Groundwave Attenuation Function for Propagation Over A Highly Inductive Earth

Several approximate extensions of the semi-empirical De Jong model ͓De Jong et al., J. Sound and Vib. 86, 23-46 ͑1983͔͒ are considered for the prediction of sound propagation over multiple impedance discontinuities. A limitation in the original formulation of the De Jong model is highlighted and a modified form that overcomes this limitation is derived based on reciprocity. This leads to the development of a model for multiple impedance discontinuities that can be used for the investigation of sound-wave propagation above a mixed, striped soft ground that is created by either porous absorbent strips, embedded grooves, or wells with different depths. The accuracy of the model is validated against the boundary element method. It is then used to evaluate the importance of the imaginary part of the admittance of the ground strips on sound attenuation along welled surface. It is shown that the attenuation performance of a surface with multiple impedance discontinuities is high when the imaginary part of the average admittance is large and negative ͑with an −it convention͒, but the magnitudes of the attenuation peaks are also substantially affected by diffraction from the impedance discontinuities.

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“…To help the discussion in later sections, the following equations, which are well documented in the literature, [20][21][22] are given:…”

Section: A Original De Jong Modelmentioning

confidence: 99%

On the modeling of sound propagation over multi-impedance discontinuities using a semiempirical diffraction formulation

Lam

Monazzam

2006

The Journal of the Acoustical Society of America

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“…which is identical to the expression derived by King and Schlak (1967) for the phase velocity. Their conclusions concerning the mag· nitude of the phase velotity must therefore be altered in the light of ~he present interpretation.…”

Section: Vavgmentioning

confidence: 63%

A Note on the Groundwave Phase Velocity Over a Plane Earth

Segal¹

1968

Radio Science

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Equations are derived for the phase velocity of an electromagnetic groundwave propagating over. a plane earth having a constant surface impedance. The equations are found to differ in essence from one previously derived by King and Schlak (1967). As a result of the interpretation made here, it is concluded that the local phase velocity over a highly inductive surface exceeds the velocity of light in free space under certain conditions. For strongly capacitive surfaces, the phase velocity is expected to exceed the velocity in free space at all distances.

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“…The reason for this is that when σ 1 < σ 2 , the energy is guided between the surface and the higher conductivity boundary (Wait ). This phenomenon was derived theoretically and observed during experiments (King and Schlak ; Makarov et al . ; Bashkuev et al .…”

Section: Basic Principlesmentioning

confidence: 70%

“…The reason for this is that when σ 1 < σ 2 , the energy is guided between the surface and the higher conductivity boundary (Wait 1962). This phenomenon was derived theoretically and observed during experiments (King and Schlak 1966;Makarov et al 1991;Bashkuev et al 1999;Wait 1962Wait , 1998. The total electric field in both cases decreases continuously with increasing distance from the transmitter, with this decrease being much slower for highly inductive surfaces.…”

Section: Electrical Conductivity and Propagation Factormentioning

confidence: 79%

A new far‐field low‐frequency electromagnetic method for measurement of temporal variations in subsurface electrical conductivity averaged over a transect

Kiseleva

Brandelik

Hübner³

et al. 2018

Near Surface Geophysics

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The new far‐field low‐frequency electromagnetic method used the electromagnetic ground wave from distant radio transmitters at low frequencies to estimate temporal variations of factors affecting subsurface electrical conductivity averaged along the propagation path between either a transmitter and a receiver or two receivers that are in line with a transmitter. Phase and phase difference between two receivers depend on three factors that influence the changes in electrical conductivity: soil moisture, depth to the groundwater table and soil temperature. This dependence was investigated by simulations and evaluated by an experiment. The measurement layout was based on simulating ground wave propagation over a layered subsurface using the surface impedance method and the Sommerfeld ground wave attenuation function. A three‐layer model for the subsurface was used, which includes a soil layer, an unsaturated vadose zone and a saturated groundwater zone. The results of simulations at a frequency of 77.5 kHz showed that the phase of the ground wave is strongly influenced by natural variation of the above‐mentioned three factors; 77.5 kHz is the carrier frequency of the Normal Time Service Germany (DCF77) in Mainflingen/Germany, that was chosen as a source of the low‐frequency radio waves used in the experiment. Over a 2‐year measurement period, the amplitude and phase of the ground wave were recorded with two receivers, one 70 km and the other 110 km away from the transmitter. Additionally, phase difference between the two receivers was calculated. In situ observations of soil moisture, depth to the groundwater table, and soil temperature along the transects under investigation were used to estimate phase and phase difference dependencies. Multiple regression analysis of the measured phase and phase difference revealed a strong dependence on the depth to the groundwater table and on soil temperature, whereas the impact of soil moisture on the phase and phase difference was found to be very low. Conversely, the relations obtained can be used to estimate the variation of the depth to the groundwater table, if the phase at a given frequency and the soil temperature information are available.

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Groundwave Attenuation Function for Propagation Over A Highly Inductive Earth

Cited by 34 publications

References 23 publications

On the modeling of sound propagation over multi-impedance discontinuities using a semiempirical diffraction formulation

On the modeling of sound propagation over multi-impedance discontinuities using a semiempirical diffraction formulation

A Note on the Groundwave Phase Velocity Over a Plane Earth

A new far‐field low‐frequency electromagnetic method for measurement of temporal variations in subsurface electrical conductivity averaged over a transect

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