Tilt the Axis: VTI, TTI, HTI
Learning objectives
- See TTI as the general tilted-axis case
- Sweep one dial from VTI through TTI to HTI
- Keep the fast direction along the dipping beds
- Understand why dipping targets need tilted-axis imaging
One Dial for the Whole Part
The part opened with two special cases: VTI, the axis vertical under flat layering, and HTI, the axis horizontal across vertical fractures. Nature usually gives neither in pure form. Beds dip, fabrics fold, fracture sets lean. The honest general description is TTI, tilted transverse isotropy, where the symmetry axis points along whatever direction the rock fabric actually took.
Rather than treat it as a third thing to memorise, watch it as a continuum. Sweep the axis tilt with a single dial and the whole part flows past: at zero the beds are flat and you are in VTI; tilt partway and the beds dip into TTI; tilt to ninety degrees and the axis is horizontal, the HTI fracture case, with the fast direction now pointing vertically along the fracture faces. Through all of it the velocity surface is the same Thomsen ellipse, just rotated so its fast direction stays glued to the beds.
Why the Tilt Is Not Optional
The tilt has a hard consequence for imaging. Migration has to propagate energy through the anisotropic overburden using the true axis orientation. Assume a vertical axis over a dipping TTI shale, the classic case above a thrust sheet or against a salt flank, and the velocity model is wrong in a direction-dependent way. Reflectors below the dip focus in the wrong place, faults smear, and the error grows with the dip angle. Tilted-axis (TTI) migration exists precisely to fix this, and it needs the tilt as an input.
That closes the physics of anisotropy. A single tilted ellipse holds VTI, TTI, and HTI, three names for one idea: velocity depends on direction, and the direction that matters is set by the rock fabric. Part 8 takes the fracture end of this spectrum and turns it into a working tool, building fractured earth models and reading the fractures back out with azimuthal AVO, the user's fractured-reservoir workflow.