A Highly Accurate Traveltime Approximation for VTI media

Anisotropic waveform tomography (AWT) uses anisotropic traveltime tomography followed by anisotropic full-waveform inversion (FWI). Such an approach is required for FWI in cases in which the geology is likely to exhibit anisotropy. An important anisotropy class is that of transverse isotropy (TI), and the special case of TI media with a vertical symmetry axis (VTI) media is often used to represent elasticity in undeformed sedimentary layering. We have developed an approach for AWT that uses an acoustic approximation to simulate waves in VTI media, and we apply this approach to crosshole data. In our approach, the best-fitting models of seismic velocity and Thomsen VTI anisotropy parameters are initially obtained using anisotropic traveltime tomography, and they are then used as the starting models for VTI FWI within the acoustic approximation. One common problem with the acoustic approach to TI media is the generation of late-arriving (spurious) S-waves as a by-product of the equation system. We used a Laplace-Fourier approach that effectively damps the spurious S-waves to suppress artifacts that might otherwise corrupt the final inversion results. The results of applying AWT to synthetic data illustrate the trade-offs in resolution between the two parameter classes of velocity and anisotropy, and they also verify anisotropic traveltime tomography as a valid method for generating starting models for FWI. The synthetic study further indicates the importance of smoothing the anisotropy parameters before proceeding to FWI inversions of the velocity parameter. The AWT technique is applied to real crosshole field gathers from a sedimentary environment in Western Canada, and the results are compared with the results from a simpler (elliptical) anisotropy model. The transversely isotropic approach yields an FWI image of the vertical velocity that (1) exhibits a superior resolution and (2) better predicts the field data than does the elliptical approach.

Normal moveout (NMO) correction is one of the common steps of seismic data processing. Conventional NMO correction is generally based on a velocity function, but velocity analysis is considered time consuming and labor intensive. Moreover, the field seismic data observed in complex areas can have a low signal-to-noise ratio, resulting in inaccurate picked velocity parameters and poor NMO correction. Conventional NMO correction has stretching issues, most significantly in shallow and large-offset areas. To address these problems, a new multiscale dynamic time-warping (MSD) algorithm for velocity-independent stretch-free NMO correction is investigated. This algorithm has higher accuracy and stronger noise resistance, as our comparisons with other applications of dynamic time warping show. In our algorithm, the original seismic data are decomposed into multiple morphological scales (using mathematical morphology theory), and alignment errors are calculated separately at each scale, followed by further adaptive weighted summation. Accumulation and backtracking operations based on alignment errors produce time-shift sequences for automatic flattening of the gathers. The effectiveness of the presented approach is tested on synthetic and field data. The results determine that compared with traditional velocity-based NMO correction methods, our method can accurately flatten seismic gathers without the NMO stretch and is robust to strong noise.

Relevance of the work. The paper considers challenging problems related with outlining of intervals with oil and gas presence in the mature Khylly field by use of latest 3D seismic survey techniques in order to gain larger crude resources base. The purpose of this research is to discover the most promising intervals of target horizons with relatively high reservoir properties outlined by 3D seismic data. The subjects of research are 3D seismic survey data, downhole seismic survey – Vertical Seismic Profiling (VSP) and well logging diagrams. The object of research is the Khylly deposit. The paper describes in brief geological and geophysical characteristics, stratigraphic and lithological features of rocks making the section. It is noted that despite repeated surveys by use of various geological and geophysical techniques, the field setting is not thoroughly studied and it has been covered by 3D seismic survey in 2012. Research results. 3D seismic survey applied across Khylly area is resulted in drawing of 4 structural maps for III and I horizons of Productive Series (PS), Akchagyl and Lower Absheron suites. Taking into account the relevance of structural planes of various stratigraphic levels and III horizon of PS being one of the major reference horizons the paper gives description of structural map drawn for this horizon. The detailed velocity model is designed based on VSP data with wide use of velocity analysis data. It has been made clear that Khylly area has block structure and each block has been described in detail. Based on acquired data it has been recommended to drill exploratory well R-1. Conclusion. Processing and interpretation of seismic data are aimed at solving some geological problems; the main task was to obtain results that ensure the study of the geological structure in the seismic survey area, including tracing of seismic horizons, faults and outlining the areas and section intervals which may be of interest due to possible oil and gas presence. VSP data acquired in well 2012 and velocity analysis made it possible to design velocity model of the section under the study, with the use of which the temporary 3D cube was transformed into a depth cube. The quality of seismic data is good and made it possible to solve the tasks set for this research.

Seismic data processing is essential in hydrocarbon exploration, with normal moveout (NMO) correction being a pivotal step in enhancing seismic signal quality. However, conventional NMO correction often suffers from the stretch effect, which distorts seismic reflections and degrades data quality, especially in long-offset data. This study addresses the issue by analyzing synthetic models and proposing a nonhyperbolic stretch-free NMO correction technique. The proposed method significantly improves seismic data quality by preserving up to 90% of the original amplitude, maintaining frequency content stability at 30 Hz, and achieving a high reduction of stretch-related distortions. Compared to conventional NMO, our technique results in clearer seismic gathers, enhanced temporal resolution, and more accurate velocity models. These improvements have substantial implications for high-resolution subsurface imaging and precise reservoir characterization.This work offers a robust and computationally efficient solution to a longstanding limitation in seismic processing, advancing the reliability of exploration in geologically complex environments.

PreviousNext No Access12th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 15–18 August 2011Non-hyperbolic term estimation for VTI inversion from walkaway VSP and surface seismic dataAuthors: Emil BliasEmil BliasVSFusionhttps://doi.org/10.1190/sbgf2011-437 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Walkaway VSP data provides information for interval anisotropic parameter estimates for transverse isotropy with vertical symmetry axis (VTI). For any depth tomographic/migration velocity analysis, we need an adequate initial depth velocity model. Dix-type approach provides us with explicit inversion formulas for velocity model estimation. To estimate these interval parameters, using Dix-type inversion approach, we need to estimate non-hyperbolic term of NMO function. In walkaway VSP data, NMO function can be obtained from first breaks, while in surface seismic it is estimated through non-hyperbolic semblance analysis. In both cases, determination of non-hyperbolic term is the most unstable procedure in interval VTI inversion. Because exact explicit formula for reflected time in a layered (even isotropic) media is unknown, we have to use some approximation. Different approximations have different accuracy in different geology. Here we investigate accuracy of different approximations on four models with weak and strong anisotropy and modest and large vertical velocity changes. Keywords: VSP, VTI, seismic, inversion, velocity, NMOPermalink: https://doi.org/10.1190/sbgf2011-437FiguresReferencesRelatedDetails 12th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 15–18 August 2011ISSN (online):2159-6832Copyright: 2011 Pages: 2223 publication data© 2011 Published in electronic format with permission by the Brazilian Geophysical SocietyPublisher:Society of Exploration Geophysicists HistoryPublished Online: 13 Mar 2014 CITATION INFORMATION Emil Blias, (2011), "Non-hyperbolic term estimation for VTI inversion from walkaway VSP and surface seismic data," SEG Global Meeting Abstracts : 2102-2105. https://doi.org/10.1190/sbgf2011-437 Plain-Language Summary KeywordsVSPVTIseismicinversionvelocityNMOPDF DownloadLoading ...

Seismic data incorporation in reservoir simulation models history matching (HM) studies has been continuously growing. 4D seismic data, in contrast with well production data, can provide a very good scenario of fluids arrangement along reservoir. In this work we describe how 3D and 4D seismic data gathered in acquisitions performed in Campos Basin was incorporated in Marlim Sul deep water field geological model reconstruction and in assisted HM (AHM). It is taken advantage of both 3D and 4D seismic data in several stages of the study, for instance, in the construction of a new porosity – most influential in impedance – model by using a methodology based on the inversion of synthetic seismic (calculated by petro-elastic model) in porosity through an optimization process that aims to reduce the difference between observed and synthetic impedance, and when defining influential parameters based on fluids displacement registered by seismic signal, by using a technique based on the creation of transmissibility multipliers parameters regions that considers the fluids displacement shown in 4D signal. Another relevant point is the use of information from reservoir and 3D seismic data when weighting the 4D data in the objective function. Combining the above mentioned techniques with the knowledge of the field – supported by the 3D seismic data – which allowed, for instance, identification of faults – where fault transmissibility multipliers were used as parameters in the HM process – a fairly good agreement on the observed well and seismic production data was achieved. HM studies using AHM tools have been shown a much more time-efficient technique when compared to manual HM. The incorporation of 4D seismic data can considerably improve the HM quality by improving the reservoir description, once it increases the ability of describing fluids arrangement and pressure distribution. The techniques successfully applied in the Marlim Sul field HM support these conclusions.

Seismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter [Formula: see text] in Thomsen’s notation and the S-wave attenuation coefficient [Formula: see text] in Zhu and Tsvankin’s notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the proposed eikonal equation to realistic attenuating media, an alternative perturbation solution to the proposed eikonal equation, and the feasibility of applying the proposed nonhyperbolic equation for the imaginary part of the complex-valued traveltime to invert for interval attenuation parameters.

In an anisotropic model, traveltime can be determined approximately by numerical solution of the eikonal equation in terms of an anellipticity parameter η, using perturbation theory. However, its accuracy decreases under the effect of strong anisotropy at larger offsets. It becomes invalid for determining normal moveout velocity and anellipticity parameter in seismic processing. We propose a new approach using Levin T-transformation to transform the expanded traveltime in the transversely isotropic medium with vertical axis of symmetry (VTI) into rational form. The objective of this study is to provide a new traveltime approximation that is more accurate at larger offsets. In this study, we derive Levin algorithm and determine the optimal value of Levin parameters, which is a key step in achieving better accuracy. In a numerical experiment, we compare the accuracy between Levin T-transformation and second sequence of Shanks transformation in a homogeneous VTI medium. We also implement both approximations in a velocity analysis and stacking traces using synthetic common midpoint gathers on a multilayer earth model. The proposed method shows a superiority in accuracy to existing methods over a range of offsets with offset-to-depth ratio up to 6 and anellipticity parameter 0–0.5.

Wavelength-dependent Fresnel beam propagator and migration in VTI media

The accuracy and limitations of the near-offset P-wave NMO velocity estimation in transversely isotropic media have been studied using numerical and physical modelling studies. An expression for the near-offset P-wave NMO velocity for a single horizontal reflector in a vertically transversely isotropic layer has been previously obtained: vnmo=αo1+2δwhere αo and δ respectively represent the vertical P-wave velocity and the P-wave critical anisotropy at oblique angles. The above equation is presented as being valid for any degree of anisotropy. The accuracy of this expression is subject to practical testing in this paper.Single layered horizontal models were used to carry out the numerical modelling studies. A computer program that calculates P-wave NMO velocities in transversely isotropic media was used. This program uses the exact ray and phase velocity equations in generating velocity functions to be used in ray tracing and is known to give accurate results. Using the elastic parameters for measured anisotropy in sedimentary rocks, the near-offset NMO velocities are computed using our computer program and the above expression. The results obtained at varying degrees of P-wave anisotropy are compared. The degree of anisotropy varied from very weak to strong and contrasting velocity functions were used in numerical modelling simulations.Phenolite materials with contrasting velocity functions were used to simulate transversely isotropic media with vertical axes of symmetry in physical modelling tests. Experimental reflection data were collected and velocity analysis was conducted for near-offset traces, and the NMO velocity determined by the maximum stack response. The elastic parameters, αo, and δ, of the Phenolite materials were recovered by an iterative inversion of first arrival travel times. These parameters were used to estimate the nearoffset P-wave NMO velocity in Phenolite using the NMO expression and also with our computer program. The NMO velocities obtained from these two methods were compared to that obtained from velocity analysis of the experimental seismic data. These comparisons enabled the validity of the above expression in yielding an accurate P-wave NMO velocity to be tested, in the limit of small offsets.Numerical and physical modelling results obtained from this study indicate that the accuracy of the near-offset P-wave NMO equation depends on the nature and degree of anisotropy encountered in a given area, and is not valid for all degrees of P-wave anisotropy. Since this equation is commonly used in estimating the near-offset P-wave NMO velocity when processing seismic data acquired over anisotropic sedimentary basins, processing geophysicists should proceed with caution when using this equation.

Anisotropic P-wave velocity analysis and seismic imaging in onshore Kutch sedimentary basin of India

We have developed a novel framework for combining physics-based forward models and neural networks to advance seismic processing and inversion algorithms. Migration is an effective tool in seismic data processing and imaging. Over the years, the scope of these algorithms has broadened; today, migration is a central step in the seismic data processing workflow. However, no single migration technique is suitable for all kinds of data and all styles of acquisition. There is always a compromise on the accuracy, cost, and flexibility of these algorithms. On the other hand, machine-learning algorithms and artificial intelligence methods have been found immensely successful in applications in which big data are available. The applicability of these algorithms is being extensively investigated in scientific disciplines such as exploration geophysics with the goal of reducing exploration and development costs. In this context, we have used a special kind of unsupervised recurrent neural network and its variants, Hopfield neural networks and the Boltzmann machine, to solve the problems of Kirchhoff and reverse time migrations. We use the network to migrate seismic data in a least-squares sense using simulated annealing to globally optimize the cost function of the neural network. The weights and biases of the neural network are derived from the physics-based forward models that are used to generate seismic data. The optimal configuration of the neural network after training corresponds to the minimum energy of the network and thus gives the reflectivity solution of the migration problem. Using synthetic examples, we determine that (1) Hopfield neural networks are fast and efficient and (2) they provide reflectivity images with mitigated migration artifacts and improved spatial resolution. Specifically, the presented approach minimizes the artifacts that arise from limited aperture, low subsurface illumination, coarse sampling, and gaps in the data.

Anelliptic approximations for qP-phase and group velocities in transversely isotropic (TI) media have been widely implemented in various seismic data processing and imaging techniques. We revisit several successful anelliptic approximations and suggest two modifications. The first modification involves an alteration of the anelliptic parameter term to achieve better fitting along the non-symmetry axis. The second modification involves finding an empirical connection between anelliptic parameters along symmetry and non-symmetry axes, on the basis of laboratory measurements of anisotropy of rock samples from various sources. These modifications lead to new three-parameter approximations that are more accurate than the previous approximations and produce remarkably accurate four-parameter approximations for both velocities.

To improve the accuracy of carbonate lithofacies modeling, mainly well data such as core, thin section and well logging data had been adopted in conventional methods. Although the reservoir types classification is very detailed, but it is usually difficult to integrate with seismic data to make 3D lithofacies model. To address the issue of carbonate lithofacies modeling, a new integrated carbonate lithofacies modeling technique was summarized based on thin section, core, well logging, 3D seismic data and production performance data. The integrated carbonate lithofacies modeling workflow mainly contains 5 steps. 1) Integrated lithofacies classification based on the core, thin section, well logging, FMI, CMR and production performance data. 2) Petrophysics lithofacies classification based on the cross-plot analysis between sensitive well log curves. 3) Petrophysics lithofacies prediction based on the sensitive well log curve by deep learning method, and verification by core lithofacies analysis. 4) Seismic inversion volume optimization by well lithofacies calibration. 5) Lithofacies modelling based seismic inversion based on the seismic inversion cut-off analysis (Fig.2). This workflow integrated seismic impedance (continuous variable) with lithofacies (discrete variable), and converts seismic inversion into lithofacies directly. According to the certification of new wells, this technique had been applied successfully in carbonate reservoir of M oil field in Middle East, it not only improves the accuracy of 1D lithofacies prediction for wells by deep learning method, but also improves the accuracy of 3D lithofacies modeling for the whole oilfield by well and seismic inversion integrated. The lithofacies modeling not only matched with lithofacies from core analysis and petrophysics lithofacies prediction from well log analysis, but also matched with seismic inversion data in no well area. The integrated carbonate lithofacies modeling workflow integrated thin section, core, well logging, 3D seismic data and production performance data, and improved the improves the accuracy of 3D lithofacies modeling for no well area. It’s useful for new wells optimization and high efficiency development with lower cost. The integrated carbonate lithofacies modeling workflow not only suit for carbonate reservoir, but also suit for clastic reservoir.

Reflection moveout approximations written as explicit functions of offset are convenient tools commonly applied in seismic data modeling, processing, and inversion. The generalized moveout approximation (GMA) has a flexible functional form that accommodates various causes of moveout nonhyperbolicity. We have developed a novel parameterization for the existing six-parameter version of GMA by changing the definition of one of its parameters. Three parameters of the proposed GMA approximation are obtained by fitting the traveltime, the normal moveout velocity, and the fourth-order Taylor series coefficient of traveltime squared at zero offset. The remaining three parameters are obtained by fitting kinematic properties at another two nonzero reference offsets. Through numerical tests on linear sloth models, circular reflector models, and acoustic transversely isotropic media with a vertical symmetry axis (acoustic VTI media), the proposed new GMA method is compared with other published GMA methods in terms of their accuracy. Numerical tests on the three models demonstrate that, when the far reference offset is fixed, the location of the middle reference offset has a considerable impact on the proposed GMA accuracy. We propose a moveout inversion method in a layer-stripping fashion for layered acoustic VTI media based on the proposed and other published GMA methods.