Complex Permittivity of Volcanic Rock and Ash at Millimeter Wave Frequencies

Abstract

Millimeter wave radar has shown to be of great use in the field of volcanology in terrain mapping applications. One area less studied to date is its use in ash cloud monitoring applications. In order for this to be realized, a quantitative study of the dielectric properties of volcanic rock and ash is required. In this letter, we present a method for accurately determining the complex dielectric permittivity of volcanic samples using a quasi-optical technique on the pellets of pulverized rock and present the results obtained. When averaged across our sample set, the results show agreement with those obtained by previous authors for both the permittivity of the volcanic material at lower frequencies and the permittivity of other rocks at millimeter wave frequencies. The results also show good levels of consistency between the multiple splits of each sample. In order to relate the measurements of the porous collections of ash to a continuous rock equivalent that is needed for use in the distributed target radar equation, mixing formulas are required. A measurement technique is presented for validating the mixing formulas using pressed pellets and loose ash. Bottcher's formula is found to be both accurate and sufficient for our purposes and is used further to relate our measurements to the continuous rock equivalents. These equivalents show that, for andesitic ash, the radar reflectivity factor may be taken to be an average value of K = |(e - 1)/(e + 2)|2 = 0.39 ± 0.03 , showing no measurable deviation from that reported previously at frequencies of up to 19 GHz.