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Modeling

The TRIP synthetic dataset was created from a model with a constant-reflectivity flat reflector lying beneath a Gaussian low velocity anomaly (Figure [*]). The data was modeled with the following acquisition geometry: the shots and receivers were positioned every 10 m on the interval $ { \bf x}=[-2.0, 2.0 ]$ km .

 
rays
rays
Figure 1
Gaussian anomaly velocity model with overlay rays showing the uneven illumination of the reflector.
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The Gaussian anomaly distorts the direction in which the energy is propagated (from small to high angles) and it also makes the velocity change with x position, thus the effect of using one-way vs. two-way modeling should be noticeable. One important difference between these two data sets is the assumed AVA of the flat reflector. I assumed a constant AVA when modeling the one-way data with equation 5. Conversely, a AVA corresponding to a constant density is implicit in the TRIP two-way finite-differences modeling code.

Figure [*] shows a comparison of the two-way (Figures [*]a, [*]c) modeled data provided by TRIP vs. the one-way (Figures [*]b, [*]d) modeled using equation 5. The first row correspond to a shot located at x=-2 km, and the bottom row corresponds to a shot located at x=1 km.

The main differences (besides the artifact in the two-way modeling with linear moveout) can be spotted in the top row. The one-way modeled data (Figure [*]a) shows a decay of the amplitude with offset (compare with Figure [*]b) that could be related to the errors in the amplitude (absence of the Jacobian) in the one-way extrapolator. There is also an overturning event arriving at far offset (Figure [*]b), which is impossible to model with the one-way extrapolator. Besides the AVO differences (dynamic) a very good agreement of the kinematics can be observed.

 
compare
compare
Figure 2
Comparison of the two-way (b,d) modeled data provided by TRIP vs. the one-way (a,c) modeled using equation 5. The top row shows the data from a shot located at x=-2 km, and the bottom row corresponds to a shot located at x=1 km.
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next up previous print clean
Next: Migration Up: Numerical results Previous: Numerical results
Stanford Exploration Project
5/6/2007