Synthetic example

Figure  shows 2-D cross-sections through the simple 3-D synthetic model used to test lateral velocity variations. The velocity model consisted of a linear gradient of 0.85 s^-1 dipping at 45$^\circ$.The reflectivity model consisted of three `bench'-shaped reflectors with dips of 15$^\circ$, 35$^\circ$ and 50$^\circ$. The synthetic data were modeled with a Kirchhoff method, and a dip-limited impulse was added to the zero-offset section to illustrate the 3-D nature of the algorithm.

 

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Figure 4 Cross-sections through zero-offset reflectivity model (top), and laterally variable velocity model (bottom).

For the migration, we used 20 reference velocities, and truncated filter coefficients when they became 10³ times smaller than the leading value, with a maximum of 20 points. Filters contained 8-10 coefficients for average frequencies.

Figure  shows the results of the migration. The three dipping beds are well imaged in cross-section, and in the depth-slice the effect of the velocity gradient is apparent from the slight azimuthal anisotropy of the impulse response.