Phase-shift modelling for HTI media

Ritesh Sharma and Robert J. Ferguson


Fractures play an important role in hydrocarbon production as they determine the pathways and volume of crustal fluid movement. The horizontal tra nsverse isotropic (HTI) is the simplest effective model of a formation that contain a single fracture system. By following the same theory as discussed in paper entitled "9C-3D modelling for VTI media", we present phase shift modelling in order to seek the dynamic and kinematic signature of the seismic waves in HTI media as these analysis can be useful for fracture analysis. The only difference in this case resides on the way of computing the polarization angle of the incident body waves at each grid point of the interface. Consequently, a layer of infinitesimal thickness above the HTI media is taken into account conducive to define the initial wavefield propagation direction. The incident wavefield pro pagation direction is governed by the cross product of the unit normal vector in the directio n of propagation with unit normal vector associated with rotation-symmetry axis. This cr oss-product yields the effective ray parameter that is the prerequisite for obtaining vertic al slowness of the refracted wave in the HTI media. On being acquainted with the effective ray parameter and the vertical slowness of the refracted wave in HTI media, the unit normal vector in propagation direction in HTI media is computed and used in the cross-product of it with the unit normal vector associated with a 3C geophone at a grid location. This cross-product leads to the computation of polarization angle of propagating body waves in HTI media at the interface and nurture to the rotation matrix. Therefore, the rotation matrix, build on bases of the polarization angle and azimuth, is applied on the extrapolated wavefield in order to model 9C data. It is observed that the amplitude and travel time of seismic waves are affected by HTI medium. The presented 9C-3D modelling will contribute to fracture detection from the surface seismic data since the information about the fractu re system can be extracted from the three dimensional behavior of the shear wave splitting. Subsequently, this modelling will be applicable for VSP and micro-seismicity modelling in the presence of anisotropy.

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