Travel Time Of Electromagnetic Waves Research Articles

Recent Advances in Dielectric Properties-Based Soil Water Content Measurements

Dielectric properties are crucial in understanding the behavior of water within soil, particularly the soil water content (SWC), as they measure a material’s ability to store an electric charge and are influenced by water and other minerals in the soil. However, a comprehensive review paper is needed that synthesizes the latest developments in this field, identifies the key challenges and limitations, and outlines future research directions. In addition, various factors, such as soil salinity, temperature, texture, probing space, installation gap, density, clay content, sampling volume, and environmental factors, influence the measurement of the dielectric permittivity of the soil. Therefore, this review aims to address the research gap by critically analyzing the current state-of-the-art dielectric properties-based methods for SWC measurements. The motivation for this review is the increasing importance of precise SWC data for various applications such as agriculture, environmental monitoring, and hydrological studies. We examine time domain reflectometry (TDR), frequency domain reflectometry (FDR), ground-penetrating radar (GPR), remote sensing (RS), and capacitance, which are accurate and cost-effective, enabling real-time water resource management and soil health understanding through measuring the travel time of electromagnetic waves in soil and the reflection coefficient of these waves. SWC can be estimated using various approaches, such as TDR, FDR, GPR, and microwave-based techniques. These methods are made possible by increasing the dielectric permittivity and loss factor with SWC. The available dielectric properties are further synthesized on the basis of mathematical models relating apparent permittivity to water content, providing an updated understanding of their development, applications, and monitoring. It also analyzes recent mathematical calibration models, applications, algorithms, challenges, and trends in dielectric permittivity methods for estimating SWC. By consolidating recent advances and highlighting the remaining challenges, this review article aims to guide researchers and practitioners toward more effective strategies for SWC measurements.

Revisiting the light time correction in gravimetric missions like GRACE and GRACE follow-on

The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.

GPR geophysical method as a remediation tool to determine zones of high penetration resistance of soil

In this study, we demonstrated application of ground penetrating radar towards assessing zones of high penetration resistance (PR) within soil horizons with a view to characterize the subsurface media. Soil attributes changes both in time and space can be difficult to understand. This may be largely due to concealing nature of subsurface media and convectional methods of soil investigations that are usually restricted to observation at the surface and discrete points. Thus making interpolations, inferences and conclusions from such methods inadequate and less reliable. However, ground penetrating radar (GPR) – a geophysical method of investigation was used in this study in lieu of the traditional methods. Soil variability measured in its PR (strength) is related to its compactness-function of bulk density. GPR utilizes electromagnetic (EM) energy in the range of 10 MHz to 3GHz that propagates through the investigative materials. Analysis of the two-way travel time of EM wave gives information about the velocity of the travelling wave. Data were acquired on a loamy silty soil at a farmland in Krakow as a test site simulated with compaction by tractor passes to induce densification of the subsurface layers. Results of the test depicted distinguishing feature of the compacted zones which is reduction in (EM) waveform amplitude and rapid decay of the EM frequency spectra. The research outcome shows swift, cheap and less cumbersome method of soil investigation.

Non-destructive Method for Evaluating Grouted Ratio of Soil Nail Using Electromagnetic Wave

Although soil nails have been widely used for stabilizing slopes, they are often only partially grouted. Thus, grouted ratio of soil nails should be evaluated to prevent landslides. The purpose of this study was to investigate the suitability of a non-destructive method using electromagnetic waves for evaluating grouted ratio of soil nails. Experimental studies were performed with steel bars, partially grouted steel bars, and fully grouted steel bars in air. Partially and fully grouted steel bars were also installed in soils to simulate soil nails installed on slopes. Electromagnetic waves were generated and received using a time domain reflectometer by configuring a two-conductor transmission line formed by two parallel steel bars or two parallel grouted steel bars. Results of experiments showed that the respective round-trip travel time of electromagnetic waves increased with increasing length of the steel bar, grouted steel bar in air, and grouted steel bar in soils. The velocity of electromagnetic waves was the greatest in steel bars but the lowest in grouted steel bars in soils. In addition, the velocity of the electromagnetic waves decreased with increasing grouted ratio. This study suggests that electromagnetic waves might be useful for evaluating grouted ratios of soil nails to stabilize slopes.

Evaluation of Water Content in an Active Layer Using Penetration-Type Time Domain Reflectometry

The moisture condition of the active layer in Arctic regions can induce severe problems, such as ground subsidence and frost heave. Thus, the water content in the active layer needs to be estimated using a light and portable in-situ testing device. In this study, a penetration-type time domain reflectometry (PTDR) device is developed for the estimation of volumetric water content in the active layer. The developed PTDR is applied at a site for an electrical resistivity survey to characterize the water distribution along a measurement line. A PTDR consists of a PTDR module, connecting rods, and a guide with a hammer. The PTDR module can determine the dielectric constant of a material from the measurement of the travel time of electromagnetic waves. Using remolded soil samples, the dielectric constants measured from the PTDR are calibrated with the volumetric water content. The PTDR calibration demonstrates that the dielectric constant increases with the water content. For the temperature of 0.1 to 15.2 °C, the travel time only slightly depends on the temperature variance. For field application, a PTDR is pressed into the ground and measures the electromagnetic waves and temperature with depth. The results of the field tests show that the volumetric water content measured by the PTDR increases with depth due to the impermeable layer located underneath the active layer. The electrical resistivity survey conducted at the same site provides the electrical resistivity profile for a long distance and shallow depth soils. Furthermore, the electrical resistivity survey and PTDR establish a significant correlation between electrical resistivity and water content. The PTDR developed in this study can be effectively used as an advanced in-situ testing method to estimate the water distribution in the active layer.

Inverse upscaling of hydraulic parameters during constant flux infiltration using borehole radar

Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil.

Time Domain Reflectometry Surface Reflections for Dielectric Constant in Highly Conductive Soils

This paper presents a model-based approach to determine dielectric constants from time domain reflectometry (TDR) measurement in highly conductive soils. It makes use of information contained in the TDR signal from the reflection at the surface of the soil rather than the reflection from the end of the probe. The TDR method is widely used to determine the volumetric water content of soils. Commonly used information from the TDR signals includes the apparent dielectric constant and the electrical conductivity. The apparent dielectric constant is generally measured by analyzing the travel time of electromagnetic waves reflected from the end of the soil probe. In soils with high electrical conductivities, the attenuation of the signal can eliminate the reflection from the end of the probe, which limits the application of TDR to these materials. A simplified frequency-independent dielectric model is utilized to invert the dielectric constant from the reflected signals at the soil surface. Results indicate that the dielectric constant can be determined with reasonable accuracy by the proposed approach for soils with high electrical conductivity, where the conventional travel time analysis fails due to significant signal attenuation.

Refinement in the Reflection Properties of Electromagnetic Waves at a Stratigraphic Interface

The travel time of electromagnetic waves in conductive strata has a quantitative relation to the conductivity, permittivity, and permeability of the strata. Using these parameters, geologists can determine the lithology of rocks. But current logging and exploration methods take the time between incidence and reflection as zero and do not take into account the effect of the lateral shift delay when the electromagnetic wave is reflected on the interface of strata. In this article, the lateral shift delay will be considered and a more accurate relationship between petrophysics and electromagnetic wave travel time will be derived. The lateral shift delay of quasi-total reflection of inhomogeneous s-polarized electromagnetic waves (whose electric field is perpendicular to the incident plane) caused by the Goos–Hanchen effect is derived using the phase shift of the wave. The result fits both low and high frequency electromagnetic waves. But for geologists, the most valuable frequency range is between 106 and 109 Hz (1 MHz–1 GHz, wavelengths between 0.1 and 100 m). A numerical example where the frequency equals to 1 GHz. shows three discontinuous points at the critical angle of phase shift, the critical angle of attenuation and 90∘. When the incident angle equals one of these three angles, the lateral shift delay will become infinite. That is, the electromagnetic wave will propagate along the interface. Even when the incident angle is close to one of them, the lateral shift delay is very large. The results also indicate that the two critical angles have an important relation to conductivity and permittivity of the two strata, and that the lateral shift delay has a relation to the incident angle. These results can be used to determine the lithology of the strata and to divide the strata more effectively. It is suggested that this approach may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.

Distance measurements, splitting of electromagnetic waves caused by the dispersion and GPS retrieval of the model atmosphere

An atmosphere above a half space is considered with the dispersion represented by a relation between the electric field and the induction which contains derivatives of rational order and is similar to the empirical formula of Cole and Cole (1941), commonly used in experimental physics, and to the formula used by Jacquelin (1991) in studying the dispersion of energy in electric networks. The consequent index of refractionn contains a rational power of the imaginary frequencyif and is a polymorphic function off; this function, for each frequency, gives a set of different velocity fields whose number depends on the rational exponent ofif. Each electromagnetic wave leaving the source, with givenf and direction, is split in a number of waves with different velocities; ifn is a function of position, the paths of the waves are different and reach a given elevation at different points and times. Ifn is independent of the position, the paths of the waves coincide although the waves have different velocities. The length of a path and the travel time of electromagnetic waves in the atmosphere of a flat Earth model are computed. It is found that the difference between the arc length of the ray and the chord is nil to the second order of the refractivity. It is also seen that a change of water content in layers of the atmosphere, leaving the average velocity to a given elevation unchanged, may change the length of the ray paths to that elevation. It is found that the separation of the rays with the same frequency and direction at the source, causes small uncertainties in electromagnetic distance measurements which increase with the frequency. In the Liebe (1985) atmospheric model we considered frequencies on the range 1 GHz to 2 GHz and found that the arrival of the phases of the rays, with the same frequency in this range, with a zenithal angle smaller than 2π/5 and at a distance of about 104 km, are spread in less than 0.01 ns or 0.3 cm; which does not influence the accuracy presently achieved in distance measurements with electromagnetic waves. The dissipation of energy of the rays in the atmospheric model used, for zenithal angles smaller than 2π/5, is negligible for any length of the path. Formulae are given for the retrieval of a spherical model of the atmosphere of the Earth from a set of differences of the times of arrival, at two observing stations, of the waves emitted from satellites of known orbits.

Group Travel Time of EM Waves with Frequencies near the Ion Cyclotron Frequency in the Two-ion Magnetosphere

The oblique propagation of electromagnetic (EM) waves with frequencies below the equatorial proton cyclotron frequency is investigated for a two-ion magnetospheric plasma. Attention is focused on the wave group travel time along a geomagnetic field line rom the equatorial wave source region to the ionosphere or the location where the wave is reflected. It is found that the coupling between eft- and right-hand polarised waves occurring at a crossover frequency significantly modifies features of the frequency-time spectrum. ecause of this modification, the spectral tone change of Pc 1 waves observed on the ground (e.g. Dowden 1966; Gendrin and Laurent 1979) is not caused solely by dispersion effects in a multi-component plasma.