Tilted transverse isotropy (TTI) is increasingly recognized as a more geologically plausible description of anisotropy in sedimentary formations than vertical transverse isotropy (VTI). Although model-building approaches for VTI media are well understood, similar approaches for TTI media are in their infancy, even when the symmetry-axis direction is assumed known. We describe a tomographic approach that builds localized anisotropic models by jointly inverting surface-seismic and well data. We present a synthetic data example of anisotropic tomography applied to a layered TTI model with a symmetry-axis tilt of 45 degrees. We demonstrate three scenarios for constraining the solution. In the first scenario, velocity along the symmetry axis is known and tomography inverts for Thomsen’s [Formula: see text] and [Formula: see text] parame-ters. In the second scenario, tomography inverts for [Formula: see text], [Formula: see text], and velocity, using surface-seismic data and vertical check-shot traveltimes. In contrast to the VTI case, both these inversions are nonunique. To combat nonuniqueness, in the third scenario, we supplement check-shot and seismic data with the [Formula: see text] profile from an offset well. This allows recovery of the correct profiles for velocity along the symmetry axis and [Formula: see text]. We conclude that TTI is more ambiguous than VTI for model building. Additional well data or rock-physics assumptions may be required to constrain the tomography and arrive at geologically plausible TTI models. Furthermore, we demonstrate that VTI models with atypical Thomsen parameters can also fit the same joint seismic and check-shot data set. In this case, although imaging with VTI models can focus the TTI data and match vertical event depths, it leads to substantial lateral mispositioning of the reflections.

Although properties of bulk heavy oil can be approximated by an appropriate viscoelastic model, only a few attempts to model properties of rocks saturated with heavy oil have been reported. Rock-physics models used for rocks saturated with conventional fluids are inapplicable to those saturated with heavy oil because its viscoelastic rheology invalidates the main assumptions of the Gassmann and Biot theories. We estimate viscoelastic properties of mixtures of rock and heavy oil by considering ͑1͒ a system of layers of a solid and a viscoelastic medium and ͑2͒ by computing Hashin-Shtrikman ͑HS͒ bounds for this system. These two methods give approximate bounds for the frequency-and temperature-dependent velocities and attenuation coefficients in rocks saturated with heavy oil. We also propose a method to compute a realistic estimate of these properties that lie between those bounds. This estimate is based on a self-consistent equivalent-medium approach known as coherent-potential approximation. In a more general form, this approximation can be used for approximate fluid substitution for heavy oil. This approach gives frequency-dependent velocities and attenuation values that are qualitatively consistent with experimental observations.

Tomographic velocity model building has become an industry standard for depth migration. Anisotropy of the Earth challenges tomography because the inverse problem becomes severely ill-posed. Singular value decomposition (SVD) of tomographic operators or, similarly, eigendecomposition of the corresponding normal equations, are well known as a useful framework for analysis of the most significant dependencies between model and data. However, application of this approach in velocity model building has been limited, primarily because of the perception that it is computationally prohibitively expensive, especially for the anisotropic case. In this paper, we extend our prior work (Osypov et al., 2008) to VTI tomography, modify the process of regularization optimization, and propose an updated way for uncertainty and resolution quantification using the apparatus of eigendecomposition. We demonstrate the simultaneous tomographic estimation of VTI parameters on a real dataset. Our approach provides extra capabilities for regularization optimization and uncertainty analysis in anisotropic model parameter space which can be further translated into the structural uncertainty within the image.

Estimation of anisotropic parameters for depth models requires some type of joint inversion of seismic and borehole data. We demonstrate that conventional grid reflection tomography can be adapted to simultaneously invert for all parameters of a local 3D anisotropic model. Success requires three key ingredients: jointly invert seismic and well data, localize tomography to a small volume around the borehole, and steer the updates along seismic horizons with steering filters. We describe steering filters and demonstrate 3D anisotropic tomography regularized with steering-filter preconditioners on a synthetic data set.

Uncertainty is inherent in every stage of the oil and gas exploration and production (E&P) business and understanding uncertainty enables mitigation of E&P risks. Therefore, quantification of uncertainty is beneficial for decision making and uncertainty should be managed along with other aspects of business. For example, decisions on well positioning should take into account the structural uncertainty related to the non‐uniqueness of a velocity model used to create a seismic depth image. Moreover, recent advances in seismic acquisition technology, such as full‐azimuth, long‐offset techniques, combined with high‐accuracy migration algorithms such as reverse‐time migration, can greatly enhance images even in highly complex structural settings, provided that an Earth velocity model with sufficient resolution is available. Modern practices often use non‐seismic observation to better constrain velocity model building. However, even with additional information, there is still ambiguity in our velocity models caused by the inherent non‐uniqueness of the seismic experiment. Many different Earth velocity models exist that match the observed seismic (and well) data and this ambiguity grows rapidly away from well controls. The result is uncertainty in the seismic velocity model and the true positions of events in our images. Tracking these uncertainties can lead to significant improvement in the quantification of exploration risk (e.g., trap failure when well‐logging data are not representative), drilling risk (e.g., dry wells and abnormal pore pressure) and volumetric uncertainties. Whilst the underlying ambiguity can never be fully eradicated, a quantified measure of these uncertainties provides a valuable tool for understanding and evaluating the risks and for development of better risk‐mitigation plans and decision‐making strategies.

Tomographic velocity model building has become an industry standard for depth migration. However, regularizing tomography still remains a subjective virtue, if not black magic. Singular value decomposition (SVD) of a tomographic operator or, similarly, eigendecomposition of corresponding normal equations, are well known as a useful framework for analysis of most significant dependencies between model and data. However, application of this approach in velocity model building has been limited, primarily because of the perception that it is computationally prohibitively expensive for the contemporary actual tomographic problems. In this paper, we demonstrate that iterative decomposition for such problems is practical with the computer clusters available today, and as a result, this allows us to efficiently optimize regularization and conduct uncertainty and resolution analysis.

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We develop a concept of localized seismic grid tomography constrained by well information and apply it to building vertically transversely isotropic (VTI) velocity models in depth. The goal is to use a highly automated migration velocity analysis to build anisotropic models that combine optimal image focusing with accurate depth positioning in one step. We localize tomography to a limited volume around the well and jointly invert the surface seismic and well data. Well information is propagated into the local volume by using the method of preconditioning, whereby model updates are shaped to follow geologic layers with spatial smoothing constraints. We analyze our concept with a synthetic data example of anisotropic tomography applied to a 1D VTI model. We demonstrate four cases of introducing additionalinformation. In the first case, vertical velocity is assumed to be known, and the tomography inverts only for Thomsen’s [Formula: see text] and [Formula: see text] profiles using surface seismic data alone. In the second case, tomography simultaneously inverts for all three VTI parameters, including vertical velocity, using a joint data set that consists of surface seismic data and vertical check-shot traveltimes. In the third and fourth cases, sparse depth markers and walkaway vertical seismic profiling (VSP) are used, respectively, to supplement the seismic data. For all four examples, tomography reliably recovers the anisotropic velocity field up to a vertical resolution comparable to that of the well data. Even though walkaway VSP has the additional dimension of angle or offset, it offers no further increase in this resolution limit. Anisotropic tomography with well constraints has multiple advantages over other approaches and deserves a place in the portfolio of model-building tools.