Azimuthal AVO (AVAz)

The Gradient That Depends on Compass Direction

Here the whole part pays off. A fractured HTI reservoir gives a reflection whose AVO gradient depends on the azimuth of the shot. Ruger wrote it compactly:

The intercept $R\_0$ and the isotropic gradient $B\_{iso}$ behave as in ordinary AVO. The new term is the anisotropic gradient $B\_{ani}$, which scales with crack density and fluid through the Hudson model and rides on $\\cos^2$ of the azimuth measured from the symmetry axis $\\phi\_{sym}$, the crack normal, ninety degrees from the fracture strike. A line shot ALONG the fractures stays in the isotropy plane and keeps the plain gradient $B\_{iso}$; a line shot ACROSS them feels the full $B\_{ani}$. The two share an intercept but fan apart as the offset grows, and the amplitude at a fixed angle traces an ellipse around the compass with its long axis on the strike.

Inverting Data Back to Geology

The star move is the inversion. Sample that azimuthal amplitude at the handful of azimuths a real survey provides, add realistic gauge noise, and fit a $\\cos(2\\phi)$ ellipse through the points. The axis of the fitted ellipse hands back the fracture strike, the very number the model was built with. Geology went in as a strike; rock physics and the wave turned it into a synthetic azimuthal amplitude; and a least-squares fit brings it back out as a strike. Turn the noise up and the recovery degrades gracefully, which is exactly why fracture surveys chase wide azimuths and strong contrasts: you need enough azimuthal signal to beat the gauge noise.

Two caveats close the argument. Because $B\_{ani}$ weakens when the fractures are wet, brine-filled fractures are harder to orient from P-wave data alone, the fluid loophole from earlier in the part. And the fitted axis alone carries a ninety-degree ambiguity between strike and its normal, resolved with the sign of the anisotropic gradient or with shear data. That shear companion, geometry-only and fluid-blind, is the subject of the closing section.