Effects of earth curvature on two-dimensional ray tracing in underwater acoustics

The objective of this paper is to investigate the effects of earth curvatur e on two-dimensional ray tracing. This is done by comparing numerical solut ions of different ray equations. From numerical results, it is concluded th at (1) at very long ranges, a 2-D ray path constructed without earth curvat ure correction may have less turning points than an actual ray; (2) compute d travel times of eigenrays may be longer than measurements, and this trave l-time error will increase with launch angle; (3) the error of launch angle s of eigenrays decreases with launch angle; and (4) both the travel-time er ror and the launch-angle error increase with propagation range. Conclusions (2) and (3) are consistent with a published result in ocean acoustic tomog raphy. Within a 1000 km range, the effect of earth flattening is not signif icant, and spherical earth is a good approximation. A set of 2-D ray equati ons with spherical earth curvature correction is presented in this paper, w hich can considerably extend the range of validity of 2-D ray tracing while being as simple as the traditional 2-D equations. (C) 1998 Elsevier Scienc e Ltd. All rights reserved.