Nabil Masmoudi

Scanning anisotropy parameters in horizontal transversely isotropic media

ABSTRACT The horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth &phis; of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylors series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle &phis;. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and &phis;, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and &phis; reveals that travel times are more sensitive to η than to the symmetry axis azimuth &phis;. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and &phis; differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in &phis;, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.

Feasibility of High-resolution Fracture Characterization Using Waveform Inversion

Wide-azimuth surface seismic data contain valuable information about the fracture properties, such as crack density, fluid content and fracture direction. Although this information can be obtained from standard techniques such as tomographic velocity analysis or amplitude variation with offset and azimuth, full-waveform inversion (FWI) has the potential of higher-resolution fracture characterization. Building a wavefield-based inversion framework for the fracture parameters requires identifying parameter combinations that minimize trade-offs and ensure high-resolution of the results. Using the Born approximation, which is the central ingredient of the FWI updating process, we derive the radiation patterns of different parameters of the effective orthorhombic medium formed by a vertical fracture set embedded in a VTI (transversely isotropic with a vertical symmetry axis) background. The radiation patterns describe the angular influence of each parameter, in the considered parametrization, on seismic data, and thus give insights into the resolution of the fracture properties. We show that the high-resolution recovery of crack density depends on the fracture infill, while the fracture direction might not be well-resolved because of the trade-off between different parameters.

Scattering Potential of Acoustic Orthorhombic Parametrization - An Inversion Prospective

Orthorhombic anisotropic model inversion is extra challenging because of the multiple-parameter nature of the inversion problem. The high number of parameters required to describe the medium exerts considerable trade-off as well as additional non-linearity to a full-waveform inversion (FWI) application. Choosing a suitable set of parameters to describe the model and designing an effective inversion strategy can help in mitigating this problem. Using the Born approximation which is the central ingredient of the FWI update process, we derive radiation patterns for the acoustic orthorhombic parametrization. The analysis of the radiation patterns leads us to introduce a new set of parameters for a new orthorhombic parametrization. The new parameters are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. The main feature, of any parametrization based on these new parameters, is the azimuthal independency of the modelled data with respect to the vertical transversely isotropic (VTI) parameters, which allows us to propose practical inversion strategies based on our experience with the VTI parameters inversion.

Approximate P-wave Ray Tracing and Dynamic Ray Tracing in Weakly Orthorhombic Media of Varying Symmetry Orientation

We present an approximate, but efficient and sufficiently accurate P-wave ray tracing and dynamic ray tracing procedure for 3D inhomogeneous, weakly orthorhombic media with varying orientation of symmetry planes. In contrast to commonly used approaches, the orthorhombic symmetry is preserved at any point of the model. The model is described by six weak-anisotropy parameters and three Euler angles, which may vary arbitrarily, but smoothly, throughout the model. We use the procedure for the calculation of rays and corresponding two-point traveltimes in a VSP experiment in a part of the BP benchmark model generalized to orthorhombic symmetry.