AVO Uncertainty Inversion Based on Multitask Variational Bayesian Neural Network

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.

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

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.

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.

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.

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.

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.

The conventional amplitude-variation-with-offset (AVO) inversion method based on the amplitude attribute of prestack gathers calculates the elastic parameters of underground media through the variation of amplitude with offset. However, when the underground medium is a thin interlayer, the tuning effect will occur, which is the aliasing phenomenon of amplitude at the reflection interface. The tuning effect makes the conventional AVO inversion method based on amplitude attributes difficult to solve the problem of thin interlayer recognition. In addition, the same reflection interface will have different AVO characteristics at different frequencies, whereas the frequency factor is not included in conventional AVO inversion methods. Two-stage neural network approaches based on deep learning are combined to improve the resolution of thin interlayers and to accurately invert the elastic parameters. For the first-stage neural network, a fully connected network is used to solve the inversion spectral decomposition problem. It can eliminate the thin interlayer tuning effect, effectively improve the resolution, and obtain reflection coefficients at different frequencies. For the second-stage neural network, a multichannel convolutional neural network is used to establish the mapping relationship between multifrequency reflection coefficients and elastic parameters, so that the multifrequency joint inversion of the elastic parameters could be realized. This procedure is applied to synthetic data (with and without noise) to indicate the resistance to noise interference of the two-stage deep-learning method. Compared with the method of directly predicting elastic parameters using seismic data and the conventional AVO inversion method, the two-stage deep-learning method can describe the elastic parameters of thin interbeds more accurately. The same procedure is applied to the field data, and the inversion results indicate that they can well match with the well-logging data. Hence, it is promising for practical applications.

Amplitude-variation-with-offset (AVO) inversion and neural networks (NN) are widely used to invert elastic parameters. With more constraints from well-log data, neural network-based inversion may estimate elastic parameters with greater precision and resolution than traditional AVO inversion; however, neural network approaches necessitate a massive number of reliable training samples. Furthermore, because the lack of low-frequency information in seismic gathers leads to multiple solutions of the inverse problem, both inversions rely heavily on proper low-frequency initial models. To mitigate the dependence of inversions on accurate training samples and initial models, we have adopted solving inverse problems with the recently developed invertible neural networks (INNs). Unlike conventional neural networks, which address the ambiguous inverse issues directly, INNs learn definite forward modeling and use additional latent variables to increase the uniqueness of solutions. Motivated by the newly developed neural networks, we adopt an INN-based AVO inversion method, which can reliably invert low- to medium-frequency velocities and densities with randomly generated easy-to-access data sets rather than trustworthy training samples or well-prepared initial models. Tests on synthetic and field data indicate that our method is feasible, antinoise capable, and practicable.

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.

Reservoir characterization has a leading role in the reservoir geophysics and reservoir management. Since the interests of the reservoir geophysics and reservoir managements are the elastic properties and reservoir properties of the subsurface rock for their purposes, a robust method is required for converting seismic data into elastic properties. Accordingly, by employing a rock physics model and using the inverted seismic data, one can describe the reservoir for purposes such as improvement in the production of the reservoir. In the present study, we employ one of the methods for converting the seismic data into the elastic properties. This method of inversion is known as simultaneous inversion, which is grouped in amplitude-variation-with-offset (AVO) inversion category. In this method, unlike the other methods of AVO inversion, the pre-stack seismic data are directly inverted into the elastic properties of the rock and an excellent lithology and fluid indicator (VP/VS) are provided. Then, this indicator is tested on one of the oilfields of the Persian Gulf. Moreover, by means of this method, one can locate the fluids contact and the lithological interlayers; also, by the inversion results, which are the cubes of the seismic properties of the rock, one can generate sections of the elastic properties of the rock such as Poisson’s ratio and Young modulus which are useful for geomechanical analysis. Therefore, this kind of method is a quick way for the prior analysis of the studied area.

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 [Formula: see text] of hydrocarbon‐bearing sediments normally deviates from the [Formula: see text] trend of the background rocks. This causes anomalous reflection amplitude variation with offset (AVO) in the seismic data. The estimation of these AVOs is inevitably affected by wave propagation effects and inversion algorithm limitations, such as thin‐bed tuning and migration stretch. A logical point is to determine the minimum [Formula: see text] change required for an anomalous AVO to be detectable beyond the background tuning and stretching effects. Assuming Ricker wavelet for the seismic data, this study addresses this point by quantifying the errors in the intercept/slope estimate. Using these results, two detectability conditions are derived. Denoting the background [Formula: see text] by γ and its variation by δγ, the thin‐bed parameter (thickness/wavelength) by ξ, the maximum background intercept closest to the AVO by |A|max, and the thin‐bed intercept value by |A|thinthe two conditions are [Formula: see text] [Formula: see text] for detectability against stretching and tuning plus stretching, respectively. Tests on synthetic data confirm their validity and accuracy. These conditions provide a quantitative guideline for evaluating AVO applicability and effectiveness in seismic exploration. They can eliminate some of the subjectivity when interpreting AVO results in different attribute spaces. To improve AVO detectability, a procedure is suggested for removing the tuning and stretching effects.

Accurate characterization of subsurface reservoirs is a core objective in hydrocarbon exploration and development. The quality of seismic reservoir characterization directly influences well placement, field development strategies, and reserve estimation workflows. When seismic inversion is constrained by limited bandwidth and tuning effects, thin beds are merged into composite responses, subtle facies transitions are obscured, and small-scale structural or stratigraphic features are either poorly resolved or completely masked. These limitations have direct operational consequences: missed pay intervals, incorrect mapping of reservoir connectivity, suboptimal placement of production and injection wells, and development plans burdened by unnecessary uncertainty. Challenges are especially acute in geologically heterogeneous settings where vertical and lateral variations occur at scales close to or below seismic tuning thickness. In these cases, the blending of reflectors caused by limited frequency content in the seismic data can obscure stratigraphic terminations, make thin impermeable baffles invisible, and reduce confidence in both qualitative and quantitative interpretations. The Jurassic Plover Formation in the Poseidon area of the Browse Basin, offshore North-West Australia, is a compelling example. Its interbedded sandstones, siltstones, and shales, deposited in variable-energy environments, form a complex internal architecture that strongly influences reservoir performance. Thin, laterally variable sand bodies and shale drapes exert significant control on fluid flow and sweep efficiency. In such settings, conventional post-stack inversion often reproduces regional impedance trends but fails to resolve the finer-scale architecture that governs production behavior. Over the past four decades, inversion methods have evolved considerably. Early deterministic acoustic impedance inversions, grounded in the convolutional model, provided a first step in transforming seismic amplitudes into impedance volumes for structural mapping and gross lithologic interpretation. Pre-stack inversion expanded capabilities by integrating amplitude variation with offset (AVO) information to estimate elastic parameters and improve lithology and fluid discrimination. Stochastic and geostatistical inversions sought to inject high-frequency detail through simulation, aiming to honor both seismic data and geologic plausibility. Spectral inversion and thin-bed reflectivity methods attempted to extend usable bandwidth and de-tune seismic responses, offering improvements in vertical resolution. Despite these advances, the vertical resolution achievable with most conventional methods remains fundamentally tied to the seismic bandwidth and physics of wave propagation (Russell and Hampson, 1991; Partyka et al., 1999). Features thinner than approximately one-quarter of the dominant wavelength are difficult to recover reliably, and any attempt to artificially increase resolution risks introducing noise or geological inconsistency without tight constraints.