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## The lens equation

The parabolic wave-equation operator can be split into two parts, a complicated part called the diffraction or migration part, and an easy part called the lens part. The lens equation applies a time shift that is a function of x. The lens equation acquires its name because it acts just like a thin optical lens when a light beam enters on-axis (vertically). Corrections for nonvertical incidence are buried somehow in the diffraction part. The lens equation has an analytical solution, namely, .It is better to use this analytical solution than to use a finite-difference solution because there are no approximations in it to go bad. The only reason the lens equation is mentioned at all in a chapter on finite differencing is that the companion diffraction equation must be marched forward along with the lens equation, so the analytic solutions are marched along in small steps.

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Stanford Exploration Project
12/26/2000