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 .

 

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Figure 1 Gaussian anomaly velocity model with overlay rays showing the uneven illumination of the reflector.

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.

 

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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.