  The angular spectrum approach (ASA)---a fast, frequency domain method for
calculation of the acoustic field---enables passive source localization and
modeling forward propagation in homogeneous media with high computational
efficiency. Here we show that, if the medium is continuously stratified, a
first-order analytical solution may be obtained for the field at arbitrary
depth. Our simulations show that the stratified ASA solution enables accurate
source localization as compared to the uncorrected ASA (error from 1.2$\pm$0.3
to 0.49$\pm$0.3 wavelengths) at scalings relevant to biomedical ($kL \sim$ 500,
where $L$ is the length of the measurement aperture), underwater ($kL \sim$
800), and atmospheric ($kL \sim$ 10) acoustic applications. Overall the total
computation was on the order milliseconds on standard hardware (225$\pm$84 ms,
compared with $78\pm63$ ms for the homogeneous ASA formulation over all cases).
Collectively, the results suggest the proposed ASA phase correction enables
efficient and accurate method for source localization in continuously
stratified environments.
