No description available.

The cross-spread formed by intersecting source and receiver lines, or “hybrid gather” consisting of all common mid-points (CMPs) in a reflection patch defined by the acquisition geometry, has been revived in recent years as a possible solution to the increasing need for ever-improving imaging of 3-D seismic reflection data. These hybrid gathers, however, are currently not widely used in processing. Development of processing procedures for hybrid gathers is needed to further the efficiency of their application. The use of hybrid gathers in processing is justified by their performance as an areal array in attenuating both random and coherent noise from all azimuthal directions. Hybrid gathers also allow for azimuthal filtering to correct for wave propagation effects. Through an azimuthal analysis in an azimuthally anisotropic medium, the effects of structural dip on reflection time can be isolated and separated from pre-stack propagation effects of the media, particularly distortions due to azimuthal anisotropy. A binning strategy is determined for hybrid gathers which best allows for azimuthal anisotropy to be observed and distinguished from structural dip. This allows for improved velocity estimation for imaging and separate analysis of azimuthal variations in propagation properties of subsurface media at an early stage in the processing sequence. The degree and orientation of the anisotropy can then be estimated using a semblance method. / text

No description available.

Azimuthal resistivity was performed at the King site, near Birsay, Saskatchewan to characterize the orientation and extent of fracturing in a glacial till. The target consisted of shallow (less than 4m deep) fractures in the upper oxidized portion of the Battleford Formation.<p> The fractures were visible in soil cores, but their orientation and extent were not known at the time of investigation. It was hoped that if the azimuthal resistivity method could be successfully applied at this site it could be used as an in situ fracture mapping tool at other sites. <p> Preliminary azimuthal resistivity surveys failed to detect a consistent anisotropic pattern that could be attributed to fracturing. A refined method of azimuthal resistivity was developed that built a 3D resistivity model of the site assuming a heterogeneous, isotropic earth. This model was used to predict and remove the effect of heterogeneity on the azimuthal resitivity observations. The results from the refined method also failed to detect a consistent anisotropic pattern. <p>Any single azimuthal resistivity observation from either the preliminary or refined surveys would have provided data that could have been interpreted as anisotropy due to fractures. It was only by comparing many azimuthal observations across the site that the lack of consistent azimuthal pattern became apparent. <p>It is recomended that an analysis of several observations be made before any interpretation of anisotropy is made for azimuthal resistivity sureveys in general.

Azimuthal resistivity was performed at the King site, near Birsay, Saskatchewan to characterize the orientation and extent of fracturing in a glacial till. The target consisted of shallow (less than 4m deep) fractures in the upper oxidized portion of the Battleford Formation.<p> The fractures were visible in soil cores, but their orientation and extent were not known at the time of investigation. It was hoped that if the azimuthal resistivity method could be successfully applied at this site it could be used as an in situ fracture mapping tool at other sites. <p> Preliminary azimuthal resistivity surveys failed to detect a consistent anisotropic pattern that could be attributed to fracturing. A refined method of azimuthal resistivity was developed that built a 3D resistivity model of the site assuming a heterogeneous, isotropic earth. This model was used to predict and remove the effect of heterogeneity on the azimuthal resitivity observations. The results from the refined method also failed to detect a consistent anisotropic pattern. <p>Any single azimuthal resistivity observation from either the preliminary or refined surveys would have provided data that could have been interpreted as anisotropy due to fractures. It was only by comparing many azimuthal observations across the site that the lack of consistent azimuthal pattern became apparent. <p>It is recomended that an analysis of several observations be made before any interpretation of anisotropy is made for azimuthal resistivity sureveys in general.

Shear-wave splitting and azimuthal variations of seismic attributes are two major anisotropic effects induced by vertically-aligned fractures. They both have influences on seismic data processing and interpretation, and provide information on fracture properties. Azimuthal variations in P-wave data have been intensively studied to improve imaging and obtain fracture parameters. However, azimuthal variations in PS-converted wave seismic data, particularly the velocity variation in PS-converted wave data, have not been well studied. Shear-wave splitting has been frequently used to estimate fracture directions and densities. However, its influence on the azimuthal variations of PS-converted wave data has also lacked a proper analysis. In this thesis, I analyse the anisotropic behaviour of PS-converted wave seismic data in the presence of azimuthal anisotropy, which includes the azimuthal variation of the PSconverted wave and PS-converted wave splitting. First, I demonstrate the robustness of PS-converted wave splitting for fracture characterisation. PS-converted wave seismic data is also influenced by the splitting effect due to its upgoing shear-wave leg. This important feature enables the application of shear-wave splitting analysis to PS-converted wave seismic data. I use synthetic data to show the necessity for separation of the split PS-converted waves. Then I apply the PS-converted wave splitting analysis to Sanhu 3D3C land seismic data. By separation of the fast and slow PS-converted waves and compensation for the time delays, the imaging quality has been improved. Dominant fracture properties obtained from the splitting analysis show a good correlation with the stress-field data. However, this work is accomplished by assuming only one set of vertical fractures in processing a given time window. In future work a specific layer-stripping algorithm could be constructed and applied. . Second, I study azimuthal variations of velocities in PS-converted wave seismic data. It involves two major parts: analysing azimuthal variations of NMO velocities to improve imaging, and examining the sensitivity of azimuthal variations to different fluid saturations. For a layer with HTI anisotropy induced by a set of vertical fractures, seismologists usually analyse the azimuthal behaviour exhibited on the radial and transverse components, on which PS-converted wave data are recorded. However, PS-converted waves also undergo shear-wave splitting, which complicates the azimuthal variations of PS-converted wave data. I demonstrate that it is essential to separate the fast P-SV1 wave from the slow P-SV2 wave, before applying any azimuthal analysis. I derive an equation describing the azimuthal variation in PSconverted wave NMO velocities, which shows the variation can be approximated into an ellipse. Based on this theory, I build a workflow to analyse the azimuthal variations of velocities in PS-converted wave data and apply this workflow to synthetic data. The imaging quality can be improved by using this workflow. Different fluid saturations in fractures have different influences on the azimuthal variations of both P-wave and PS-converted wave data. I perform a numerical study to understand how dry or water-saturated fractures control the azimuthal variations. Through theoretical and synthetic studies, I find that the azimuthal variation of velocities in PS-converted wave data is sensitive to different fluid saturations. By analysing the azimuthal variation, the fracture properties can also be estimated, but results are not as robust as those from PS-converted wave splitting analysis. I find that azimuthal variations of fast P-SV1 and slow P-SV2 waves show in-phase characteristics in dry fractures, but exhibit out-of-phase characteristics in water-saturated fractures. This important feature could open a new application for using PS-converted wave seismic data to distinguish oil-filled fractures from gas-filled fractures. In cases where multiple HTI layers are involved, I have developed a specific layer-stripping method to analyse both azimuthal variations and splitting effects of PS-converted waves. By applying this method to synthetic data, the fracture properties of each HTI layer can be estimated. The analysis of azimuthal variations in PS-converted wave velocities is applied to Daqing 3D3C land data. By using azimuthal velocity models in the PS-converted wave seismic data processing, the imaging quality is improved, especially in the anticline area where intensive fractures are likely to be developed. Furthermore, all fracture information obtained from analysis of azimuthal variations and splitting effects is compared with the stress-field data. The results from splitting analysis show a better correlation with the stress-field study. Finally, it is important to conclude that the analysis of PS-converted wave splitting is a robust method to estimate fracture directions and densities. However, it is not sensitive to different fluid saturations, which limits its application to fractured reservoir characterisation. Azimuthal variations of PS-converted wave seismic data can be analysed to improve imaging quality. Moreover their sensitivity to fluid saturations may provide a new way to discriminate between oil-filled and gas-filled fractures. However, the analysis of azimuthal variations is not as robust as the analysis of splitting effects, and it may require appropriate calibration with other fracture characterisation methods.

A measurement of the azimuthal decorrelation in di-jet events in proton-proton collisions at $\sqrt{s}= 7\,$TeV is presented. Using $19.6\,$nb$^{-1}$ of data collected in the ATLAS detector this measurement uses the angle ($\Delta\phi$) in the transverse plane between the two leading $p_T$ jets to measure the normalized differential cross section $\frac{1}{\sigma_{tot}}\frac{d\sigma}{d(\Delta\phi)}$. An unfolding correction is a applied to give a jet-level result. The unfolded spectrum is compared to the predictions of two Monte Carlo event generators: Pythia and Herwig++.

A measurement of the azimuthal decorrelation in di-jet events in proton-proton collisions at $\sqrt{s}= 7\,$TeV is presented. Using $19.6\,$nb$^{-1}$ of data collected in the ATLAS detector this measurement uses the angle ($\Delta\phi$) in the transverse plane between the two leading $p_T$ jets to measure the normalized differential cross section $\frac{1}{\sigma_{tot}}\frac{d\sigma}{d(\Delta\phi)}$. An unfolding correction is a applied to give a jet-level result. The unfolded spectrum is compared to the predictions of two Monte Carlo event generators: Pythia and Herwig++.

The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays “base” quadrature with a simple linear adaptive and an Abu-Shumays “base” quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.

The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays â baseâ quadrature with a simple linear adaptive and an Abu-Shumays â baseâ quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.