A low frequency stable plane wave addition theorem

2009 ◽  
Vol 228 (4) ◽  
pp. 1000-1016 ◽  
Author(s):  
Ignace Bogaert ◽  
Femke Olyslager
2005 ◽  
Vol 15 (10) ◽  
pp. 1459-1468 ◽  
Author(s):  
GEORGE VENKOV

This paper deals with the scattering of time-harmonic acoustic waves by inhomogeneous medium. We study the problem to recover the near and the far field using a priori information about the refractive index and the support of inhomogeneity. The incident spherical wave is modified in such a way as to recover the plane wave incidence when the source point approaches infinity. Applying the low-frequency expansions, the scattering medium problem is reduced to a sequence of potential problems for the approximation coefficients in the presence of a monopole singularity located at the source of incidence. Complete expansions for the integral representation formula in the near field as well as for the scattering amplitude in the far field are provided. The method is applied to the case of a spherical region of inhomogeneity and a radial dependent refractive index. As the point singularity tends to infinity, the relative results recover the scattering medium problem for plane wave incidence.


Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1596-1606 ◽  
Author(s):  
Ari Poikonen ◽  
Ilkka Suppala

Numerical models employed in ground VLF modeling use a normally incident (homogeneous) plane wave as a primary field. We show that these models are not directly applicable to modeling the impedance and wavetilt in the air, quantities needed in the interpretation of airborne VLF resistivity measurements. Instead, the primary field must be replaced by an inhomogeneous plane wave incident on the ground at an angle close to 90 degrees in order to provide the correct behavior of the apparent resistivities in the air. VLF magnetic polarization parameters, however, can be modeled in the air using the normally incident plane wave as a primary field. We also show that the plane‐wave analysis provides the same attenuation characteristics for the wavetilt in the air that is predicted by the Norton’s surface wave obtained by using the vertical electric dipole as a source. Use of the inhomogeneous plane wave introduces the vertical component of the electric field in the model. A 2‐D modeling technique based on the network solution is used to demonstrate the effects of the vertical electric field in the H‐polarization case. The vertical electric field generates charge distributions on the horizontal boundaries of conductors. In the case of a vertical sheet‐like conductor, these charges cause a slight asymmetry in apparent‐resistivity anomalies. Attenuation characteristics of various VLF anomalies with altitude are also presented. The H‐polarization anomalies attenuate much more rapidly in the air than those for E‐polarization due to the difference in the dominating source of EM fields in each polarization.


1967 ◽  
Vol 63 (4) ◽  
pp. 1273-1280 ◽  
Author(s):  
B. D. Sleeman

SummaryThe problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.


2008 ◽  
Vol 38 (8) ◽  
pp. 1794-1806 ◽  
Author(s):  
Lucia Bunge ◽  
Christine Provost ◽  
Bach Lien Hua ◽  
Annie Kartavtseff

Abstract Time series of high vertical resolution current meter measurements between 600-m and 1800-m depths on the equator in the Atlantic were obtained at two locations, 10° and 23°W. The measurements have a time span of almost 7 years (2000–06) and provide insights into the temporal scales and vertical structure of variability at intermediate depths. Variability in the zonal velocity component records is dominated by semiannual, annual, and interannual fluctuations. At semiannual and annual periodicities, vertical scales are large, on the order of 2000 stretched meters (sm), and show upward phase propagation. In contrast, interannual variability is associated with small vertical scale flows, called equatorial deep jets (EDJs), presenting downward phase propagation most of the time. Fitting a plane wave to these small vertical-scale flows leads to velocity amplitude, vertical scale, and temporal scale estimates of 8 (normalized) cm s−1, 440 sm, and 4.4 yr. However, this plane wave cannot explain all the variability presenting small vertical scales. Indeed, the data suggest that, along with a seasonal cycle of much larger vertical scale, different features with EDJ vertical scale coexist, with the possibility of a semipermanent eastward jet at around 1500 sm. Variability in the meridional velocity component is dominated by intraseasonal fluctuations. In addition, at 23°W, the meridional component shows low-frequency flows that may be due to the interaction of zonal fluctuations with the Mid-Atlantic Ridge.


Sign in / Sign up

Export Citation Format

Share Document