The asymptotic solution for the sound field diffracted into the refrac
tive shadow zone in a static atmosphere with a linear adiabatic sound
speed profile above an impedance plane is well known. This paper prese
nts a high-frequency approximation for the sound field in a more gener
al environment consisting of a moving stratified atmosphere with arbit
rary profiles of sound speed and vector wind velocity above a finite i
mpedance ground. The sound field in the refractive shadow zone is calc
ulated as the sum of quasimodes. The horizontal wave numbers and compl
ex phases of the quasimodes are calculated for linear profiles of soun
d speed and vector wind velocity. This allows examination of the range
of applicability of the effective sound speed approximation which has
been used widely in atmospheric acoustics. The azimuthal dependence o
f the excess attenuation of the sound field in the shadow zone is stud
ied.