Laboratory measurements of electromagnetic wave velocity in layered sands

Abstract

The velocity of an electromagnetic (EM) wave in a system of layered geologic materials is determined by the velocities and volume fractions of the individual layers and by the ratio between the wavelength of the EM wave (λ) and the average layer thickness (t). For the case λ < t the EM wave velocity is given by ray theory; for the case λ > t the velocity is given by effective medium theory (EMT). Previous numerical studies have shown the transition from ray theory to effective medium theory to occur at λ/t approximately equal to 4. Using laboratory time domain reflectometry (TDR), we measured the EM velocities of six layered samples composed of 50% dry coarse sand and 50% saturated fine sand. The λ/t for these measurements range from ∼0.5 to 25. For λ/t < 4 we measured the faster EM velocity predicted by ray theory; and when λ/t > 4, we measured the slower EM velocity predicted by EMT. Reasonable agreement is found with numerical modeling of the experiments. In these experiments a 20% change in velocity is caused by a change in the thickness of the layers, with no change in the volume fraction of the coarse and fine sands. This illustrates the importance of accounting for heterogeneity in the interpretation of EM velocity.