  Spectra of Seyfert Is are commonly modelled as emission from an X-ray
illuminated flat accretion disc orbiting a central black hole. This provides
both a reprocessed and direct component of the X-ray emission as required by
observations of individual objects and possibly a fraction of the cosmological
X-ray background. There is some observational motivation to at least consider
the role that an effectively concave disc surface might play: (1) a reprocessed
fraction $\gsim 1/2$ in some Seyferts and possibly in the X-ray background, and
(2) the commonality of a sharp iron line peak for Seyferts at 6.4KeV despite a
dependence of peak location on inclination angle for flat disc models. Here it
is shown that a concave disc may not only provide a larger total fraction of
reprocessed photons, but can also reprocess a much larger fraction of photons
in its outer regions when compared to a flat disc. This reduces the sensitivity
of the 6.4KeV peak location to the inner disc inclination angle because the
outer regions are less affected by Doppler and gravitational effects. If the
X-ray source is isotropic, the reprocessed fraction is directly determined by
the concavity. If the X-ray source is anisotropic, the location of iron line
peak can still be determined by concavity but the total reflected fraction need
not be as large as for the isotropic emitter case. The geometric calculations
herein are applicable to general accretion disc systems illuminated from the
center.
