Using the PML ABC for Air/Soil Wave Interaction Modeling in the Time and Frequency Domains

The Perfectly Matched Layer (PML) and absorbing boundary condition (ABC) is applied to two-dimensional Finite Difference Time Domain (FDTD) and Finite Difference Frequency Domain (FDFD) simulations of wave interactions with a two-layer air and soil geometry. Since the soil medium is lossy and dispersive, modeling of wave propagation and scattering is significantly more difficult than for free space and pure dielectrics. In addition, specifying an ABC which efficiently prevents reflections from both the free space termination and the adjacent soil is challenging. The theoretical basis for terminating dispersive media for both the time and frequency domains is presented, and simulation results for plane wave and point source excitations are demonstrated. For the former case, scattering is computed from a buried mine-like target. Although the absorbing characteristics of the PML for the air/soil interface are not as good as for free space, it is shown that maximum local reflections of as low as –15dB for FDTD and –50dB for FDFD are possible.     

Linear Programs for the Reconstruction of 2D Images from Geophysical Electromagnetic Measurements

In this paper we present an approach for constructing vertical sections of the electrical conductivity of the earth on the basis of surface measurements. We assume that the conductivity of the earth varies with depth and laterally but not along the third dimension or strike. Electromagnetic measurements are effected every few meters across strike using pairs of horizontal and vertical coils, with the separation between source and receiver varying in order to sample different depths. The data thus provides information about the vertical and horizontal distribution of electrical conductivity of a section of the earth. Recovering the true conductivity distribution from the measurements is a nonlinear inverse problem that allows some useful linear approximations, which we exploit here using linear programming techniques. We apply a regularization approach using -insensitive functions for both, the fitness to the data and the penalizing function. This representation enforces a model structure of blocks immersed in a homogeneous basement, a useful model in many practical instances. Applications of the technique to synthetic and field data in one and two dimensions illustrate the usefulness of the technique.     

Determination of Soil Moisture Profile from Surface Reflection Coefficient Measurements

The in situ of volumetric soil moisture content (SMC) as a function of depth may be determined using surface reflection coefficient measurements at multiple discrete electromagnetic frequencies. The feasibility of this technique is demonstrated through computer simulation by deriving empirical relationships between the number of frequencies, the frequency range, and the number of soil layers for which the SMC is estimated. The SMC profile was obtained to a depth of 1.5 m by inverting, through function minimization, a simulation of the reflection coefficient from layered dielectric materials. The number of soil layers in which SMC could be resolved was found to be twice the number of frequencies used. The required bandwidth increased with the number of soil layers from 20 MHz for 6 layers to 140 MHz for 16 layers. Within some assumptions about the nature of the radio wave propagation, the theoretical accuracy of the estimate depended only on the quantization errorintroduced by having to consider discrete layers of uniform soil with finite widths. The method will enable sensitive measurements of SMC profiles at lower cost and lower complexity than methods which use analysis of steps or pulses, such as time-domain reflectometry (TDR), and should be well suited for routine use by horticulturists and soil researchers.