On Backus average for oblique incidence
  We postulate that validity of the Backus (1962) average, whose weights are layer thicknesses, is limited to waves whose incidence is nearly vertical. The accuracy of this average decreases with the increase of the source-receiver offset. However, if the weighting is adjusted by the distance travelled by a signal in each layer, such a modified average results in accurate predictions of traveltimes through these layers. 
David R. Dalton and Ayiaz Kaderali
physics.geo-ph