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 km .
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.