Interval anisotropic parameter estimation using velocity‐independent layer stripping

Conventional fracture-characterization methods assume the presence of a single set of cracks in the subsurface. We relax this assumption and demonstrate the feasibility of seismic characterization of multiple fracture sets. Our technique relies on recent findings indicating that multiple, differently oriented, possibly intersecting cracks embedded in an otherwise isotropic host rock result in nearly orthotropic effective media. Here, we estimate the governing parameters of crack-induced orthotropy from 3D, wide-azimuth, multicomponent seismic reflection data acquired over the tight-gas Rulison Field in Colorado. We translate azimuthal variations of the normal-moveout velocities into interval crack densities, fracture orientations, type of fluid infill, and velocities of P- and S-waves in an unfractured rock. Our inversion procedure identifies one set of cracks in the western part of the study area and multiple, likely intersecting fractures in its eastern part. We validate both our underlying theoretical model and the obtained estimates by two independent measurements: the estimated fluid-infill parameter indicates dry cracks as expected for the gas-producing sandstones at Rulison; and the obtained crack orientations are supported by well observations. As a by-product of fracture characterization, we build an orthorhombic velocity model of the Rulison reservoir.

The critical angle plays a crucial role in data processing for refraction seismology. In the context of three‐dimensional data, the critical angle exhibits azimuthal dependence, particularly in the presence of an anisotropic model. In this paper, we propose a method to determine the critical angle (phase angle) and analyse the sensitivity of the critical angle to the model parameters and the available azimuthal range for both transversely isotropic medium with a vertical symmetry axis and orthorhombic models. For more complex orthorhombic models, the critical angle can be computed while considering changes in azimuth. In a numerical example, we apply sensitivity analysis to examine the existence of the critical angle and determine its corresponding values to variations in model parameters and the azimuthal range. Additionally, we conduct computations of the critical angle for the simplified acoustic and elliptical orthorhombic models. This analysis can be extended to encompass all model parameters for different wave modes (pure and converted waves), and they provide generalized predictions for the available range of data in seismic data processing applications.

This invited overview paper discusses recent advances in seismic data processing and inversion for azimuthally anisotropic media and application of kinematic and amplitude signatures of reflected waves in fracture characterization. Because of the complexity of fractured reservoir models, it is beneficial to acquire wide-azimuth, multicomponent data and combine the results of moveout and AVO (amplitude-variation-with-offset) analysis. Still, quantitative fracture characterization faces significant challenges, especially for reservoirs with multiple fracture networks. The transition from the effective parameters that control seismic signatures to fracture orientations and compliances requires using additional information (e.g., well logs, core measurements, and geologic data). The potential and pitfalls of using long-spread, wide-azimuth P-wave data in fracture detection is illustrated on a case study from Rulison field in Colorado. A comprehensive processing sequence designed for layered azimuthally anisotropic media helped to identify pronounced azimuthal AVO anomalies at the top and bottom of the tight gas sand reservoir. Geologic and well-log information indicates that these anomalies correspond to areas of intense fracturing. Estimation of the fracture parameters, however, is complicated by a poor correlation between the AVO and NMO (normal-moveout) ellipses.

F-42 A STRATEGY FOR ANISOTROPIC P-WAVE PRESTACK IMAGING Summary The prestack depth imaging process has been and is continuously evolving with the goal of accurately position the seismic events in space. To achieve this goal the prestack imaging process should account for anisotropy. If the presence of anisotropy is important then ignoring it will have a significant impact in the final imaging accuracy. In this paper we restrict our discussion to vertical transverse isotropy (VTI) or polar anisotropy. 1 We propose a strategy that combines anisotropic prestack time and depth imaging. The strategy consists of a prestack time migration for

ABSTRACTOrthorhombic models are often used in the seismic industry nowadays to describe azimuthal and polar anisotropy and reasonably realistic in capturing the features of the earth interior. It is challenging to handle so many model parameters in the seismic data processing. In order to reduce the number of the parameters for P wave, the acoustic orthorhombic medium is proposed by setting all on‐axis S wave velocities to zero. However, due to the coupled behaviour for P and S waves in the orthorhombic model, the ‘S wave artefacts’ are still remained in the acoustic orthorhombic model, which kinematics needs to be defined and analysed. In this paper, we analyse the behaviour of S wave in acoustic orthorhombic media. By analysis of the slowness surface in acoustic orthorhombic media, we define the S waves (or S wave artefacts) that are more complicated in shape comparing to the one propagating in an acoustic transversely isotropic medium with a vertical symmetry axis. The kinematic properties of these waves are defined and analysed in both phase and group domain. The caustics, amplitude and the multi‐layered case for S wave in acoustic orthorhombic model are also discussed. It is shown that there are two waves propagating in this acoustic orthorhombic medium. One of these waves is similar to the one propagating in acoustic vertical symmetry axis media, whereas another one has a very complicated shape consisting of two crossing surfaces.

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.

Fracture systems in nature are complicated. Normally vertical fractures develop in an isotropic background. However, the presence of horizontal fine layering or horizontal fractures in reservoirs makes the vertical fractures develop in a VTI (a transversely isotropic media with a vertical symmetry axis) background. In this case, reservoirs can be described better by using an orthorhombic medium instead of a traditional HTI (a transversely isotropic media with a horizontal symmetry axis) medium. In this paper, we focus on the fracture prediction study within an orthorhombic medium for oil-bearing reservoirs. Firstly, we simplify the reflection coefficient approximation in an orthorhombic medium. Secondly, the impact of horizontal fracturing on the reflection coefficient approximation is analyzed theoretically. Then based on that approximation, we compare and analyze the relative impact of vertical fracturing, horizontal fracturing and fluid indicative factor on traditional ellipse fitting results and the scaled B attributes. We find that scaled B attributes are more sensitive to vertical fractures, so scaled B attributes are proposed to predict vertical fractures. Finally, a test is developed to predict the fracture development intensity of an oil-bearing reservoir. The fracture development observed in cores is used to validate the study method. The findings of both theoretical analyses and practical application reveal that compared with traditional methods, this new approach has improved the prediction of fracture development intensity in oil-bearing reservoirs.

A stack of horizontal homogeneous elastic arbitrary anisotropic layers in welded contact in the long-wavelength limit is equivalent to an elastic anisotropic homogeneous medium. Such a medium is characterized by an effective average description adhering to previously derived closed-form formalism. We have used this formalism to study three different inhomogeneous orthorhombic (ORT) models that could represent real geologic scenarios. We have determined that a stack of thin orthorhombic layers with arbitrary azimuths of vertical symmetry planes can be approximated by an effective orthorhombic medium. The most suitable approach for this is to minimize the misfit between the effective anisotropic medium, monoclinic in that case, and the desirable orthorhombic medium. The second model is an interbedding of VTI (transversely isotropic with a vertical symmetry axis) layers with the same layers containing vertical fractures (shales are intrinsically anisotropic and often fractured). We have derived a weak-anisotropy approximation for important P-wave processing parameters as a function of the relative amount of the fractured lithology. To accurately characterize fractures, inversion for the fracture parameters should use a priori information on the relative amount of a fractured medium. However, we have determined that the cracks’ fluid saturation can be estimated without prior knowledge of the relative amount of the fractured layer. We have used field well-log data to demonstrate how fractures can be included in the interval of interest during upscaling. Finally, the third model that we have considered is a useful representation of tilted orthorhombic medium in the case of two-way propagation of seismic waves through it. We have derived a weak anisotropy approximation for traveltime parameters of the reflected P-wave that propagates through a stack of thin beds of tilted orthorhombic symmetry. The tilt of symmetry planes in an orthorhombic medium significantly affects the kinematics of the reflected P-wave and should be properly accounted for to avoid mispositioning of geologic structures in seismic imaging.

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.

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 ...

Summary The rock physical experiments show that shale is often moderately even strong anisotropy. This paper discusses the effect for strong anisotropy on AVO according to the quasi Zoeppritz equation for incident qP wave in TI medium with vertical symmetry axis (VTI medium). Theoretical analysis and numerical examples are indicated that the strong anisotropy will cause observable changes to the reflection coefficient. When the anisotropy is strong, d has a great effect on Rpp at both small and large angles. In the case of strong anisotropy, the effect of e on Rpp at large angle is much greater than that of d.

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.

We develop a low-frequency dynamic effective medium for a horizontally layered transversely isotropic medium with vertical symmetry axis (VTI), and approximate this effective medium by a homogeneous VTI medium. This results in frequency-dependent anisotropy parameters valid for low frequencies and quasi-vertical propagation.

Summary Transversely isotropic with vertical symmetry axis (VTI) is a practical assumption for wave propagation environment in many 2D seismic data, due to its acceptable accuracy and limited number of input parameters. Explicit VTI traveltime approximations are commonly used in many seismic data processing and inversion algorithms. In this study we propose a new traveltime approximation for P-wave propagation in VTI media that is more accurate than the previously reported most accurate approximations. We compare its accuracy, and show that it can outperform other three-parameter approximations in velocity analysis and normal moveout correction.

Surface reflection tomography is an inversion method that attempts to determine simultaneously the subsurface elastic parameters and reflector depths from pre-stack seismic data. To date, this technique has been applied to acoustic and isotropic elastic media. In this paper, we study surface reflection tomography in the anisotropic elastic case. Anisotropic media are described by many more elastic parameters than are needed to describe isotropic media; these additional parameters are useful for obtaining rock properties such as crack density, pore shape and fracture strike that cannot be found with isotropic methods. Similar to isotropic surface reflection tomography, many features of an anisotropic model are poorly resolved due to limited ray path coverage; the vertical smearing of isotropic tomography occurs in each elastic parameter in the anisotropic problem. Unlike the isotropic problem, however, there is additional indeterminacy in the solution of the anisotropic tomography problem because of ambiguity amongst the several elastic parameters needed to describe anisotropic media. Also unlike the isotropic problem, the reflector depths participate very strongly in this ambiguity. We investigate the nature of this indeterminacy by studying the null space for linearized tomography, that is, the class of model perturbations of a background medium which, to first order, cause no perturbation at all in the surface reflection traveltimes. Such model perturbations cannot be determined from the traveltime perturbations; describing these null space model perturbations gives insight into the indeterminacy in the anisotropic problem. Complementary to computational approaches towards identifying the null space for discrete formulations of tomography, we study a continuum formulation. Our first set of results concerns the ‘elastic’ null space: perturbations of the elastic parameters (with zero depth perturbation) which cause no perturbation in the traveltimes. The results here are very similar to previous results for cross-well transmission tomography. As expected, the ‘elastic’ null space is larger than the isotropic null space due to the ambiguity amongst the elastic parameters. We identify three categories of model perturbations in the ‘elastic’ null space. The first category consists of model perturbations for which the perturbation in each of the individual elastic parameters is itself either in the isotropic null space, or in a closely related set of model perturbations which we call the odd isotropic null space. Elements in the second category are anisotropic versions of the most well-known isotropic null space elements: perturbations which are polynomials in the horizontal variable with coefficients which are functions of the depth variable satisfying certain linear integral constraints; unlike the isotropic problem, the integral constraints in the anisotropic problem couple together the several elastic parameters. The third category consists of model perturbations satisfying zero boundary conditions at the surface and at the reflector for which a specific linear combination of integrals and derivatives of the several elastic parameters is in the isotropic null space. In particular, there are model perturbations in this third category which represent anomalies that are completely contained in the interior of the model and yet are in the ‘elastic’ null space; this behaviour is different from the isotropic problem. These categories are sufficient to describe the ‘elastic’ null space completely. We demonstrate that every model perturbation in the ‘elastic’ null space is the sum of an element in the first category (indicating an indeterminacy of the same nature as in the isotropic problem in each of the elastic parameters separately) and an element in the third category (indicating an ambiguity amongst the parameters). The second category gives a rich family of examples of sums of null space elements in the first and third categories, and thereby gives a sense of just how large the ‘elastic’ null space is. Moreover, we show that the traveltime perturbations caused by an elastic perturbation determine only a small number of features of the elastic perturbation which distinguish between the several elastic parameters. We identify these features pre-cisely: they are functions of the horizontal variable representing vertical averages of combinations of the elastic parameters and their derivatives. Elastic parameters influencing the vertical velocity appear more prominently in these features than those influencing the horizontal velocity, and these features are closely related to the zero-offset traveltimes and the normal moveout velocities. Our second set of results concerns the so-called velocity–depth ambiguity, more precisely here the elastic parameter versus the depth parameter ambiguity. We demonstrate that for any smooth depth perturbation, there is a perturbation in the elastic parameters for which the combined elastic and depth perturbations cause zero traveltime perturbations; moreover, this can be accomplished by an elliptically anisotropic elastic perturbation with a vertical axis of symmetry, perturbing the vertical velocity alone. This implies that the velocity–depth ambiguity cannot be resolved here as it can be in the isotropic case. We show an example of an anticlinal structure embedded in a homogeneous background whose reflection traveltimes exactly match those from a model with elliptically anisotropic elastic perturbations overlying a flat reflector. We also draw a number of conclusions from these results for the special case of transversely isotropic media with a vertical symmetry axis.