to other published estimators, but minor differences in coefficients may become important in AVO modeling.