Observations of anomalous acoustic penetration into sediment at shallow grazing angles.

1996 ◽  
Vol 99 (4) ◽  
pp. 2473-2500 ◽  
Author(s):  
Joseph L. Lopes
Keyword(s):  
Acoustic Penetration ◽  
Grazing Angles

Acoustic penetration at subcritical grazing angles: Measurements and comparison with simulations based on perturbation theory

2000 ◽  
Vol 108 (5) ◽  
pp. 2510-2510
Author(s):  
Darrell R. Jackson ◽  
Kevin L. Williams ◽  
Dajun Tang ◽  
Eric I. Thorsos
Keyword(s):  
Perturbation Theory ◽  
Acoustic Penetration ◽  
Grazing Angles

Intensity of Choppy Sea Radar Backscattering for Small Grazing Angles

2004 ◽  
Vol 61 (2) ◽  
pp. 104-115
Author(s):  
V. G. Gutnik ◽  
G. P. Kulemin ◽  
L. I. Sharapov ◽  
E. A. Goroshko
Keyword(s):  
Radar Backscattering ◽  
Grazing Angles

scholarly journals Accurate analytic approximation for the Chapman grazing incidence function

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Dmytro Vasylyev
Keyword(s):  
Asymptotic Expansion ◽  
Radiative Transfer ◽  
Bessel Functions ◽  
Grazing Incidence ◽  
Analytical Approximation ◽  
Analytic Approximation ◽  
Atmospheric Physics ◽  
Uniform Asymptotic Expansion ◽  
Grazing Angles ◽  
Physical And Chemical

AbstractA new analytical approximation for the Chapman mapping integral, $${\text {Ch}}$$ Ch , for exponential atmospheres is proposed. This formulation is based on the derived relation of the Chapman function to several classes of the incomplete Bessel functions. Application of the uniform asymptotic expansion to the incomplete Bessel functions allowed us to establish the precise analytical approximation to $${\text {Ch}}$$ Ch , which outperforms established analytical results. In this way the resource consuming numerical integration can be replaced by the derived approximation with higher accuracy. The obtained results are useful for various branches of atmospheric physics such as the calculations of optical depths in exponential atmospheres at large grazing angles, physical and chemical aeronomy, atmospheric optics, ionospheric modeling, and radiative transfer theory.

scholarly journals DOPPLER SPECTRUM MATHEMATICAL MODEL OF SIGNAL SCATTERING FROM SEA SURFACE AT LOW GRAZING ANGLES

2019 ◽  
Vol 22 (3) ◽  
pp. 63-73
Author(s):  
Mikhail A. Borodin ◽  
Vyacheslav N. Mikhaylov ◽  
Polina A. Filippova
Keyword(s):  
Mathematical Model ◽  
Electromagnetic Field ◽  
Surface Condition ◽  
Scattering Problem ◽  
Microwave Frequency ◽  
Ecological Monitoring ◽  
Sea Surface ◽  
Doppler Spectrum ◽  
Random Component ◽  
Grazing Angles

Introduction. Doppler spectra of signals which are scattered from sea surface and received by radar is used in oceanology and ecological monitoring applications. Existing models of Doppler spectra have the limitation of application because they are based on empirical data in changing conditions. Variability of the observation conditions critically influence on microwaves scattering by sea surface at low grazing angles which is typical for marine radiolocations. Objective. The goal of investigation proposed in this article is to develop the mathematical model of Doppler spectra at low grazing angles for microwave frequency range. Materials and methods. The two-dimensional problem of the scattering of an electromagnetic field on a cylindrical deterministic surface is considered. For generating of sea surface realizations is used linear model with spatial sea spectrum Elfohaily. The solution of the scattering problem is obtained for the case of vertical polarization of the incident electromagnetic field by the method of an integral equation with the control of the error of the solution. The mathematical modeling of the Doppler Spectrum of signal scattered by sea surface is produced by method of statistical trial. The case where the direction of the observation of the sea surface by radar is perpendicular to the direction of the wind is considered. The electromagnetic filed scattered in the direction of the radar receiver as a function of time is calculated for each generated sea surface realizations. Further, the set of variables of the implementation of scattered field is calculated for implementation of the Doppler spectrum. Results. The set of implementations of the Doppler spectrum provided its mathematical model with consist of deterministic and random component. The approximation of each aforesaid component is suggested and mathematical expressions for value component calculation are presented. The analyze of modeling result is produced. Conclusion. The developed mathematical model is offered to use for the design of algorithm sea surface condition estimation and pollutant detection using the signal which received by radar.

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