Upscaling of Finely Layered Media in the Presence of Tilted Transverse Isotropy. Application on Well-Log Data.
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The primary focus of this project is to analyze the effect of tilt angle on effective medium properties in a tilted transversely isotropic (TTI) medium. A well log has been divided into nine blocks, where eight is vertical transverse isotropic (VTI) and one is TTI. The blocks are upscaled by using Backus (1962) averaging for the VTI-blocks, and Schoenberg & Muir (1989) averaging for the TTI-block. Several methods have been used to evaluate the responses of the effective parameters resulting from a variation in the tilt angle. These methods include direct comparison of the effective parameters from Schoenberg & Muir averaging, phase velocities and corresponding slowness curves and synthetic seismograms.Upscaling with different tilt angles results in increased effective velocities and reduced effective anisotropy parameters for increasing tilt angles. From the phase velocities and slowness curves, it has been found that the effective tilt behaves differently for P- and SV-waves. It starts at 0 degrees; for both waveforms in the case of VTI, but during the transition to horizontal transverse isotropy (HTI) their respective effective tilt is different. For SV-velocity the effective tilt gradually decreases to -45 degrees;. The effective tilt for P-waves is rotated to 15.2 degrees; for corresponding intrinsic tilt of 60 degrees, before returning back to 0 degrees; for HTI. Signs of tilt can be found in the synthetic seismograms, but it is difficult to uniquely connect it to tilt, without additional information. As the tilt angle increases, the reflectors below the TTI-block are slightly rotated counter-clockwise. For both slowness curves, phase velocities and the synthetic seismograms the biggest differences are found for higher tilt angles, in the range 50-90 degrees.