Wave Tilt Research Articles

Wave tilt of radio waves propagating over a layered ground

We call attention here to the limitation of the “Q approximation” in characterizing the complex wave tilt W over a layered half‐space. Using an improved formulation the frequency dependence of W is shown to be a discriminator of the electrical characteristic of the subsurface. The height dependence of the observer is also illustrated.

Measurement of horizontal electric fields associated with distant cloud‐to‐ground strokes

A broadband sensor for the horizontal component of the electric field associated with lightning discharges was developed. The vertical electric field component contaminating the output of this sensor was, on the average, only about 0.5% of the output. Simultaneous measurement of both vertical and horizontal electric field components, associated with lightning striking at more than 16 km away, confirms that the horizontal electric field is accurately evaluated from the measured vertical electric field with the help of the wave tilt formula, irrespective of the propagation path or the polarity of the cloud‐to‐ground stroke. From this simultaneous measurement, it is possible to estimate the effective conductivity and permittivity of the ground in the vicinity of the measuring site. These local electrical parameters are independent of those of the ground beneath the propagation path, which are estimated by comparing the attenuated electromagnetic waves propagated over land with relatively unattenuated electromagnetic waves propagated over seawater. The estimation becomes easier by measuring the horizontal electric field, as it is more sensitive to the attenuation.

Horizontal fields generated by return strokes

Horizontal fields generated by return strokes play an important role in the interaction of lightning‐generated electromagnetic fields with overhead power lines. In many of the recent investigations on the interaction of lightning electromagnetic fields with power lines, the horizontal field was calculated by employing the expression for the tilt of the electric field of a plane wave propagating over the finitely conducting Earth. In this paper we show that the horizontal field generated by return strokes over the finitely conducting ground can be obtained to a high accuracy by using the expression for the surface impedance of the finitely conducting Earth. The method is suitable to calculate horizontal fields generated by return strokes at distances as close as 200 m. At these close ranges the use of the wave tilt expression can cause large errors.

Correction of spherical aberration in an interferometric system with nonzero difference between optical paths and fringeless observation field

The influence of fifth-order spherical aberration in the measurement error in an interferometer system is analyzed. The criterion of the aberration correction and the optimum correction are proposed. The influence of the focusing error and the wave tilt as the adjustment errors are determined. As a practical example, the optimum wave spherical aberration, optimum longitudinal spherical aberration and the error distribution in the observation field are given.

Detection of near‐water ducts by the wave tilt probing method

A theoretical study indicates that near‐water ducts can be detected by airborne wave tilt measurements. Sea roughness and trapping refractivity gradients are incorporated in an iterative procedure which results in wave tilt versus frequency diagrams at low altitudes above sea level. The diagram that corresponds to ducting conditions appears shifted with respect to the reference diagram, which corresponds to the standard refractivity profile. The frequency shift Δf between corresponding ducting and standard diagrams, being rather insensitive to variations of sea state and duct thickness, is strongly dependent on the duct intensity ΔM. The diagram Δf−ΔM is almost linear up to mid‐VHF. The phase quadrature technique offers itself for ΔM estimation through measurements of Δf, provided that the refractivity at sea level is accurately known.

Potentialities of electric and magnetic wave tilt measurements

A comparative study of TM and TE mode wave tilt magnitude and phase variations in the extended frequency range have been carried out for some electrical parameters of the earth's surface as a half‐space model. The TM and TE mode wave tilts show complementary behavior in the extended frequency range. The problem of excitation and propagation of TE mode wave has been discussed. It is shown that the measurement of Wm and We in the extended frequency range would reveal the surface and subsurface features.

Wave tilt calculations in the layered troposphere above a slightly rough sea

The tilt of an EM wave propagating above the sea in a direction parallel to its mean surface is theoretically calculated in an attempt to investigate the possibility to use the wave tilt probing method for the approximate determination of the sea state. A layered tropospheric slab having a typical index profile is considered above the slightly rough sea; the effective surface impedance of the sea is calculated according to a known model for a number of characterisitc wind speeds in the band 10–50 MHz. These models are combined for the calculation of the wave tilt for both horizontally and vertically polarized electromagnetic waves at various altitudes in the troposphere. Results show that the effect of the roughness of the sea surface on the wave tilt in the lower troposphere is not negligible and can also be measured at certain frequencies by using ordinary airborne wave tilt measurement methods.

Wave Tilt Fluctuations near a Vertical Discontinuity in a Flat Ground Plane

Using microwaves (4.8 GHz) and laboratory models, the electric field tilt was measured across a horizontal plane having an abrupt transition from a highly inductive surface to a highly conductive surface. The wave tilt was found to exhibit an interference pattern in front of the boundary. This phenomenon can be explained in terms of the reflection and backscattering from the boundary region. It is predicted that this effect will be observable in wave tilt measurements made on the earth's surface, and may result in the misleading interpretation of field data in addition to obscuring the effect of real changes in local ground conductivity. Surface impedance measurements, however, should not suffer from this problem. The experimental results further support the idea that accurate interpretation of ground parameters from wave tilt and surface impedance measurements cannot be made within a distance of one wavelength (measured in the earth) from any substantial lateral discontinuity. The highly inductive surface consisted of a grounded pin bed (aniso. tropic) structure. Since the subsurface field in such a structure must propagate normal to the surface, it is ideal for synthesizing surface impedances for propagation over the earth which has a large index of refraction.

Electromagnetic scattering by a layered earth with arbitrarily varying subsurface impedance

The problem of scattering of a plane electromagnetic wave from a two‐layered earth with laterally varying substrate surface impedance is considered. A formal iterative solution which is applicable to any arbitrary profile of the substrate surface impedance is derived and is adapted for use of the fast Fourier transform (FFT) technique to obtain numerical results for the scattered fields and hence for the effective surface impedance and wave tilt. The aim is to study the effect of a finite lateral extent of an underground conducting layer, such as water, on the above quantities, which are measurable at the earth's surface. Numerical examples show that the effective surface impedance and wave tilt are good indicators of the variations in the substrate surface impedance.

Phase difference measurements on identical frequency modulated signals

Phase difference measurements to an accuracy of 0.05 degrees were made between two FM signals having an identical modulation structure. The relevant circuit contains commonly available phase-locked loops and a TTL phase comparator. The technique is useful in electromagnetic wave tilt and surface impedance measurements.

Relative wave tilt measurements at VLF

A new technique for making relative wave tilt measurements of the electric field component of a vertically polarized VLF signal propagating across the surface of the earth is outlined. The horizontal component of the electric field was monitored using an electrically short whip antenna lying on the earth's surface, the vertical electric field component was monitored indirectly via a loop antenna in the vertical plane and the amplitudes and the phase difference between the two signals was recorded. Traverses over a highly conductive ore body yielded significant changes in the relative wave tilt.

Wave tilt sounding of multilayered structures

The relationship between the wave tilt and the electrical parameters of a multilayered structure is investigated. Particular emphasis is placed on the inverse problem associated with the sounding of planetary surfaces. An inversion technique, based on multifrequency wave tilt, is proposed and demonstrated with several computer models. There is close agreement between the electrical parameters used in the models and the inversion values.

Wave tilt sounding of a linearly inhomogeneous layered half-space

The wave tilt of a transverse electric (TE) electromagnetic wave over a linearly inhomogeneous lossy layer overlying a homogeneous half-space is studied. Two approaches are used: an exact formulation using solutions of Airy's equation and an approximate numerical solution using a large number of homogeneous layers with a linearly increasing dielectric constant. The numerical results of both solutions are practically identical as long as the thickness of the layers in the approximate model are somewhat smaller than a quarter-wavelength.

Electromagnetic fields of a vertical magnetic dipole above a laterally inhomogeneous thin layer of conductive overburden

An analytical formulation is developed for the resultant electromagnetic field of an oscillating vertical magnetic dipole located over a thin conductive sheet of infinite extent. The sheet is characterized by a conductivity-thickness product or conductance σd that may be a function of the horizontal coordinates. The system of integral equations arising in the general formulation is simplified greatly when azimuthal symmetry prevails. Numerical results for a Gaussian variation of σd in the radial direction are presented for the case of a symmetrically located source. These results are for the fields at the level of the source dipole over the conductive sheet. It is shown that the quadrature response of the sheet is enhanced when there is rapid variation of the conductance. The null in the resultant wave tilt is also found to be shifted toward the direction of increasing conductance.

On airborne wave tilt measurements

The relationship between the wave tilt and the local surface impedance for ground waves propagating over a nonhomogeneous surface has been studied. It is shown that a sufficient condition for their equivalence is that the normal (vertical) electric field and the tangential (horizontal) magnetic field be simply related by the intrinsic impedance of free space. The “phase quadrature” airborne method of measuring the imaginary part of the wave tilt is modified to allow measurement of the imaginary part of the surface impedance. A second method for airborne measurement of the wave tilt is also proposed. It uses two orthogonal electric dipoles lying in the plane of incidence, oriented so that errors resulting from small mechanical misalignment are second order. Both the magnitude and imaginary part of the wave tilt can be measured. The system is best suited for airborne reconnaissance mapping of poorly conducting areas, giving basic information concerning the electrical properties and structure of the uppermost few meters of ground. The basic instrumentation is described but the tasks of development and testing remain.

A discus-hulled wave measuring buoy

Abstract Described herein is a self-contained, discus-hulled buoy 1.5 m dia., weighing 150 kg, which uses inertial instruments to measure wave height and tilt. Wave tank calibration and the theory of shallow draft buoys demonstrate such a hull accurately follows waves with length greater than twice the buoy diameter. The non-linear response of the buoy determines its sensitivity to low-frequency waves in a sea. And the ratio of wave signal to instrument “noise” is constant over the energetic part of the ocean-wave spectrum for measurements of wave acceleration and slope.

INFLUENCE OF ALTITUDE AND DISPLACEMENT CURRENTS ON PLANE‐WAVE EM FIELDS

Airborne electromagnetic mapping by wavetilt measurement is especially suitable for highly resistive strata like the permafrost terrains of northern Canada. A theoretical study has been made on the influence of the altitude of the aircraft and displacement currents on the measured wave tilt values over a range of frequency from VLF (very low frequency) to BCB (broadcast band). A computer modeling study has shown that the effects of displacement currents cannot be ignored over resistive ground if the frequency is greater than 100 kHz. The altitude effect is significant beyond 20 m for medium frequencies and resistive ground. The phase of the wavetilt is almost always more sensitive to these factors than the amplitude. When the top layer is thicker than three skin depths in that layer, the effects of lower layers on the wavetilt is negligible. It is also apparent that before attempting to interpret wavetilt data over a layered medium, one should carefully determine the nature of the source field. The results are readily applied to the Barringer E-phase System, an airborne EM technique which measures the quadrature part of the wavetilt at three frequencies from VLF to BCB range. If the effects of altitude and displacement currents are ignored, the calculated apparent resistivities from E-phase data will be much less than the true resistivities, even for moderately resistive ground. A graphical technique is presented for correctly estimating the resistivity values from two‐frequency E-phase measurements when the electrical constants are not frequency dependent.

Subsurface Probing by High-Frequency Measurements of the Wave Tilt of Electromagnetic Surface Waves

An overview of the tilt of an electromagnetic surface wave propagating along the surface of the earth is given. High-frequency wave-tilt measurements can have important applications in low conductivity regions such as desert and permafrost areas. A specific application includes determining the depth of permafrost. Past applications of wave-tilt measurements were primarily with lower frequencies in regions with high ground conductivities. Thus low frequencies ( 1 MHz). This enables resolution of thicknesses of layers, a result that has not been possible at low frequencies in the higher conductivity media. It is noted that differences in wave tilt occur for vertically and horizontally polarized surface waves. These wave-tilt differences are useful because they indicate profile characteristics that are sensitive in different ways to the two polarizations.

Theory relating to remote electromagnetic probing of a nonuniform‐thickness coal seam

The effect of lateral inhomogeneities on electromagnetic remote probing of layered structures is considered. The excitation is taken to be an incident transverse electric (TE) plane wave. The fields, the surface admittance, and the wave tilt depend upon the angle of incidence, the distance from the air‐coal interface, the electrical contrast, and the layer profile (e.g., sinusoidal, step, and slant profiles). Both low‐ and high‐frequency cases are illustrated and compared with corresponding results having no lateral inhomogeneities. Results indicate that the surface admittance and the fields tangential to the surface are “good” indicators of the local structure, whereas the field normal to the surface and the wave tilt are not. However, the wave tilt and the field normal to the surface give good indication of subsurface anomalies. As the observation point is moved away from the air‐coal interface, the “information content” regarding the lateral inhomogeneities rapidly decreases. Thus, measurements performed on the surface, or measurements dependent upon the fields at the surface, e.g., reflection coefficients, are more sensitive to lateral inhomogeneities than measurements performed away from the surface.

Theory of electromagnetic scattering from a layered medium with a laterally varying substrate

An analysis is given for scattering of a plane wave from a two‐layer conducting medium where the upper layer is homogeneous but where the lower layer or substrate is characterized by a periodically varying surface impedance. The exact solution obtained is expressed in terms of continued fraction expansions that converge rapidly for most cases of physical interest. The motivation was to provide understanding of how electromagnetic waves can be used to determine the thickness of a layer of coal that is backed by a relatively highly conducting region of slate. It is shown that, if the slate varies sufficiently slowly in the horizontal direction, the observed surface impedance and wave tilt at the air/coal interface is related directly to the local properties at the point of measurement.