scholarly journals On application of the finite-difference Padé approximation of the pseudo-differential parabolic equation to the tropospheric radio wave propagation problem

2020 ◽  
pp. 405-419
Author(s):  
М.С. Лытаев
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Electromagnetic Wave Propagation ◽  
Padé Approximation ◽  
Fourier Method ◽  
Geometric Theory ◽  
Wide Angle ◽  
Pade Approximation ◽  
Propagation Angle ◽  
Wave Propagation Problem

Рассматривается задача численного моделирования распространения электромагнитных волн в неоднородной тропосфере на основе широкоугольных обобщений метода параболического уравнения. Используется конечно-разностная аппроксимация Паде оператора распространения. Существенно, что в предлагаемом подходе указанная аппроксимация осуществляется одновременно по продольной и поперечной координатам. При этом допускается моделирование произвольного коэффициента преломления тропосферы. Метод не накладывает ограничений на максимальный угол распространения. Для различных условий распространения радиоволн проведено сравнение с методом расщепления Фурье и методом геометрической теории дифракции. Показаны преимущества предлагаемого подхода. This paper is devoted to the numerical simulation of electromagnetic wave propagation in an inhomogeneous troposphere. The study is based on the wide-angle generalizations of the parabolic wave equation. The finite-difference Padé approximation is used to approximate the propagation operator. It is important that, within the proposed approach, the Padé approximation is carried out simultaneously along with the longitudinal and transverse coordinates. At the same time, the proposed approach gives an opportunity to model an arbitrary tropospheric refractive index. The method does not impose restrictions on the maximum propagation angle. The comparison with the split-step Fourier method and the geometric theory of diffraction is discussed. The advantages of the proposed approach are shown.

The Alekseev–Mikhailenko method applied to P–SV wave propagation in an elastic medium

1988 ◽  
Vol 25 (2) ◽  
pp. 226-234
Author(s):  
L. J. Pascoe ◽  
F. Hron ◽  
P. F. Daley
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Half Space ◽  
Elastic Half Space ◽  
Low Velocity ◽  
Seismic Modelling ◽  
Wave Propagation Problem ◽  
Modelling Techniques ◽  
Explicit Finite Difference ◽  
The Stability

The Alekseev–Mikhailenko method (AMM) is the name given to a series of algorithms that use one or more finite spatial transforms to reduce the dimensionality of a wave-propagation problem to that of one space dimension and time. This reduced equation is then solved using finite-difference techniques, and the space–time solution is recovered by applying inverse finite spatial transform(s). In this paper the elastodynamic wave equation that governs the coupled P–Sv motion in an isotropic, vertically inhomogeneous elastic half space is investigated using the AMM. Two types of impulsive body forces that may be used to excite the medium are examined, as is the problem of obtaining accurate transformed finite-difference analogues at the free surface. The second of these is accomplished by introducing the boundary conditions that the shear and normal stress must vanish here and by incorporating their transforms into the transformed elastodynamic equations. The stability criterion for the explicit finite-difference method is given cursory treatment, as detailed discussion of this aspect may be found in many texts that deal with the subject of finite differences.A coal-seam model (two thin, low-velocity layers embedded in a half space) illustrates the method. Both horizontal and vertical seismic traces are computed for this model and the results examined in relation to other seismic-modelling techniques.

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

2011 ◽  
Author(s):  
Carlos A. N. Costa ◽  
Itamara S. Campos ◽  
Jessé C. Costa ◽  
Francisco A. Silva Neto ◽  
Jörg Schleicher ◽  
...  
Keyword(s):  
Finite Difference ◽  
Iterative Methods ◽  
Padé Approximation ◽  
Pade Approximation ◽  
Implicit Finite Difference

Optimum split-step Fourier 3D depth migration: Developments and practical aspects

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S167-S175 ◽  
Author(s):  
Jianfeng Zhang ◽  
Linong Liu
Keyword(s):  
Finite Difference ◽  
Heterogeneous Media ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Fourier Method ◽  
Approximate Algorithm ◽  
Wide Angle ◽  
Data Set ◽  
Depth Migration ◽  
Varying Coefficients

We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.

scholarly journals NUMERICAL METHOD FOR ELECTROMAGNETIC WAVE PROPAGATION PROBLEM IN A CYLINDRICAL INHOMOGENEOUS METAL DIELECTRIC WAVEGUIDING STRUCTURES

2017 ◽  
Vol 22 (3) ◽  
pp. 271-282 ◽  
Author(s):  
Eugene Smolkin
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Electromagnetic Waves ◽  
Electromagnetic Wave Propagation ◽  
Physical Problem ◽  
Dielectric Waveguides ◽  
Spectral Parameters ◽  
Transmission Eigenvalue ◽  
Wave Propagation Problem ◽  
Transmission Eigenvalue Problem

The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguides filled with inhomogeneous medium is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with a projection method. The comparison with known exact solutions (for particular values of parameters) is made.

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