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The Kirchhoff migration is computationally the most economic choice of migration currently available. From its beginning, the Kirchhoff migration has been developed and improved separately from wave-equation based migrations although they are founded on the same principle. In this paper, we reveal a link between the Kirchhoff depth migration and the wave-equation based migration such as reverse-time migration and least squares migration in terms of the partial derivative wavefield and the virtual source. The Kirchhoff prestack depth migration uses the partial derivative wavefield approximated by the Dirac delta function to migrate the seismic signals. Accordingly, the Kirchhoff hyperbola is defined as kinematic approximation of the partial derivative wavefield. ; This work was financially supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by Korea government (MOST) (No.R0A-2006-000-10291-0) and the Brain Korea 21 project of the Ministry of Education.