Integral Equation Approach to the Propagation of Low-Frequency Groundwaves over Irregular Terrains: II. Two-Dimensional Terrain Features and Elevated Receivers.

This report presents solutions of the one- and two-dimensional integral equations that describe groundware propagation. Considered are the effects of 1 terrain irregularities that are narrower than a Fresnel zone, and 2 receiver elevations. The results define the conditions under which the simpler one-dimensional equation can be used, as well as those that demand the more complicated two-dimensional form. A frequency of 100 kHz is assumed throughout, although certain results are easily scaled to other frequencies. It is well known that the one-dimensional equation is invalid unless the terrain is nearly uniform across a Fresnel zone. It has been found that for obstacles narrower than about 10 km and typical path-lengths the one-dimensional equation erroneously predicts propagation anomalies that 1 are independent of width, and therefore too large, and 2 diminish too slowly at long distances. Considerable error can be incurred by applying the one-dimension equation to moderately sized terrain features. For examples, for a path-length of 500 km, that equation overstates by a factor of four the effect of an obstacle 6 km in diameter. It cannot give accurate results unless the diameter approaches a Fresnel zone width-which exceeds 10 km for long propagation paths. Even for wide obstacles, the one-dimensional formulation neglects reflection and interference phenomena.