Spatial attenuation rates of interfacial waves: Field and numerical tests of Sommerfeld theory using ground-penetrating radar pulses

We tested the geometric amplitude attenuation rates predicted by classic Sommerfeld theory for horizontally polarized interfacial waves propagating over dielectric ground. We used ground-penetrating radar pulses, the brief time duration of which allowed different interfacial wave modes to separate. We tested rates in the intermediate range of tens of wavelengths, and for azimuthal and radial polarizations. For azimuthal polarization, a closed form solution predicts inverse range-squared rates, and for radial polarization, calculations suggest an inverse range exponent between 1 and 2. Over low loss frozen ground having a dielectric constant of 6.8 azimuthally polarized air waves centered at 46 MHz attenuated nearly in proportion to the square of range, as predicted, while the radial rate at 37 MHz was close to the 1.6 power of range, as generally expected. At 360–390 MHz, air wave rates were higher than expected and likely caused by scattering losses. Three D time domain modeling at 37 MHz confirmed the rate for azimuthal polarization and the qualitative difference in rates between the two polarizations, but the exponent may be about 26% too high for the radial case. Not readily extractable from Sommerfeld theory are rates for subsurface direct waves, for which our models show that both polarizations attenuate in proportion to the square of range after about 5 subsurface wavelengths. This suggests that geometric rates for all horizontally polarized subsurface interfacial waves spatially attenuate in proportion to range-squared in both intermediate and far field ranges, and so could be subtracted from actual rates to determine loss rates caused by intrinsic attenuation and scattering.

► Field and numerical model tests of Sommerfeld attenuation rates.
► Use of pulses to separate modes over dielectric ground.
► Verifies less than range-squared intermediate-range rates for radial polarization.
► Radial rate attains range-squared dependency at far shorter ranges than in air.