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Triangle length and scaling

To take advantage of the efficiency of the nearest-neighbor triangle interpolation in terms of minimizing indirect memory addressing, I use a minimum triangle length such that $N \ge 3$.Above, I discussed the danger of over-smoothing resulting from this choice. I also limit the maximum triangle length such that $N \le (2 f_{min})^{-1}$, where fmin is a user-specified parameter indicating the minimum frequency at which real signal is present. This prevents the lowpass anti-aliasing filters from enhancing low-frequency noise (and even d.c.) that may be present in the data, and/or boosted by the double trace integration process. Additionally, to preserve the relative amplitude of a low-frequency anti-aliased reflection compared to a fullband unaliased reflection, I scale the triangles by inverse height instead of the usual inverse area factor. This boosts the peak amplitudes of lowpassed steep dip events to compensate for their loss of bandwidth due to the anti-aliasing process. This inverse height triangle scaling is a first order amplitude effect on the migration impulse responses, and warrants future study. Finally, I weight the anti-aliased migration operator with the conventional migration aperture and $\cos^n\theta$ obliquity factors to suppress post-vertical (evanescent) time-migration impulse response energy.


previous up next print clean
Next: DATA EXAMPLE Up: PRACTICAL IMPLEMENTATION Previous: Indirect memory addressing
Stanford Exploration Project
11/17/1997