Top panel: surfaces S_free, S_int and Σ used in applying the representation theorem of eq. (A2) to incident waves. The geometry of P- or S-wave incidence on a hypothetical seismic discontinuity at point ξ is depicted with the incidence angle θ of |$\hat{\mathbf {\gamma }}_P$| (or |$\hat{\mathbf {\gamma }}_S$|⁠) with respect to the discontinuity plane, plus the normal vector and tangent vector defined with eq. (A14) or eq. (A24). In three dimensions, the depicted plane need be only that which contains |$\hat{\mathbf {\gamma }}_P$| (or |$\hat{\mathbf {\gamma }}_S$|⁠), |$\hat{\mathbf {n}}$| and |$\hat{\mathbf {t}}$|⁠; the dip of the planar discontinuity may be only an apparent dip and not the true dip. Bottom panel: illustration of the total wavefield at the free surface as being composed of the incident wavefield u^inc from a source at depth and a corresponding reflected wavefield off the free surface u^refl. The incident wavefield also interacts with a discontinuity to produce a converted wave δu.