Amplitude Versus Angle Inversion Research Articles

Amplitude-Versus-Angle (AVA) Inversion for Pre-Stack Seismic Data with L0-Norm-Gradient Regularization

Amplitude-versus-angle (AVA) inversion for pre-stack seismic data is a key technology in oil and gas reservoir prediction. Conventional AVA inversion contains two main stages. Stage one estimates the relative change rates of P-wave velocity, S-wave velocity and density, and stage two obtains the P-wave velocity, S-wave velocity and density based on their relative change rates through trace integration. An alternative way merges these two stages to estimate P-wave velocity, S-wave velocity and density directly. This way is less sensitive to noise in seismic data compared to conventional two-stage AVA inversion. However, the regularization for the direct AVA inversion is more complex. To regularize this merged inverse problem, the L0-norm-gradient of P-wave velocity, S-wave velocity and density was used. L0-norm-gradient regularization can provide inversion results with blocky features to make formation interfaces and geological edges precise. Then, L0-norm-gradient regularized AVA inversion was performed on the synthetic seismic traces. Next, a real seismic data line that contains three partial angle stack profiles was used to test the practice application. The inversion results from synthetic and real seismic data showed that L0-norm-gradient regularized AVA inversion is an effective way to estimate P-wave velocity, S-wave velocity and density.

Geostatistical Seismic Rock Physics AVA Inversion With Data-Driven Elastic Properties Update

Geostatistical seismic rock physics amplitude-versus-angle (AVA) inversion allows the joint prediction of rock and fluid properties from seismic reflection data. In these seismic inversion methods, the model perturbation and update occur iteratively in the petrophysical domain. A facies-dependent precalibrated rock physics model is applied to the simulated rock properties to calculate elastic properties. Synthetic seismic reflection data are computed from these elastic models. The rock physics models are calibrated at the well locations and act as the link between the rock and the elastic domains, remaining unchanged during the inversion procedure: the convergence of the inversion and the geological plausibility of the inverted rock property models depend on the quality of the calibration and available well-log data. To overcome this limitation, account for calibration errors and geological scenarios not sampled at the well locations, we introduce an iterative geostatistical seismic AVA inversion where the elastic predictions from a facies-dependent precalibrated rock physics model are updated iteratively, based on the mismatch between observed and synthetic data. We assume an initial <inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <i>priori</i> uncertainty in the rock physics model and update it iteratively based on the data mismatch. The proposed method is applied in a 1-D synthetic example to illustrate the concept and validate the method. Then, we apply the inversion method to a 3-D real data set. In this application, we use a blind well to assess locally the performance of the technique. The results show that the parameters of space exploration is not compromised by the rock physics model&#x2019;s uncertainty.

True Amplitude Angle Gathers from Reverse Time Migration by Wavefield Decomposition at Excitation Amplitude Time

Reservoir parameter estimation is one of the goals of amplitude-versus-angle (AVA) inversion and angle-domain common image gathers are the basis of AVA inversion. Therefore, the accuracy of kinematic and kinetic information on angle gathers is very important for reservoir characterization. Reverse time migration is one of the most physically accurate migration method. Generating angle gathers from reverse time migration with the Poynting vector method is very efficient. However, due to inaccurate angle measurement and uneven illumination, angle gathers calculated by the Poynting vector method are often not suitable for AVA inversion. In this paper, we propose an efficient method of angle gathers with accurate angular information and amplitude from reverse time migration. We firstly decompose source and receiver wavefield to their up-going and down-going parts by using analytic wavefield. We calculate propagation directions for source down-going wavefield and receiver up-going wavefield by the Poynting vector method and form the angle gathers with these angle information and decomposed wavefield. To reduce memory storage and improve computational efficiency, we decompose wavefield at excitation amplitude time by using a local spatial Fourier transform. We also use a spatial smoothed Poynting vector to improve the stability of angle measurement. We apply an illumination compensation image condition to recover the true amplitude. Numerical examples on Marmousi model and the SEAM two-dimensional (2D) model demonstrate the advantages of our proposed method. The angle gathers based on our method are cleaner with more focus on events energy and better continuity, suffering from less low-frequency noise in the shallow parts and with a distinct cutoff at large angle where reflection terminates. At last, we demonstrate the effectiveness of proposed method on a 2D marine field data example.

Discrete cosine transform for parameter space reduction in linear and non-linear AVA inversions

Geophysical inversions estimate subsurface physical parameters from the acquired data and because of the large number of model unknowns, it is common practice reparametrizing the parameter space to reduce the dimension of the problem. This strategy could be particularly useful to decrease the computational complexity of non-linear inverse problems solved through an iterative sampling procedure. However, part of the information in the original parameter space is lost in the reduced space and for this reason the model parameterization must always constitute a compromise between model resolution and model uncertainty. In this work, we use the Discrete Cosine Transform (DCT) to reparametrize linear and non-linear elastic amplitude versus angle (AVA) inversions cast into a Bayesian setting. In this framework the unknown parameters become the series of coefficients associated to the DCT base functions. We first run linear AVA inversions to exactly quantify the trade-off between model resolution and posterior uncertainties with and without the model reduction. Then, we employ the DCT to reparametrize non-linear AVA inversions numerically solved through the Differential Evolution Markov Chain and the Hamiltonian Monte Carlo algorithm. To draw general conclusions about the benefits provided by the DCT reparameterization of AVA inversion, we focus the attention on synthetic data examples in which the true models have been derived from actual well log data. The linear inversions demonstrate that the same level of model accuracy, model resolution, and data fitting can be achieved by employing a number of DCT coefficients much lower than the number of model parameters spanning the unreduced space. The non-linear inversions illustrate that an optimal model compression (a compression that guarantees optimal resolution and accurate uncertainty estimations) guarantees faster convergences toward a stable posterior distribution and reduces the burn-in period and the computational cost of the sampling procedure.

Including edge preserving smoothing filter within blocky- constrained, target-oriented AVA inversions

Resolving thin layers and achieve focused layer boundaries is one of the major challenges in seismic inversion. This translates into recovering a blocky solution with sparse spatial derivatives of model parameters. Here, we present two iterative focusing regularization techniques for target-oriented Amplitude Versus Angle (AVA) inversion. Target-oriented means that only the AVA responses of the reflections of interest are inverted for the simultaneous estimation of P-wave, S-wave and density reflectivities. The first approach imposes Cauchy constraints on the spatial model derivatives whereas, the second is inspired by the minimum gradient support regularization. Both the implemented algorithms enhance their focusing and edge-preserving abilities by exploiting an Edge Preserving Smoothing (EPS) filter that is used to compute both the model constraints and the model update. We include a-priori model information into the inversion kernel to guide the convergence of the algorithms toward physically plausible solutions. The two approaches are compared against the standard Bayesian inversion that simply considers Gaussian distributed model parameters, and with the well-known edge-preserving method that assumes Cauchy-distributed derivative of model parameters. For the lack of available field seismic data, we limit the attention to synthetic inversion experiments in which we simulate different signal-to noise (S/N) ratios. The inversion tests prove the suitability of the two proposed approaches for target-oriented AVA inversion and demonstrate their focusing and anti-noise abilities. In particular, the two implemented algorithms outperform the standard Bayesian inversion and the Cauchy approach in cases of low S/N ratios. The two implemented methods are also extremely flexible and can be applied to other linear or non-linear geophysical inverse problems.

Prestack Stochastic Frequency-Dependent Velocity Inversion With Rock-Physics Constraints and Statistical Associated Hydrocarbon Attributes

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.

Estimation of reservoir properties from seismic data through a Markov Chain Monte Carlo-AVA inversion algorithm

We formulate the amplitude versus angle (AVA) inversion in terms of a Markov Chain Monte Carlo (MCMC) algorithm and apply it for reservoir characterisation and litho-fluid facies prediction in offshore Nile Delta. A linear empirical rock physics model is used to link the petrophysical properties (porosity, water saturation and shaliness) to the elastic attributes (P-wave velocity, S-wave velocity and density), whereas the exact Zoeppritz equations are used to convert the elastic properties into AVA responses. The exact Zoeppritz equations allow us to take advantage of the long offset seismic acquisition and thus to consider a wide range of incidence angles in the inversion. The proposed algorithm reliably estimates the non-uniqueness of the solution that is the uncertainties affecting the estimated subsurface characteristics (both in terms of litho-fluid facies and petrophysical properties), taking into consideration the uncertainties in the prior information, the uncertainties in the estimated rock-physics model and the errors affecting the observed AVA responses. A blind test, based on available well log information, demonstrates the applicability of the proposed method and the reliability of the results. In addition, comparisons between the results provided by the implemented MCMC algorithm with those yielded by a linear AVA inversion and an analytical approach to facies prediction, show the benefits introduced by wide-angle reflections in better constraining the inverted parameters and in attenuating the noise in the predicted subsurface models.

Probabilistic estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical reformulation of the Zoeppritz equations

We apply a target-oriented amplitude versus angle (AVA) inversion to estimate the petrophysical properties of a gas-saturated reservoir in offshore Nile Delta. A linear empirical rock-physics model derived from well log data provides the link between the petrophysical properties (porosity, shaliness and saturation) and the P-wave, S-wave velocities and density. This rock-physics model, properly calibrated for the investigated reservoir, is used to re-parameterize the exact Zoeppritz equations. The so derived equations are the forward model engine of a linearized Bayesian AVA-petrophysical inversion that, for each data gather, inverts the AVA of the target reflections to estimate the petrophysical properties of the reservoir layer, keeping fixed the cap-rock properties. We make use of the iterative Gauss-Newton method to solve the inversion problem. For each petrophysical property of interest, we discuss the benefits introduced by wide-angle reflections in constraining the inversion and we compare the posterior probability distributions (PPDs) analytically obtained via a local linearization of the inversion with the PPDs numerically computed with a Markov Chain Monte Carlo (MCMC) method. It results that the porosity is the best resolved parameter and that wide-angle reflections effectively constrain the shaliness estimates but do not guarantee reliable saturation estimates. It also results that the local linearization returns accurate PPDs in good agreement with the MCMC estimates.

Amplitude-versus-angle inversion based on theL1-norm-based likelihood function and the total variation regularization constraint

In prestack seismic data, outlier errors occur and can negatively influence the outcome of the amplitude-versus-angle (AVA) inversion process. Hence, their effect needs to be minimized during AVA inversion. AVA inversion based on the [Formula: see text]-norm-based likelihood function is highly sensitive to outlier errors. In comparison, AVA inversion based on the [Formula: see text]-norm-based likelihood function is less affected by outlier errors, and for this reason we have used it with the total variation regularization method used as a constraint to invert discontinuities from geologic bodies. To ensure that the inversion results contain low-frequency components, prior information constraints from model parameters are added to the inverse objective function, which is then solved by the iterative reweighted least-squares method. Results of numerical tests and real-data examples from the application of this method indicate that the algorithm is strongly robust against noise, especially abnormal outlier errors, and that the results of the inversion are reasonable.

The limits of narrow and wide-angle AVA inversions for high Vp/Vs ratios: An application to elastic seabed characterization

Since its introduction in the oil and gas industry, amplitude versus angle (AVA) inversion has become a standard tool in deep hydrocarbon exploration. However, with the intensification of offshore construction activity, applications of this method have been extended to evaluate the elastic properties of seabed sediments and of the shallowest part of the subsurface. These regions are often characterized by undercompacted sediments with very low S-wave velocities (Vs) and high P-wave velocity to S-wave velocity (Vp/Vs) ratios. However, the importance of the Vp/Vs ratio is usually underrated in AVA inversion. In this study, we analyse the limits of the AVA method in cases of high Vp/Vs ratios and the benefits introduced by wide-angle reflections in constraining the inversion results. A simplified seabed model that is characterized by a high Vp/Vs ratio is used to study the influence of the elastic and viscoelastic parameters on the P-wave reflection coefficients and to compute the error function of the AVA inversion. In addition, a synthetic AVA inversion is performed on this simplified model, which enables us to apply the sensitivity analysis tools to the inversion kernel. These theoretical analyses show that in the case of high Vp/Vs ratios, the Vs contrast at the reflecting interface plays a very minor role in determining the P-wave reflection coefficients and that the viscoelastic effects can be neglected when only pre-critical angles are considered in the inversion. In addition, wide-angle reflections are essential to reducing both the cross-talk between the inverted elastic parameters and the uncertainties in the Vp and density estimations, but they are not sufficient to better constrain the Vs estimation. As an application to field data, we derive the elastic properties of the seabed interface by applying AVA inversion to a 2D seismic dataset from a well-site survey acquisition. The limited water depth, the maximum available source-to-receiver offset, and the high frequency content of the data allow two different ranges of incidence angles to be considered: 0–30° and 0–60°. The results of the field data inversion confirm the conclusions from the theoretical analysis.

Common‐Angle Gathers Based on Kirchhoff Pre‐Stack Time Migration

AbstractIn this paper we present the improved algorithm for common‐angle gathers based on Kirchhoff pre‐stack time migration. The algorithm can calculate relatively true incident angle under three‐dimensional circumstance, while the traditional ray‐parameter method could not gain the incident angle between incident ray and dipping reflector normal. Compared with straight‐ray Kirchhoff angle domain gathers method proposed in recent years, our method is able to extract much wider angle for taking interval velocity and ray bending into account. Moreover, we apply non‐hyperbolic moveout equation to calculate the travel time, thus the commonangle gathers are flatter at large angle than straight ray method. Efficient true‐amplitude weighting function as well as hit‐count correction is beneficial for AVA inversion. The results of synthetic model data have verified that, compared with angle gathers transformed from offset to angle domain with CMP gathers or CRP gathers after migration, common‐angle gathers based on Kirchhoff pre‐stack time migration have following advantages: much more accurate incident angle, the amplitude versus angle (AVA) is robust and clear. The real 3‐D data test shows that angle gathers provided with our method are beneficial for AVA analysis and AVA inversion, and could improve pre‐stack inversion's resolution.

Joint inversion of AVA data for elastic parameters by bootstrapping

A joint inversion method is developed to estimate the elastic constants of two elastic, homogeneous, isotropic media separated by a flat horizontal boundary. The method jointly uses P and S-converted wave reflection amplitude-versus-angle (AVA) data and seeks the Poisson's ratios of each layer, ratios of the densities and bulk modulus of the layers. The generalized linear inversion (GLI) method is used as a mathematical tool and the Zoeppritz equations defining the seismic energy partitioning at a boundary are used as the physical model. The P and S-converted wave velocity terms in the Zoeppritz equations were replaced by the bulk modulus ( k 1 , k 2 ) , Poisson's ratios ( σ 1 , σ 2 ) , and densities ( ρ 1 , ρ 2 ) of each layer. After expressing the equations in these six elastic constants, reflection coefficients of P and S-converted waves ( R pp , R ps ) are obtained as functions of ratios of bulk modulus and densities of the lower layer to those of the upper layer ( k 2 / k 1 and ρ 2 / ρ 1 ) and Poisson's ratios of the upper and lower layers ( σ 1 and σ 2 ) . Using the ratios of bulk modulus and densities, the number of unknown parameters is reduced from 6 to 4 and this improves the success of inversion. The other contribution is that the calculation of R pp and R ps and their derivatives with respect to elastic constants and their ratios in the inversion are calculated analytically and coded in the Fortran programming language. In this way, the approach has an important advantage among the other AVA inversion methods, which are mostly based on numerical solutions or approximations to the Zoeppritz equations. A bootstrapping method of statistical analysis is combined with the GLI method to find the most likely elastic parameters and their confidence limits for repeated inversions for a large number of times by rearranging the noise distribution of the AVA data.

Acoustic nonlinear amplitude versus angle inversion and data-driven depth imaging in stratified media derived from inverse scattering approximations

This paper presents a new theory for nonlinear direct amplitude versus angle (AVA) inversion and data-driven depth imaging for a depth-variable acoustic medium. The method which is derived by direct inversion of the forward model of acoustic single scattering requires no information of the velocity and density potentials (subsurface properties), except for the velocity and density of the uppermost layer which is the reference medium where the source and receiver are situated at a finite distance above the scattering medium. The vertically varying velocity and density of the scattering medium are estimated in a data-driven manner solely from the angle- and depth-dependent Born potential profile. The inversion method is obtained in three main steps. In step one, the Born potential profile is computed by constant-velocity imaging (migration) of the single scattering data in the time intercept-slowness domain. Generally, interfaces in the Born potential are severely mislocated in depth compared to the true potential. In step two, ‘squeezed’ depth-dependent velocity and density potentials are estimated by nonlinear direct AVA inversion of the Born potential after residual-moveout correction. Step three estimates the actual depth-dependent velocity and density potentials by stretching the squeezed potentials so that their interfaces are moved towards the correct depth. In the nomenclature of seismic processing, the three steps can be described by the sequence constant-velocity (partial) migration–inversion–residual migration. In contrast to conventional, velocity-dependent depth migration, which requires an accurate estimate of the velocities of the actual medium to obtain the proper image, the depth imaging in step three requires the squeezed actual velocity potential with interfaces matching those of the zero-angle Born potential depth profile. This is exactly the velocity potential that is found in step two.

Postmigration processing for AVA inversion

This paper demonstrates the importance of postprocessing the migrated images in amplitude versus angle (AVA) inversion analysis on prestack depth-migrated data. In so-called “kinematic” processing where only the traveltimes are used (NMO, DMO, prestack time or depth migration), the amplitude of the recorded signal is corrected by estimating the decay due to wave propagation in a layered homogeneous media. The reflectivity values are simply the amplitudes of preprocessed prestack CDPs or CIGs. We propose an alternative approach—process the data with a preserved amplitude prestack depth migration (PAPsDM) algorithm in which migration weights fully account for dynamic propagation effects and acquisition effects (Figure 1).

Multiangle, multiscale inversion of migrated seismic data

The relation between the angle‐dependent reflectivity of an interface in a target zone and the amplitude‐variation‐with‐offset (AVO) effects observed in the seismic data at the earth’s surface is complicated by many factors, as was pointed out in Ostrander’s classic paper (Geophysics, 1984). Some factors are “reflection related” (such as thin‐bed tuning, reflector curvature), others “propagation related” (such as geometrical spreading, transmission and/or anelastic losses), or “acquisition related” (such as source/receiver directivity, geophone coupling). Amplitude‐versus‐angle (AVA) inversion in a target zone can be carried out successfully only when these effects are taken into account, either by forward modeling or by stepwise processing prior to AVA inversion. In the Delphi research program, we opt for the latter. For example, by decomposing multicomponent ocean‐bottom measurements into P- and S-wave responses, the effects of receiver directivity are implicitly suppressed. Furthermore, the geometrical...