Olga Zdraveva

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.

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.

Anisotropic model building with wells and horizons: Gulf of Mexico case study comparing different approaches

Anisotropic depth imaging with ver-tical transversely isotropic (VTI) models has become the dominant practice in the industry. However, anisotropic parameters for these models continue to be derived by basic practices without the use of tomography. Hanging a single profile of Thomsens parameters from the water bottom still remains the most common practice. In a simple structural setting, it is usually possible to focus the data and obtain a good image despite having a simple and unrealistic model for Thomsens parameters. However, depth positioning of such images is usually suboptimal. Better positioning requires more geologically plausible models. In addition, imaging in complex settings may require tilted transversely isotropic (TTI) models.

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.

From Quantifying Seismic Uncertainty to Assessing E&P Risks And the Value of Information

Accurate well placement in oil and gas exploration and production (E&P) requires accurate positioning of interpreted geological structure in the depth domain. In the past decade, with the advancement of sensor and computer hardware technology, the seismic industry has made great improvements in the data acquisition designs as well as depth imaging and model building algorithms. However, the cost/benefit justification for the value of information (VOI) obtained by utilization of these technologies remains mainly to be qualitative. This paper discusses how seismic uncertainty analysis can lead to quantifying the VOI and technical risks associated with E&P projects.

Building TTI depth models using anisotropic tomography with well information

Tilted transverse isotropy (TTI) is becoming recognized as a more realistic description of anisotropy in sedimentary formations than vertical transverse isotropy (VTI). This is especially true in complex geological settings. While model building approaches for VTI are well understood, similar approaches for TTI media are in their infancy, even when symmetry-axis direction is known. We present an approach that allows building localized anisotropic models utilizing joint inversion of 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 cases of introducing additional information. In the first case velocity along the symmetry axis is known and tomography inverts for Thomsen’s e and δ. In the second case, tomography inverts two Thomsen parameters and velocity from a joint dataset that consists of seismic data and vertical checkshot traveltimes. In contrast to the VTI case, such inversion is non-unique. To combat non-uniqueness in the third case we supplement checkshot and seismic data with the Thomsen’s δ profile from an offset well. This allows recovery of correct profiles for velocity along the symmetry axis and Thomsen’s e. We conclude that TTI model building may remain non-unique even in the presence of well information. Therefore additional assumptions need to be added or uncertainty analysis has to be conducted to pick a geologically plausible model from a range of equivalent models.

Can We Distinguish TTI And VTI Media

Modern depth imaging requires the ability to build transversely isotropic models of the subsurface. Vertical transverse isotropy (VTI) assumes that the symmetry axis is vertical, whereas the more general case of tilted transverse isotropy (TTI) may have a symmetry axis away from vertical. While VTI is a simpler representation, TTI may be more geologically plausible for sedimentary formations such as shales. We examine a simple TTI model and demonstrate that even in the presence of additional well information such as a checkshot, obtaining a symmetry axis orientation from data alone may be ambiguous. Therefore additional geological information from wells, basin evolution and geomechanics may be required.

Tomography with geological constraints: an alternative solution for resolving of carbonates

Carbonates are often present in close proximity to salt in the sedimentary basins around the world. They could be highly heterogeneous and in addition are often interspersed with lower-velocity sediments. The occurrence of high-velocity contrast layering in some portion of the lithology section could pose a problem for grid tomography and may result in insufficient resolution and poor delineation of the layer boundaries, unless many iterations of high-resolution tomography are run. We present a method for successful delineation of carbonate layers by introducing implicit and explicit geological constraints during the global common image point (CIP) tomography updates. The use of geological constraints in the CIP tomography yields high-resolution models over large areas of significant complexity with a reduced number of iterations. In addition, it eliminates the need to consider separate geobodies and multilayer representation of the medium. We show examples of successful application of this method to data sets with variable acquisition geometries from the Gulf of Mexico and offshore West Africa.