Dave Nichols

A decade of tomography

Over the past 10 years, ray-based postmigration grid tomography has become the standard model-building tool for seismic depth imaging. While the basics of the method have remained unchanged since the late 1990s, the problems it solves have changed dramatically. This evolution has been driven by exploration demands and enabled by computer power. There are three main areas of change. First, standard model resolution has increased from a few thousand meters to a few hundred meters. This order of magnitude improvement may be attributed to both high-quality, complex residual-moveout data picked as densely as 25 m to 50 m vertically and horizontally, and to a strategy of working down from long-wavelength to short-wavelength solutions. Second, more and more seismic data sets are being acquired along multiple azimuths, for improved illumination and multiple suppression. High-resolution velocity tomography must solve for all azimuths simultaneously, to prevent short-wavelength velocity heterogeneity from being mistaken for azimuthal anisotropy. Third, there has been a shift from predominantly isotropic to predominantly anisotropic models, both VTI and TTI. With four-component data, anisotropic grid tomography can be used to build models that tie PZ and PS images in depth.

Building tilted transversely isotropic depth models using localized anisotropic tomography with well information

Tilted transverse isotropyTTI is increasingly recognized as a more geologically plausible description of anisotropy in sedimentary formations than vertical transverse isotropy VTI .A lthough 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 and parameters. In the second scenario, tomography inverts for, , 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 profile from an offset well. This allows recovery of the correct profiles for velocity along the symmetry axis and. 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.

Efficient RTM Angle Gathers Using Source Directions

In general, the pre-imaging condition methods for generating angle-domain common-image gathers are computationally expensive. Algorithms that require full or partial wavefield decomposition at every image point prior to imaging are considered prohibitive for their application to full wide-azimuth surveys. Direction-vector-based methods are an attractive alternative to reduce the cost, but are often troubled by complicated wavefields that exist in geologically complex areas. In this paper, we present a method that reduces the cost of most preimaging condition methods and in particular, direction-vectorbased methods while improving their quality considerably. We present the detailed workflow and substantiate our claims with the help of synthetic and real data examples. In 3D, it is also very important to choose opening angles and azimuths such that they uniformly sample the surface of the unit sphere around the image point. However, this is usually not the case, and we discuss a possible scheme to achieve that.

Localized anisotropic tomography with well information in VTI media

We develop a concept of localized seismic grid tomography constrainedbywellinformationandapplyittobuildingvertically 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 withaccuratedepthpositioninginonestep.Welocalizetomographytoalimitedvolumearoundthewellandjointlyinvertthesurface seismic and well data. Well information is propagated into thelocalvolumebyusingthemethodofpreconditioning,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 additional information. In the first case, vertical velocity is assumed to be known, and the tomography inverts only for Thomsen’s and 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 thirdandfourthcases,sparsedepthmarkersandwalkawayverticalseismicprofilingVSPareused,respectively,tosupplement 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 walkawayVSP hastheadditionaldimensionofangleoroffset,itoffersnofurther increase in this resolution limit. Anisotropic tomography with well constraints has multiple advantages over other approaches anddeservesaplaceintheportfolioofmodel-buildingtools.

Uncertainty And Resolution Analysis For Anisotropic Tomography Using Iterative Eigendecomposition

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.

Application of Steering Filters to Localized Anisotropic Tomography With Well Data

Andrey Bakulin, Marta Woodward*, Yangjun (Kevin) Liu, Olga Zdraveva, Dave Nichols, Konstantin Osypov WesternGeco Summary 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.

Model‐uncertainty quantification in seismic tomography: method and applications

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 ntechniques, 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 nEarth velocity models exist that match the observed seismic (and well) data and nthis 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

Anisotropic model building with uncertainty analysis

Velocity estimation is usually an ill-posed problem even for isotropic media. Widespread use of anisotropic imaging has been shown to aid better focusing and positioning. However, it greatly escalates the complexity of the model building and makes the velocity estimation much more illposed. Conventional techniques continue to rely on gradient-based methods that deliver a single solution (or realization) of the model to the user. Here we demonstrate an alternative approach that acknowledges the nonuniqueness of the problem. It delivers an entire suite of models that fit the data equally well, allowing the user to select the most geologically plausible solution.

Angle gathers for RTM using extended imaging conditions

We can use extended imaging conditions in general, and the time lag imaging condition in particular, to compute angle gathers for reverse-time migration (RTM). The transformation of time lags to angles was proposed previously by other authors; however, the proposed workflow requires a dip field and is increasingly inaccurate in areas with conflicting dips and for dips greater than 60◦. In this paper, we propose methods to overcome the dip limitation and to do the angle transformation without explicitly using the dip field. We discuss the angular resolution present on these gathers and allude to the effects of acquisition geometry. We use a synthetic 2D model to compare results obtained using our proposed methods and the conventional workflow. Finally, we show RTM angle gathers for the SEAM model using our methods.

On the separation of simultaneous‐source data by inversion

Simultaneous-source data can be adequately separated using an inversion formulation. To recover component shot records, we formulate the data-separation as a simultaneous Radon inversion problem. By minimizing the resulting objective function with a robust hybrid solver, we obtain high-quality estimates of the component shot records. Furthermore, regularization with directional Laplacians improves the data quality. In our approach, we estimate a single model that predicts all recorded data, and we treat all components of the recorded data as signal. Our method can be applied to any number of sources within a single survey and can be easily extended to multiple (time-lapse) surveys. Using 2D sections the SEAM model and simultaneous-source data from a 2D land data set, we show that our method can give results of quality comparable to the reference independent shot records.