Appendix

A natural question occurs when removing a common assumption like regular sampling: Has it been discreetly incorporated into some mathematical result which may be used unknowingly? This is why I will present a derivation of the $15^\circ$ and $45^\circ$ approximations of the wave equation, starting from the basic laws of mechanics. The derivation will not ``open'' the Laplacian in (1), keeping it as an invariant to the very end. The derivation is not original: it is based on Claerbout (1985a) and Kjartansson (1978).