Introduction

Residual migration has proved to be a useful tool in imaging and in velocity analysis.

Rothman 1983 shows that post-stack residual migration can be successfully used to improve the focusing of the migrated sections. He also showed that migration with a given velocity v_m is equivalent to migration with a reference velocity v₀ followed by residual migration with a velocity v_r that can be expressed as a function of v₀ and v_m.

Residual migration has also been used as a tool in velocity analysis. Al-Yahya 1987 discusses a residual migration operator in the prestack domain, and shows that it can be posed as a function of a nondimensional parameter $\gamma$ that is the ratio of the correct velocity and the reference velocity used for the initial migration. Etgen (1988, 1989) defines a kinematic residual migration operator as a cascade of NMO and DMO, and shows that it, again, is only a function of the nondimensional parameter $\gamma$ defined by Al-Yahya. Finally, Stolt 1996 defines a prestack residual migration operator in the (f,k) domain, and shows that it depends on the reference (v₀) and the correct (v_m) migration velocities.

In this short note, I review the prestack residual Stolt migration, and show that it also can be formulated as a function of a nondimensional parameter that is the ratio of the reference (v₀) and correct (v_m) velocities. Consequently, we can use Stolt residual migration in the prestack domain to obtain a better focused image without making any assumption about the velocity. This approach has a direct application to migration velocity analysis, for instance in cases when we repeatedly do residual migration on data that have been depth-migrated with an arbitrary velocity function that cannot be approximated by a constant velocity Biondi and Sava (1999).