Browsing by Subject "Anisotropy--Mathematical models"
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Item Seismic characterization of naturally fractured reservoirs(2007-05) Bansal, Reeshidev, 1978-; Sen, Mrinal K.Many hydrocarbon reservoirs have sufficient porosity but low permeability (for example, tight gas sands and coal beds). However, such reservoirs are often naturally fractured. The fracture patterns in these reservoirs can control flow and transport properties, and therefore, play an important role in drilling production wells. On the scale of seismic wavelengths, closely spaced parallel fractures behave like an anisotropic media, which precludes the response of individual fractures in the seismic data. There are a number of fracture parameters which are needed to fully characterize a fractured reservoir. However, seismic data may reveal only certain fracture parameters and those are fracture orientation, crack density and fracture infill. Most of the widely used fracture characterization methods such as Swave splitting analysis or amplitude vs. offset and azimuth (AVOA) analysis fail to render desired results in laterally varying media. I have conducted a systematic study of the response of fractured reservoirs with laterally varying elastic and fracture properties, and I have developed a scheme to invert for the fracture parameters. I have implemented a 3D finite-difference method to generate multicomponent synthetic seismic data in general anisotropic media. I applied the finite-difference algorithm in both Standard and Rotated Staggered grids. Standard Staggered grid is used for media having symmetry up to orthorhombic (isotropic, transversely isotropic, and orthorhombic), whereas Rotated Staggered grid is implemented for monoclinic and triclinic media. I have also developed an efficient and accurate ray-bending algorithm to compute seismic traveltimes in 3D anisotropic media. AVOA analysis is equivalent to the first-order Born approximation. However, AVOA analysis can be applied only in a laterally uniform medium, whereas the Born-approximation does not pose any restriction on the subsurface structure. I have developed an inversion scheme based on a ray-Born approximation to invert for the fracture parameters. Best results are achieved when both vertical and horizontal components of the seismic data are inverted simultaneously. I have also developed an efficient positivity constraint which forbids the inverted fracture parameters to be negative in value. I have implemented the inversion scheme in the frequency domain and I show, using various numerical examples, that all frequency samples up to the Nyquist are not required to achieve desired inversion results.Item Seismic data processing in transversely isotropic media: a plane wave approach(2002) Mukherjee, Anubrati; Stoffa, Paul L.; Sen, Mrinal K.Occurrences of anisotropy in the seismic data are widespread at all scales. Thus inclusion of these anisotropic effects becomes important for obtaining correct images and target depths. This dissertation addresses some problems pertaining to seismic data processing in transversely isotropic media. I have formulated an interactive traveltime analysis procedure for P-waves in delay-time, slowness domain for wave propagation in the transversely isotropic media with a vertical axis of symmetry (VTI). Using the assumption of weak anisotropy I obtained a simple and physically intuitive two-term expression for vertical slowness, which can be used in direct estimation of interval elliptic velocity and the anisotropic parameter kappa. I have also developed a method to automatically estimate these parameters using a non linear inversion technique called very fast simulated annealing. Conventional ray tracing methods are difficult to apply in the VTI media. Unavailability of vertical P wave velocity restricts us to use the time gridded elliptic velocity and kappa as inputs for traveltime computation in offset-time domain. However I have formulated a ray tracing technique based on the Fermat's principle and perturbation theory. The method uses phase velocities unlike other methods, which use group velocities. Head wave paths are not included in the traveltime computation. Comparison with more exact Finite Difference Eikonal solvers for both 1-D and 2-D models show small residuals. I have used source traveltimes computed using the interval elliptic velocity and kappa models to perform prestack split-step Fourier and Kirchhoff time migration in the VTI media. Migration using parameters estimated from moveout analysis and computed source traveltimes for Gulf of Mexico data show good results. The common image gathers show increased flattening after incorporation of anisotropic effects.