Velocity and depth calculation Sample Clauses

Velocity and depth calculation. The velocity of EM waves through a material is mainly influenced by the permittivity of the ground (or the material), but is also to a lesser extent controlled by electric conduction and the radar wave frequency, as mentioned above (Xxxxxxx and Xxxxxxx, 2005). Velocities of electromagnetic waves in different mediums are shown in table 2. Table 2: Electrical properties for different materials. Modified from Plewels and Xxxxxxx (2001), Xxxxxx Xxxxx (2012) and MALÅ Geoscience (2011a). Material Relative electrical permittivity (ɛr) Electrical conductivity (σ) (mS m-1) Velocity (V) (× 108 ms-1) Attenuation (α) (dB m-1) Air 1 0 3.0 0 Distilled water 80 0.01 0.33 0.002 Fresh water 80 0.5 0.33 0.1 Salt water 80 3000 0.1 1000 Clay 4-40 2-1000 0.6 1-300 Granite 4-6 0.01-1 1.3 0.01-1 Polar snow 1.4-3 - 1.94-2.52 - Polar ice 3-3.15 - 1.68 - Ice 3-4 0.01 1.50-1.73 0.01 Permafrost 4-8 - 1.06-1.50 Velocity in ice is given by the rearranged equation 3. Measurements of the velocity of radar waves in ice have been done both in the field and in laboratories, and have given an approximate velocity of 1.67×108 ms-1 (Xxxxxxx and Xxxxxxx, 2005). This value differs depending on the type of ice the EM waves travels through: the velocity is slightly higher in cold and dry glaciers (maximum 1.73×108 ms-1, table 1) and lower in temperate glacier with higher water content and warmer ice (1.50×108 ms-1, table 1). In the case of this study, the surveys were made on a temperate glacier with relatively high water content. During the accumulation season the ice is protected by a layer of insulating snow, keeping the glacier ice relatively warm. During the ablation season there will be much supra-, en-, and subglacial water because of melting, and precipitation usually takes the form of rain. Field measurements suggest a large span of velocities in ice due to the water densities and air pockets (Bradford and Xxxxxx, 2005). This is because of the large difference in velocity between ice, water and air which has values of 1.67×108 ms-1, 0.33×108 ms-1 and 3×108 ms-1 respectively. When the velocity is determined and the “two way time” (TWT) of the registered EM waves are recorded, we can calculate the depth to reflections and boundaries. This can be at the boundary between ice and water, or more relevant to our study; between ice and bed. The depth is given by a formula (Xxxxxx and Xxxxxxx, 2001): 𝑑 = 𝑇𝖶𝑇*𝑉𝑖𝑐𝑒 Equation 4