Steep dip Kirchhoff migration for linear velocity gradients

Maria Silvia Donati, Nicolas Williams Martin, John C. Bancroft

A linear-with-depth velocity function is a typical assumption in clastic basins of Tertiary-Quaternary origin sometimes associated with salt domes.

In this case, the raypaths can be approximated by arcs of circles with spherical wavefronts. The 2D Kirchhoff summation curve is no longer valid for large offsets and steep dips. It then becomes necessary to consider a non-hyperbolic summation curve for .proper time imaging of dips up to and beyond 90 degrees for these "turning" zero-offset sections.

A non-hyperbolic summation curve, based in a 8th order polynomial equation, is used to image 120 degree dipping events. It is applied to synthetic zero-offset sections generated by turning-ray modelling on depth models including a diffractor point and a 2-D sphere.