Interpretation
of Shear Wave Birefringence in P to S Converted Waves Data Using
the Propagator
Matrix Method
by
Jesús V. Sierra T.
Submitted
to the Department of Earth, Atmospheric, and Planetary Sciences on December,
1998 in partial fulfillment of the requirements for the
degree of Master of Science
ABSTRACT
We present an original method for estimating local shear wave birefringence
properties for 3D surface P to S converted waves. To accomplish this we approach
the problem using reverse VSP (RVSP). The method works in the pre-stack domain
and uses the P waves converted to S as shear wave sources. We solve the transmission
problem using the propagator matrix method. The importance of this method is that
it does not require information about layering above the zone of interest and
is accurate for estimating the anisotropy parameters. The method involves
solving a non-linear problem in the frequency domain where Simulated Annealing
is used as the global Minimization technique. The procedure allows estimation
of the propagator matrix related to the target zone, assuming plane wave propagation
allows its diagonalization by pure rotations. This matrix diagonalization ends
up with an estimation of the natural eigen directions of the medium when the range
of offset angles does not exceed 35°. The proposed method is validated
with synthetic RVSP data for two models with different densities of vertical fractures.
Results show good accuracy in the estimation of the angle of the fractures for
the whole range of offsets. The study also extends to show the dependence on the
frequency and on the offset.
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