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Finite differences are used to model wave propagation through an anisotropic
medium. The method is described in more detail in this report
Dellinger et al. (1992).
In a recent report Cunha 1991
described
a modeling scheme which takes discontinuities in medium properties into
account by applying different FD operators to the wavefield and the medium.
Different implementations of a staggered grid or derivatives can
influence the accuracy of reflection responses.
In this paper, we are not employing his method, but rather use
cascaded derivative operators. As can be seen from Figure ,
the reflection amplitudes produced by our
modeling scheme are in nearly perfect agreement with analytical solutions
to the reflection amplitudes.
Figures and show
the analytically calculated responses compared with the modeled extracted responses.
ppcalibrate
Figure 2 PP calibration curve for the FD modeling response. Reflection amplitudes were extracted using the dual experiment. Zoeppritz planewave energy reflection coefficients are calculated analytically.

 
iso1.ref
Figure 3 Analytically calculated energy reflection and transmission coefficients from Zoeppritz equations.

 
extraiso
Figure 4 Extracted amplitudes from the FD modeling experiment and the dual experiment. The dual experiment estimates all propagation effects but omits reflection at the boundary. For that reason the two signals have different phases.
Such a test is clearly necessary, if we want to make sure the modeling
algorithm produces correct reflection coefficients at medium interfaces.
The above test gives us confidence in the modeling algorithm for this type of
blocky model.
Using S&M equivalent medium theory, we ``add''
fractures to the chalkrock matrix. The cracks are vertical and have a constant
azimuth along the inline direction. We generally compare inline and
crossline amplitude effects produced by the fracturing.
Amplitude analysis
is carried out in the slantstack domain.
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Stanford Exploration Project
11/17/1997