A PLANE-WAVE ANALOGUE MODEL FOR STUDYING ELECTROMAGNETIC VARIATIONS

1966 ◽  
Vol 44 (1) ◽  
pp. 67-80 ◽  
Author(s):  
H. W. Dosso
Keyword(s):  
Surface Layer ◽  
Plane Wave ◽  
Geological Structures ◽  
Analogue Model ◽  
The Earth ◽  
Phase Angles

A plane-wave analogue model for studying the effect that various geological structures have on the natural electromagnetic variations observed at the surface of the earth is discussed. The validity of the model is discussed, and measurements of amplitudes and phase angles are obtained for a model flat earth and for cylindrical bodies embedded in the surface layer.

On computing ray‐synthetic seismograms for anelastic media using complex rays

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 422-432 ◽  
Author(s):  
D. J. Hearn ◽  
E. S. Krebes
Keyword(s):  
Surface Layer ◽  
Plane Wave ◽  
Saddle Point ◽  
Viscoelastic Medium ◽  
Observation Point ◽  
Acute Angle ◽  
Synthetic Seismograms ◽  
Propagation Angle ◽  
Source Point ◽  
Complex Rays

A plane wave propagating in a viscoelastic medium is generally inhomogeneous, meaning that the direction in which the spatial rate of amplitude attenuation is maximum is generally different from the direction of travel. The angle between these two directions, which we call the “attenuation angle,” is an acute angle. In order to trace the ray corresponding to a plane wave propagating between a source point and a receiver point in a layered viscoelastic medium, one must know both the initial propagation angle (the angle that the raypath makes with the vertical) and the initial attenuation angle at the source point. In some recent literature on the computation of ray‐synthetic seismograms in anelastic media, values for the initial attenuation angle are chosen arbitrarily; but this approach is fundamentally unsatisfactory, since different choices lead to different results for the computed waveforms. Another approach, which is more deterministic and physically acceptable, is to deduce the value of the initial attenuation angle from the value of the complex ray parameter at the saddle point of the complex traveltime function. This value can be obtained by applying the method of steepest descent to evaluate approximately the integrals giving the exact wave field at the observation point. This well‐known technique results in the ray‐theory limit. The initial propagation angle can also be determined from the saddle point. Among all possible primary rays between source and receiver, each having different initial propagation and attenuation angles, the ray determined by the saddle point, which we call a “stationary ray,” has the smallest traveltime, a result which is consistent with Fermat’s principle of least time. Such stationary rays are complex rays, i.e., the spatial (e.g., Cartesian) coordinates of points on stationary raypaths are complex numbers, whereas the arbitrarily determined rays mentioned above are usually traced as real rays. We compare examples of synthetic seismograms computed with stationary rays with those from some arbitrarily determined rays. If the initial value of the attenuation angle is arbitrarily chosen to be a constant for all initial propagation angles, the differences between the two types of seismograms are generally small or negligible in the subcritical zone, except when the constant is relatively large in value, say, within 10 degrees or so of its upper bound of 90 degrees. In that case, the differences are significant but still not large. However, if the surface layer is highly absorptive, the differences can be quite large and pronounced. For larger offsets, i.e., in the supercritical zone, large phase discrepancies can exist between the waveforms for the stationary rays and those for the arbitrarily determined rays, even if the constant initial attenuation angle is not large and even for moderate absorptivity in the surface layer.

ANALOGUE MODEL MEASUREMENTS FOR ELECTROMAGNETIC VARIATIONS NEAR VERTICAL FAULTS AND DYKES

1966 ◽  
Vol 3 (3) ◽  
pp. 287-303 ◽  
Author(s):  
H. W. Dosso
Keyword(s):  
Magnetic Field ◽  
Vertical Magnetic Field ◽  
Geological Structures ◽  
Analogue Model

An analogue model for studying the behavior of the natural geomagnetic and telluric field variations for various geological structures is described. Measurements of amplitudes and phases for the horizontal electric, the horizontal magnetic, and the vertical magnetic field components are obtained and discussed for various conducting vertical faults and dykes for both the H and the E polarizations.

REPLY BY D. RANKIN TO THE DISCUSSION BY J. T. WEAVER

Geophysics ◽  
1963 ◽  
Vol 28 (3) ◽  
pp. 490-490
Author(s):  
D. Rankin
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Radiation Field ◽  
Free Space ◽  
Wave Incident ◽  
Induction Field ◽  
The Earth ◽  
Plane Wave Incident

I am indebted to Weaver if he has indeed clarified certain points which I had previously considered to be obvious. Cagniard (1953) states explicitly the magnitude of the wavelengths in free space and it is further implicit in the work of Rankin (1962) that it is indeed this same electromagnetic field which is being considered. The plane wave aspect of the problem arises from the extent of and not the distance from the source so that truly it is the induction field and not the radiation field that is under discussion. I had believed, until this note by Weaver, that d’Erceville and Kunetz (1962) also considered a plane wave incident on the earth and in fact that I was merely following both Cagniard and d’Erceville and Kunetz in this matter. The consistency of the results would tend to confirm this belief.

scholarly journals The critical reflection theorem

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 965-972 ◽  
Author(s):  
Jacob T. Fokkema ◽  
Anton Ziolkowski
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Critical Reflection ◽  
Lower Layer ◽  
Plane Waves ◽  
Source Spectrum ◽  
Demarcation Criterion ◽  
The Earth ◽  
Reflection Theorem ◽  
Uppermost Layer

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

scholarly journals Terrestrial Planet Optical Phase Curves. I. Direct Measurements of the Earth

2021 ◽  
Vol 163 (1) ◽  
pp. 5
Author(s):  
Roderick De Cock ◽  
Timothy A. Livengood ◽  
Daphne M. Stam ◽  
Carey M. Lisse ◽  
Tilak Hewagama ◽  
...  
Keyword(s):  
Phase Angle ◽  
Terrestrial Planet ◽  
Wavelength Dependence ◽  
Deep Impact ◽  
Spectral Filters ◽  
Optical Phase ◽  
The Earth ◽  
Direct Measurements ◽  
Phase Angles ◽  
Geometric Albedo

Abstract NASA’s EPOXI mission used the Deep Impact spacecraft to observe the disk-integrated Earth as an analog to terrestial exoplanets’ appearance. The mission took five 24 hr observations in 2008–2009 at various phase angles (57.°7–86.°4) and ranges (0.11–0.34 au), of which three equatorial (E1, E4, E5) and two polar (P1, North and P2, South). The visible data taken by the HRIV instrument ranges from 0.3 to 1.0 μm, taken trough seven spectral filters that have spectral widths of about 100 nm, and which are centered about 100 nm apart, from 350 to 950 nm. The disk-integrated, 24 hr averaged signal is used in a phase angle analysis. A Lambertian-reflecting, spherical planet model is used to estimate geometric albedo for every observation and wavelength. The geometric albedos range from 0.143 (E1, 950 nm) to 0.353 (P2, 350 nm) and show wavelength dependence. The equatorial observations have similar values, while the polar observations have higher values due to the ice in view. Therefore, equatorial observations can be predicted for other phase angles, but (Earth-like) polar views (with ice) would be underestimated.

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