Transient electromagnetic calculations using the Gaver‐Stehfest inverse Laplace transform method

Geophysics ◽  
1982 ◽  
Vol 47 (1) ◽  
pp. 47-50 ◽  
Author(s):  
J. H. Knight ◽  
A. P. Raiche
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Discrete Fourier Transform ◽  
Inverse Laplace Transform ◽  
Computationally Efficient ◽  
Transform Method ◽  
Transient Electromagnetic ◽  
The Laplace Transform ◽  
Tem Method ◽  
Electromagnetic Calculations

Calculations for the transient electromagnetic (TEM) method are commonly performed by using a discrete Fourier transform method to invert the appropriate transform of the solution. We derive the Laplace transform of the solution for TEM soundings over an N‐layer earth and show how to use the Gaver‐Stehfest algorithm to invert it numerically. This is considerably more stable and computationally efficient than inversion using the discrete Fourier transform.

A memory-dependent derivative model for damping in oscillatory systems

2016 ◽  
Vol 24 (11) ◽  
pp. 2221-2229 ◽  
Author(s):  
Ahmed Al-Jamel ◽  
Mohammad F Al-Jamal ◽  
Ahmed El-Karamany
Keyword(s):  
Laplace Transform ◽  
Response Function ◽  
Interesting Case ◽  
Memory Effects ◽  
Inverse Laplace Transform ◽  
Damping Force ◽  
Transform Method ◽  
Oscillatory Systems ◽  
The Laplace Transform ◽  
Mechanical Models

Classically, damping force is described as a function of velocity in the linear theory of mechanical models. In this work, a memory-dependent derivative model with respect to displacement is proposed to describe damping in various oscillatory systems of complex dissipation mechanisms where memory effects could not be ignored. A memory-dependent derivative is characterized by its time-delay τ and kernel function K( x, t) which can be chosen freely. Thus, it is superior to the fractional derivative in that it provides more access into memory effects and thus better physical meaning. To elucidate this, an equation of motion is proposed based on the prototype mass-spring model. The analytical solution is then attempted by the Laplace transform method. Due to the complexity of finding the inverse Laplace transform, a numerical inversion treatment is carried out using the fixed Talbot method and also compared with the finite difference discretization to validate the method. The calculations show that the response function is sensitive to different choices of τ and K( x, t). It is found that this proposed model supports the existence of memory-dependence in the structure of the material. The interesting case of resonance where the response function is classically increased rapidly is found to be weakened by an appropriate choice of τ and K( x, t).

RADIATION FROM A FINITE CYLINDRICAL EXPLOSIVE SOURCE

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1384-1393 ◽  
Author(s):  
Anas M. Abo‐Zena
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Fourier Transforms ◽  
Inverse Fourier Transform ◽  
Applied Pressure ◽  
Inverse Laplace Transform ◽  
Laplace And Fourier Transforms ◽  
Explosion Pressure ◽  
Explosive Source ◽  
The Laplace Transform

For an elastic material with an infinite circular cylindrical hole, the exact solution due to a pressure on a finite length of the cylinder is obtained as a function of the Laplace transform parameter on time and Fourier transform parameter on the z-coordinate (the axis of the cylinder). The applied pressure is a function of the time and the position z. Numerical inversion of the Laplace and Fourier transforms are required to determine the field quantities in the time and space parameters. In the far field, the inverse Fourier transform can be obtained by an asymptotic expansion. It remains to obtain the inverse Laplace transform numerically. We have found that for cylinders whose radius is small compared with the smallest wavelength of interest, an analytical solution can be obtained. Graphical results for the cases of instantaneous explosion and progression of the detonation with constant velocity are given. In both cases an exponential decay of the explosion pressure is assumed.

scholarly journals Scattering of Lower Hybrid Waves in a Magnetized Plasma

Physics ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 640-653
Author(s):  
Brunello Tirozzi
Keyword(s):  
Fourier Transform ◽  
Electric Field ◽  
Laplace Transform ◽  
Electromagnetic Waves ◽  
Inverse Fourier Transform ◽  
Magnetized Plasma ◽  
Inverse Laplace Transform ◽  
Lower Hybrid ◽  
Lower Hybrid Wave ◽  
The Laplace Transform

In this paper, the Maxwell equations for the electric field in a cold magnetized plasma in the half-space of x≥0 cm are solved. The boundary conditions for the electric field include a pointwise source at the plane x=0 cm, the derivatives of the electric field that are zero statV/cm2 at x=0 cm, and the field with all its derivatives that are zero at infinity. The solution is explored in terms of the Laplace transform in x and the Fourier transform in y-z directions. The expressions of the field components are obtained by the inverse Laplace transform and the inverse Fourier transform. The saddle-point technique and power expansion have been used for evaluating the inverse Fourier transform. The model represents the propagation of a lower hybrid wave generated by a pointwise antenna located at the boundary of the plasma. Here, the antenna is the boundary condition. The validation of the model is performed assuming that the electric field component Ey=0 statV/cm and by comparing it with the model of electromagnetic waves generated by a local small antenna located near the boundary of a tokamak, and an experiment is suggested.

scholarly journals Talbot Algorithm with a Trapezoidal Wave in the 2.5D Airborne Transient Electromagnetic Method in Marine Investigations

2020 ◽  
Vol 10 (5) ◽  
pp. 1812
Author(s):  
Boya Li ◽  
Huotao Gao ◽  
Huaqiao Zhao ◽  
Lijuan Yang ◽  
Haitao Chen
Keyword(s):  
Laplace Transform ◽  
Current Source ◽  
Low Frequency ◽  
Inverse Laplace Transform ◽  
Voltage Response ◽  
Marine Research ◽  
Transient Electromagnetic ◽  
Marine Applications ◽  
Tem Method ◽  
Transmitted Waveform

The airborne transient electromagnetic (TEM) method is widely used in land applications but faces challenges in marine applications due to the strong masking effects of seawater. The accuracy of the inverse Laplace transform algorithm strongly affects the applicability of the 2.5D TEM method in marine research; thus, an appropriate transmitted waveform is required. To resolve these issues, a trapezoidal wave was utilized as the waveform of the current source, owing to the substantial energy contribution of the low-frequency range. Further, the Talbot algorithm was selected for the inverse Laplace transform as it can yield an accurate response with smaller summation terms than the commonly used Gaver–Stehfest (G-S) algorithm. On this basis, a rugged seabed and a subsea tunnel were also investigated. The voltage response is obtained when the flight heights of the loop source change. The results confirmed that the Talbot algorithm with a trapezoidal waveform is more reliable and robust for complex marine geological models and is expected to provide an effective approach for marine explorations.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

Generalized coupled transient thermoelastic problem of multilayered spheres by the hybrid numerical method

2003 ◽  
Vol 217 (12) ◽  
pp. 1315-1323
Author(s):  
Z Y Lee ◽  
C L Chang
Keyword(s):  
Laplace Transform ◽  
Finite Difference Methods ◽  
Generalized Thermoelasticity ◽  
Inverse Laplace Transform ◽  
Hybrid Numerical Method ◽  
The Matrix ◽  
The Laplace Transform ◽  
Computational Procedures ◽  
Thermoelastic Problems ◽  
Matrix Similarity

This paper deals with axisymmetric quasi-static coupled thermoelastic problems for multilayered spheres. Laplace transforms and finite difference methods are used to analyse the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions are obtained for the temperature and thermal deformation distributions for the transient and steady state. It is demonstrated that the computational procedures established in this paper are capable of solving the generalized thermoelasticity problem of multilayered spheres.

Analysis of the neutron spin structure function g1n by using the Laplace transform technique

2018 ◽  
Vol 27 (08) ◽  
pp. 1850071
Author(s):  
F. Teimoury Azadbakht ◽  
G. R. Boroun ◽  
B. Rezaei
Keyword(s):  
Laplace Transform ◽  
Structure Function ◽  
Spin Structure ◽  
Neutron Spin ◽  
Spin Structure Function ◽  
Transform Method ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Convolution Approach ◽  
Neutron Spin Structure

In this paper, the polarized neutron structure function [Formula: see text] in the [Formula: see text] nucleus is investigated and an analytical solution based on the Laplace transform method for [Formula: see text] is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of [Formula: see text]. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of [Formula: see text] nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for [Formula: see text] are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.

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