Reflectivity Inversion Research Articles

Seismic Structure, Gravity Anomalies and Flexure Along the Emperor Seamount Chain

AbstractThe Hawaiian‐Emperor seamount chain in the Pacific Ocean has provided fundamental insights into hotspot generated intraplate volcanism and the long‐term strength of oceanic lithosphere. However, only a few seismic experiments to determine crustal and upper mantle structure have been carried out on the Hawaiian Ridge, and no deep imaging has ever been carried out along the Emperor seamounts. Here, we present the results of an active source seismic experiment using 29 Ocean‐Bottom Seismometers (OBS) carried out along a strike profile of the seamounts in the region of Jimmu and Suiko guyots. Joint reflection and refraction tomographic inversion of the OBS data show the upper crust is highly heterogeneous withPwave velocities <4–5 km s−1, which are attributed to extrusive lavas and clastics. In contrast, the lower crust is remarkably homogeneous with velocities of 6.5–7.2 km s−1, which we attribute to oceanic crust and mafic intrusions. Moho is identified by a strongPmParrival at offsets of 20–80 km, yielding depths of 13–16 km. The underlying mantle is generally homogeneous with velocities in the range 7.9–8.0 km s−1. The crust and mantle velocity structure has been verified by gravity modeling. While top of oceanic crust prior to volcano loading is not recognized as a seismic or gravity discontinuity, flexural modeling reveals a ∼5.0–5.5 km thick preexisting oceanic crust that is overlain by a ∼8 km thick volcanic edifice. Unlike at the Hawaiian Ridge, we find no evidence of magmatic underplating.

Seismic reflectivity inversion using an L1-norm basis-pursuit method and GPU parallelisation

Abstract Seismic reflectivity inversion problem can be formulated using a basis-pursuit method, aiming to generate a sparse reflectivity series of the subsurface media. In the basis-pursuit method, the reflectivity series is composed by large amounts of even and odd dipoles, thus the size of the seismic response matrix is huge and the matrix operations involved in seismic inversion are very time-consuming. In order to accelerate the matrix computation, a basis-pursuit method-based seismic inversion algorithm is implemented on Graphics Processing Unit (GPU). In the basis-persuit inversion algorithm, the problem is imposed with a L1-norm model constraint for sparsity, and this L1-norm basis-pursuit inversion problem is reformulated using a linear programming method. The core problems in the inversion are large-scale linear systems, which are resolved by a parallelised conjugate gradient method. The performance of this fully parallelised implementation is evaluated and compared to the conventional serial coding. Specifically, the investigation using several field seismic data sets with different sizes indicates that GPU-based parallelisation can significantly reduce the computational time with an overall factor up to 145. This efficiency improvement demonstrates a great potential of the basis-pursuit inversion method in practical application to large-scale seismic reflectivity inversion problems.

Application of sparse-layer inversion and harmonic bandwidth extension for a channel system in Southern Alberta, Canada

Sparse-layer reflectivity inversion decomposes a seismic trace into a limited number of simple layer responses and their corresponding reflection coefficients for top and base reflections. In contrast to sparse-spike inversion, the applied sparsity constraint is less biased against layer thickness and can thus better resolve thin subtuning layers. Application to a 3D seismic data set in Southern Alberta produces inverted impedances that have better temporal resolution and lateral stability and a less blocky appearance than sparse-spike inversion. Bandwidth extension harmonically extrapolated the frequency spectra of the inverted layers and nearly doubled the usable bandwidth. Although the prospective glauconitic sand tunes at approximately 37 m, bandwidth extension reduced the tuning thickness to 22 m. Bandwidth-extended data indicate a higher correlation with synthetic traces than the original seismic data and reveal features below the original tuning thickness. After bandwidth extension, the channel top and base are more evident on inline and crossline profiles. Lateral facies changes interpreted from the inverted acoustic impedance of the bandwidth-extended data are consistent with observations in wells.

Debiasing of seismic reflectivity inversion using basis pursuit de-noising algorithm

Seismic reflectivity inversion using basis pursuit de-noising algorithm (BPDN) produces sparse solutions by applying l1-norm regularization. Due to the presence of the regularization term, there is always a deviation between the solution obtained by BPDN and the true one. A debiasing step of “adding back the residual” was introduced into seismic reflectivity inversion using BPDN to reduce the deviation, so that the accuracy of seismic reflectivity inversion using BPDN is improved. The debiasing step is carried out using a moderately large trade-off factor by iteratively performing the fast iterative soft thresholding algorithm (FISTA) to solve the objective function of BPDN with the input updated by adding back the residual to the initial input. The solution obtained by using FISTA with incorporation of the debiasing step of “adding back the residual” is a better approximation of the true solution than the result obtained by using FISTA a single time. In addition, the debiasing step of “adding back the residual” is not limited to the number of nonzero components in the solution and can be used in a low signal-to-noise ratio circumstance. A multichannel inversion method was adopted to recover the acoustic impedance from the inverted reflection coefficient, and it gained good results both in numerical and field examples.

Seismic spectral sparse reflectivity inversion based on SBL-EM: experimental analysis and application

Abstract In this paper, we propose a new method of seismic spectral sparse reflectivity inversion that, for the first time, introduces Expectation-Maximization-based sparse Bayesian learning (SBL-EM) to enhance the accuracy of stratal reflectivity estimation based on the frequency spectrum of seismic reflection data. Compared with the widely applied sequential algorithm-based sparse Bayesian learning (SBL-SA), SBL-EM is more robust to data noise and, generally, can not only find a sparse solution with higher precision, but also yield a better lateral continuity along the final profile. To investigate the potential of SBL-EM in a seismic spectral sparse reflectivity inversion, we evaluate the inversion results by comparing them with those of a SBL-SA-based approach in multiple aspects, including the sensitivity to different frequency bands, the robustness to data noise, the lateral continuity of the final profiles and so on. Furthermore, we apply the mean square error (MSE), residual variance (RV) of seismograms and residual energy (RE) between the frequency spectra of the true and inverted reflectivity model to highlight the advantages of the proposed method over the SBL-SA-based approach in terms of spectral sparse reflectivity inversion within a sparse Bayesian learning framework. Multiple examples, including both numerical and field experiments, are carried out to validate the proposed method.

Elastic least-squares reverse time migration in vertical transverse isotropic media

Using adjoint-based elastic reverse time migration, it is difficult to produce high-quality reflectivity images due to the limited acquisition apertures, band-limited source time function, and irregular subsurface illumination. Through iteratively computing the Hessian inverse, least-squares migration enables us to reduce the point-spread-function effects and improve the image resolution and amplitude fidelity. By incorporating anisotropy in the 2D elastic wave equation, we have developed an elastic least-squares reverse time migration (LSRTM) method for multicomponent data from the vertically transversely isotropic (VTI) media. Using the perturbed stiffness parameters [Formula: see text] and [Formula: see text] as PP and PS reflectivities, we linearize the elastic VTI wave equation and obtain a Born modeling (demigration) operator. Then, we use the Lagrange multiplier method to derive the corresponding adjoint wave equation and reflectivity kernels. With linearized forward modeling and adjoint migration operators, we solve a linear inverse problem to estimate the subsurface reflectivity models for [Formula: see text] and [Formula: see text]. To reduce the artifacts caused by data over-fitting, we introduce total-variation regularization into the reflectivity inversion, which promotes a sparse solution in terms of the model derivatives. To accelerate the convergence of LSRTM, we use source illumination to approximate the diagonal Hessian and use it as a preconditioner for the misfit gradient. Numerical examples help us determine that our elastic VTI LSRTM method can improve the spatial resolution and amplitude fidelity in comparison to adjoint migration.

True-amplitude linearized waveform inversion with the quasi-elastic wave equation

We present a quasi-elastic wave equation as a function of the pressure variable, which can accurately model PP reflections with elastic amplitude variation with offset effects under the first-order Born approximation. The kinematic part of the quasi-elastic wave equation accurately models the propagation of P waves, whereas the virtual-source part, which models the amplitudes of reflections, is a function of the perturbations of density and Lamé parameters [Formula: see text] and [Formula: see text]. The quasi-elastic wave equation generates a scattering radiation pattern that is exactly the same as that for the elastic wave equation, and only requires the solution of two acoustic wave equations for each shot gather. This means that the quasi-elastic wave equation can be used for true-amplitude linearized waveform inversion (also known as least-squares reverse time migration) of elastic PP reflections, in which the corresponding misfit gradients are with respect to the perturbations of density and the P- and S-wave impedances. The perturbations of elastic parameters are iteratively updated by minimizing the [Formula: see text]-norm of the difference between the recorded PP reflections and the predicted pressure data modeled from the quasi-elastic wave equation. Numerical tests on synthetic and field data indicate that true-amplitude linearized waveform inversion using the quasi-elastic wave equation can account for the elastic PP amplitudes and provide a robust estimate of the perturbations of P- and S-wave impedances and, in some cases, the density. In addition, true-amplitude linearized waveform inversion provides images with a wider bandwidth and fewer artifacts because the PP amplitudes are accurately explained. We also determine the 2D scalar quasi-elastic wave equation for P-SV reflections and the 3D vector equation for PS reflections.

High-resolution reflectivity inversion based on joint sparse representation

High-resolution reflectivity inversion is termed as a fundamental yet essential step for the prediction of thin-bedded hydrocarbon reservoirs. However, algorithms suffer from two key issues: (1) seismic inversion is an ill-posed problem that has multiple solutions, and the results of trace-by-trace seismic inversion are quite poor in lateral continuity, and (2) algorithm stability is likely to be decreased owing to the noise and distortion associated with the acquisition and processing flows. In the current article, we formulate a new joint sparse representation through the combination with L2,1-norm misfit function, which possesses superior noise robustness, in particular in the presence of outliers. On the basis of the L2,1-norm regularization, this specific approach enforces a common sparsity profile, together with consistently lowering the multiplicity of solution. Subsequent to that, the resultant algorithm is applied to the multi-trace seismic inversion. Besides, the wedge model trial and practical applications suggest that the proposed inversion algorithm is stable, in addition to having good noise robustness and lateral continuity; moreover, the vertical resolution of λ/8 is realized under the noise and outliers interference. The logging data calibration illustrates that the proposed methodology is accurate and credible.

Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

ABSTRACTThe subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q‐compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non‐stationary sparse reflectivity inversion, we evaluate a series of methods for Q‐compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q‐compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two‐phase Q‐compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q‐filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over‐determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion‐based Q estimation method handles the wave‐interference effects better than conventional spectral‐ratio‐based methods. For Q‐compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q‐compensation without knowing Q but with wavelet given.

New type of hybrid nodal line semimetal in Be2Si

Following Dirac and Weyl semimetals, nodal line semimetals represent a new type of topological semimetal and attracted extensive interest in modern condensed matter physics. Recently, a kind of hybrid nodal lines have been proposed (Zhang et al 2018 Phys. Rev. B 97 125143) and it mainly come from anisotropy interaction. Based on the first-principle calculations and k·p model, we predict a cubic Be2Si with topological nontrivial electronic states exhibiting fascinating type-I and type-II hybrid nodal line around Fermi level. Unexpectedly the low energy electronic states of Be2Si are isotropy in kx and ky directions and a new effective model has been proposed for the appearance of this new type hybrid nodal line. The four-fold degenerated type-I and type-II nodal points in the hybrid nodal lines along the high symmetry lines of Γ–K and Γ–X are protected by mirror reflection, time reversal and space inversion symmetry. The spin–orbit coupling effect only induces slight band gap in the hybrid nodal lines in Be2Si whose nontrivial nature remains. Moreover, the nontrivial hybrid nodal lines in Be2Si are robust to external strain. The results in present work indicate that Be2Si are promising candidates for future experimental studies of nontrivial topological semimetals and an excellent platform to study the interaction between the two types Dirac fermions.

Multi-trace stochastic sparse-spike inversion for reflectivity

Sparse-spike reflectivity inversion can be generally regarded as the combination of a non-linear problem of finding the locations and a linear problem of solving the amplitudes of a series of non-zero spikes. The input parameters of the inversion, including the trade-off parameter and the number of the non-zero spikes, are always determined by presetting under the rule of thumb. The improper choices of the input parameters are likely to cause the overfitting issue. Moreover, because the convergence is affected by the fitness between the observed data and the synthetic data derived by using the inverted spikes, the spikes with large amplitudes will have larger influence on the determination of the convergence. As a result, the outliers with large amplitudes are likely to affect the inversion result seriously. Under the assumption of layered-earth model and lateral continuity of subsurface layer, multi-trace stochastic inversion method is developed with adjacent seismic traces served as a constraint. By simultaneously non-linear search for the locations and the slopes of non-zero spikes of the target trace, the proposed method enhances the robustness of inversion results to the choice of input parameters and relieves the influence of outliers to some extent. As an extension of the single-trace stochastic sparse-spike inversion, the detecting ability to thin-beds is reserved and the uncertainty of the obtained reflectivities can be estimated. Synthetic data examples illustrate the effectiveness of the proposed method. The details of subsurface geologically structure are derived in the field data example, which could be helpful to the interpretation.

Geophysical inversion versus machine learning in inverse problems

Geophysical inversion and machine learning both provide solutions for inverse problems in which we estimate model parameters from observations. Geophysical inversions such as impedance inversion, amplitude-variation-with-offset inversion, and traveltime tomography are commonly used in the industry to yield physical properties from measured seismic data. Machine learning, a data-driven approach, has become popular during the past decades and is useful for solving such inverse problems. An advantage of machine learning methods is that they can be implemented without knowledge of physical equations or theories. The challenges of machine learning lie in acquiring enough training data and selecting relevant parameters, which are essential in obtaining a good quality model. In this study, we compare geophysical inversion and machine learning approaches in solving inverse problems and show similarities and differences of these approaches in a mathematical form and numerical tests. Both methods aid in solving ill-posed and nonlinear problems and use similar optimization techniques. We take reflectivity inversion as an example of the inverse problem. We apply geophysical inversion based on the least-squares method and artificial neural networks as a machine learning approach to solve reflectivity inversion using 2D synthetic data sets and 3D field data sets. A neural network with multiple hidden layers successfully generates the nonlinear mapping function to predict reflectivity. For this inverse problem, we test different L1 regularizers for both approaches. L1 regularization alleviates effects of noise in seismic traces and enhances sparsity, especially in the least-squares method. The 2D synthetic wedge model and field data examples show that neural networks yield high spatial resolution.

Optimal Seismic Reflectivity Inversion: Data-driven ℓ p -loss-ℓ q -regularization Sparse Regression.

Seismic reflectivity inversion is widely applied to improve the seismic resolution to obtain detailed underground understandings. Based on the convolution model, seismic inversion removes the wavelet effect by solving an optimization problem. Taking advantage of the sparsity property, the ℓ 1 norm is commonly adopted in the regularization terms to overcome the noise/interference vulnerability observed in the ℓ p -losses minimization. However, no one has provided a deterministic conclusion that ℓ1 norm regularization is the best choice for seismic reflectivity inversion. Instead of using an unproved fixed regularization norm, we propose an optimal seismic reflectivity inversion approach. Our method adaptively adopts a ℓ p -loss-ℓ q -regularization (i.e. ℓ p,q regularization) for p = 2, 0 < q < 1 to estimate a more accurate and detailed reflectivity profile. In addition, we employ a K fold cross-validation based approach to obtain the optimal damping factor λ to further improve the seismic inversion results. The letter starts with the introduction of non-convex constraint for seismic inversion, and the necessity of the ℓ q norm regularization. Then the majorization-minimization and cross validation algorithms are briefly described. The performance of the proposed seismic inversion approach is evaluated through synthetic examples and a field example from the Bohai Bay Basin, China.

OBS Data Analysis to Quantify Gas Hydrate and Free Gas in the South Shetland Margin (Antarctica)

The presence of a gas hydrate reservoir and free gas layer along the South Shetland margin (offshore Antarctic Peninsula) has been well documented in recent years. In order to better characterize gas hydrate reservoirs, with a particular focus on the quantification of gas hydrate and free gas and the petrophysical properties of the subsurface, we performed travel time inversion of ocean-bottom seismometer data in order to obtain detailed P- and S-wave velocity estimates of the sediments. The P-wave velocity field is determined by the inversion of P-wave refractions and reflections, while the S-wave velocity field is obtained from converted-wave reflections received on the horizontal components of ocean-bottom seismometer data. The resulting velocity fields are used to estimate gas hydrate and free gas concentrations using a modified Biot-Geertsma-Smit theory. The results show that hydrate concentration ranges from 10% to 15% of total volume and free gas concentration is approximately 0.3% to 0.8% of total volume. The comparison of Poisson’s ratio with previous studies in this area indicates that the gas hydrate reservoir shows no significant regional variations.

Q-compensated acoustic impedance inversion of attenuated seismic data: Numerical and field-data experiments

Acoustic impedance (AI) inversion is of great interest because it extracts information regarding rock properties from seismic data and has successful applications in reservoir characterization. During wave propagation, anelastic attenuation and dispersion always occur because the subsurface is not perfectly elastic, thereby diminishing the seismic resolution. AI inversion based on the convolutional model requires that the input data be free of attenuation effects; otherwise, low-resolution results are inevitable. The intrinsic instability that occurs while compensating for the anelastic effects via inverse [Formula: see text] filtering is notorious. The gain-limit inverse [Formula: see text] filtering method cannot compensate for strongly attenuated high-frequency components. A nonstationary sparse reflectivity inversion (NSRI) method can estimate the reflectivity series from attenuated seismic data without the instability issue. Although AI is obtainable from an inverted reflectivity series through recursion, small inaccuracies in the reflectivity series can result in large perturbations in the AI result because of the cumulative effects. To address these issues, we have developed a [Formula: see text]-compensated AI inversion method that directly retrieves high-resolution AI from attenuated seismic data without prior inverse [Formula: see text] filtering based on the theory of NSRI and AI inversion. This approach circumvents the intrinsic instability of inverse [Formula: see text] filtering by integrating the [Formula: see text] filtering operator into the convolutional model and solving the inverse problem iteratively. This approach also avoids the ill-conditioned nature of the recursion scheme for transforming an inverted reflectivity series to AI. Experiments on a benchmark Marmousi2 model validate the feasibility and capabilities of our method. Applications to two field data sets verify that the inversion results generated by our approach are mostly consistent with the well logs.

Multichannel block sparse Bayesian learning reflectivity inversion with lp-norm criterion-based Q estimation

The generation of attenuated seismic reflection data can be described via a nonstationary convolution model with quality factor Q. In according with the linear matrix-matrix multiplication operation that is deduced to depict the multichannel nonstationary seismic received signal, we present a spatially correlated reflectivity inversion approach with the Q estimation based on block sparse Bayesian learning (bSBL) and an lp-norm criterion. In contrast to pre-existingtime-variant deconvolution, the proposed technique can eliminate the wavelet-filtering and Q-filtering effect simultaneously and retrieve an optimal reflectivity matrix without providing Q value by anticipation. Through introducing the lp-norm criterion and scanning Q strategy, we could capture the optimal Q to calculate the blurring operator in the inversion function. The inverted reflectivity result will be satisfied with presupposition that multi-trace reflectivity is comparatively sparse corresponding to its minimum lp-norm when the optimal Q structure is applied to build the attenuation equation. In reflectivity inversion area, the relationship among reflection spikes in adjacent traces as a priori information is represented by a covariance matrix of reflectivity model in the bSBL framework and assists in solving procedure to promote the inversion precision. To diminish the influence of man-made parameter selection, the hyperparameters of reflectivity and noise model are estimated in virtue of expectation-maximization (EM) algorithm. The contribution of spatial correlation could guarantee a higher quality of reflectivity image. New method merges the multichannel reflectivity inversion and Q estimation into a single processing and avoids the drawback of the conventional Q extraction technique. Synthetic and field data sets prove the practicality of the developed technique and indicate the favorable anti-noise capability.

Three-term amplitude-variation-with-offset projections

A three-term (3T) amplitude-variation-with-offset projection is a weighted sum of three elastic reflectivities. Parameterization of the weighting coefficients requires two angle parameters, which we denote by the pair [Formula: see text]. Visualization of this pair is accomplished using a globe-like cartographic representation, in which longitude is [Formula: see text], and latitude is [Formula: see text]. Although the formal extension of existing two-term (2T) projection methods to 3T methods is trivial, practical implementation requires a more comprehensive inversion framework than is required in 2T projections. We distinguish between projections of true elastic reflectivities computed from well logs and reflectivities estimated from seismic data. When elastic reflectivities are computed from well logs, their projection relationships are straightforward, and they are given in a form that depends only on elastic properties. In contrast, projection relationships between reflectivities estimated from seismic may also depend on the maximum angle of incidence and the specific reflectivity inversion method used. Such complications related to projections of seismic-estimated elastic reflectivities are systematized in a 3T projection framework by choosing an unbiased reflectivity triplet as the projection basis. Other biased inversion estimates are then given exactly as 3T projections of the unbiased basis. The 3T projections of elastic reflectivities are connected to Bayesian inversion of other subsurface properties through the statistical notion of Bayesian sufficiency. The triplet of basis reflectivities is computed so that it is Bayes sufficient for all rock properties in the hierarchical seismic rock-physics model; that is, the projection basis contains all information about rock properties that is contained in the original seismic.

Coherence attribute applications on seismic data in various guises — Part 2

We have previously discussed some alternative means of modifying the frequency spectrum of the input seismic data to modify the resulting coherence image. The simplest method was to increase the high-frequency content by computing the first and second derivatives of the original seismic amplitudes. We also evaluated more sophisticated techniques, including the application of structure-oriented filtering to different spectral components before spectral balancing, thin-bed reflectivity inversion, bandwidth extension, and the amplitude volume technique. We further examine the value of coherence computed from individual spectral voice components, and alternative means of combining three or more such coherence images, providing a single volume for interpretation.

Revisiting Dix’s RMS approximation for Normal Move-Out Velocity

The RMS velocity approximation continues to be used in seismic data processing and interpretation while its limitations are not well understood because its derivation is opaque to most modern geophysicists. One of the reasons for this is because Dix describes in (Dix, 1955) NMO velocity functions determined by T2-X2 analysis of shot records, which very few current geophysicists have ever performed. A clearer understanding of T2-X2 analysis and the derivation of the RMS formula will enable NMO-derived velocities to be better understood and so better used in reflection seismic imaging, inversion and interpretation. Dix’s derivation closely follows the process of correcting the apparent depth from say refraction of objects in water when viewed from the air. So it is useful to search for this subject and follow the development which relies on the observer’s eye separation being small relative to the depth of the object and also relies on refraction being towards the normal of any interface so that angles of incidence will reduce and remain small. This is true for light because the speed of light in water is much slower in water than in air. Reflection seismic uses sound which in general bends away from the normal at each interface as sound velocities tend to increase with depth so that angles of incidence increase which causes a problem with the method which we will see later.

Constrained nonlinear amplitude variation with offset inversion using Zoeppritz equations

The inversion of prestack seismic data using amplitude variation with offset (AVO) has received increased attention in the past few decades because of its key role in estimating reservoir properties. AVO is mainly governed by the Zoeppritz equations, but traditional inversion techniques are based on various linear or quasilinear approximations to these nonlinear equations. We have developed an efficient algorithm for nonlinear AVO inversion of precritical reflections using the exact Zoeppritz equations in multichannel and multi-interface form for simultaneous estimation of the P-wave velocity, S-wave velocity, and density. The total variation constraint is used to overcome the ill-posedness while solving the forward nonlinear model and to preserve the sharpness of the interfaces in the parameter space. The optimization is based on a combination of Levenberg’s algorithm and the split Bregman iterative scheme, in which we have to refine the data and model parameters at each iteration. We refine the data via the original nonlinear equations, but we use the traditional cost-effective linearized AVO inversion to construct the Jacobian matrix and update the model. Numerical experiments show that this new iterative procedure is convergent and converges to a solution of the nonlinear problem. We determine the performance and optimality of our nonlinear inversion algorithm with various simulated and field seismic data sets.