Electromagnetic traveltime tomography using an approximate wavefield transform

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 68-76 ◽  
Author(s):  
Tae Jong Lee ◽  
Jung Hee Suh ◽  
Hee Joon Kim ◽  
Yoonho Song ◽  
Ki Ha Lee
Keyword(s):  
Frequency Domain ◽  
Series Expansion ◽  
Arrival Time ◽  
Integral Transform ◽  
Closed Form Solution ◽  
Form Solution ◽  
Dipole Source ◽  
Traveltime Tomography ◽  
Whole Space ◽  
Ray Series

We present an imaging scheme for mapping cross‐hole electrical conductivity using nonlinear traveltime tomography. Data used are peak arrival time estimates based on an approximate wavefield transform of the synthetic frequency‐domain electromagnetic (EM) field. Direct transformation of frequency‐domain EM fields to wavefields is known to be an ill‐posed problem because the kernel of integral transform is highly damped. In this study, instead of solving such an unstable problem, we approximate the wavefield in the transformed domain via a ray series expansion. If reflected and refracted energy is weak compared to that of direct wave, picking of the peak arrival time may be reduced to estimating the coefficients of the leading term in the ray series expansion. This simplification is valid when the conductivity contrast between background medium and the target anomalous body is small. The first three terms in the expansion are identical to the closed‐form solution for the vertical magnetic field caused by a vertical magnetic dipole source in a homogeneous whole‐space. An adaptive simulated annealing scheme is used to estimate the coefficients of ray series. For a whole‐space, exact traveltime can be extracted using only four frequency samples in our approach, whereas the direct numerical wavefield transform needed at least ten frequencies to construct a reasonable waveform. Nonlinear traveltime tomography using thusly‐extracted peak arrivals from synthetic data shows a reasonable image of the conductivity structure between boreholes.

Robust global registration of point clouds by closed-form solution in the frequency domain

2021 ◽  
Vol 171 ◽  
pp. 310-329
Author(s):  
Rong Huang ◽  
Yusheng Xu ◽  
Wei Yao ◽  
Ludwig Hoegner ◽  
Uwe Stilla
Keyword(s):  
Closed Form ◽  
Frequency Domain ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Global Registration

scholarly journals Acoustic Wave Propagation in a Trifurcated Lined Waveguide

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Ayub ◽  
M. H. Tiwana ◽  
A. B. Mann ◽  
H. Zaman
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Closed Form ◽  
Integral Transform ◽  
Closed Form Solution ◽  
Form Solution ◽  
Kernel Functions ◽  
Acoustic Wave Propagation ◽  
Proper Selection ◽  
Selection Of

The diffraction of sound from a semi-infinite soft duct is investigated. The soft duct is symmetrically located inside an acoustically lined but infinite duct. A closed-form solution is obtained using integral transform and Jones' method based on Wiener-Hopf technique. The graphical results are presented, which show how effectively the unwanted noise can be reduced by proper selection of different parameters. The kernel functions are factorized with different approaches. The results may be used to design acoustic barriers and noise reduction devices.

Low-frequency electromagnetic fields in applied geophysics: Waves or diffusion?

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. W29-W40 ◽  
Author(s):  
Lars O. Løseth ◽  
Hans M. Pedersen ◽  
Bjørn Ursin ◽  
Lasse Amundsen ◽  
Svein Ellingsrud
Keyword(s):  
Frequency Domain ◽  
Low Frequency ◽  
Wave Theory ◽  
Signal Propagation ◽  
Dipole Source ◽  
Conductive Materials ◽  
Em Field ◽  
Domain Description ◽  
Ray Series ◽  
Low Frequency Waves

Low-frequency electromagnetic (EM) signal propagation in geophysical applications is sometimes referred to as diffusion and sometimes as waves. In the following we discuss the mathematical and physical approaches behind the use of the different terms. The basic theory of EM wave propagation is reviewed. From a frequency-domain description we show that all of the well-known mathematical tools of wave theory, including an asymptotic ray-series description, can be applied for both nondispersive waves in nonconductive materials and low-frequency waves in conductive materials. We consider the EM field from an electric dipole source and show that a common frequency-domain description yields both the undistorted pulses in nonconductive materials and the strongly distorted pulses in conductive materials. We also show that the diffusion-equation approximation of low-frequency EM fields in conductive materials gives the correct mathematical description, and this equation has wave solutions. Having considered both a wave-picture approach and a diffusion approach to the problem, we discuss the possible confusion that the use of these terms might lead to.

Frequency domain analysis method of nonstationary random vibration based on evolutionary spectral representation

2018 ◽  
Vol 35 (2) ◽  
pp. 1098-1127
Author(s):  
Yan Zhao ◽  
L.T. Si ◽  
H. Ouyang
Keyword(s):  
Frequency Domain ◽  
Random Vibration ◽  
Closed Form Solution ◽  
Frequency Domain Analysis ◽  
Random Excitation ◽  
Form Solution ◽  
Computational Time ◽  
Content Type ◽  
Damped System ◽  
Evolutionary Spectrum

Purpose A novel frequency domain approach, which combines the pseudo excitation method modified by the authors and multi-domain Fourier transform (PEM-FT), is proposed for analyzing nonstationary random vibration in this paper. Design/methodology/approach For a structure subjected to a nonstationary random excitation, the closed-form solution of evolutionary power spectral density of the response is derived in frequency domain. Findings The deterministic process and random process in an evolutionary spectrum are separated effectively using this method during the analysis of nonstationary random vibration of a linear damped system, only modulation function of the system needs to be estimated, which brings about a large saving in computational time. Originality/value The method is general and highly flexible as it can deal with various damping types and nonstationary random excitations with different modulation functions.

A finite element multifrontal method for 3D CSEM modeling in the frequency domain

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. E101-E115 ◽  
Author(s):  
Nuno Vieira da Silva ◽  
Joanna V. Morgan ◽  
Lucy MacGregor ◽  
Mike Warner
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Frequency Domain ◽  
Closed Form Solution ◽  
Form Solution ◽  
Computational Domain ◽  
Order Partial Differential Equation ◽  
Primary Field ◽  
Direct Solver ◽  
Linear System Of Equations

There has been a recent increase in the use of controlled-source electromagnetic (CSEM) surveys in the exploration for oil and gas. We developed a modeling scheme for 3D CSEM modeling in the frequency domain. The electric field was decomposed in primary and secondary components to eliminate the singularity originated by the source term. The primary field was calculated using a closed form solution, and the secondary field was computed discretizing a second-order partial differential equation for the electric field with the edge finite element. The solution to the linear system of equations was obtained using a massive parallel multifrontal solver, because such solvers are robust for indefinite and ill-conditioned linear systems. Recent trends in parallel computing were investigated for their use in mitigating the computational overburden associated with the use of a direct solver, and of its feasibility for 3D CSEM forward modeling with the edge finite element. The computation of the primary field was parallelized, over the computational domain and the number of sources, using a hybrid model of parallelism. When using a direct solver, the attainment of multisource solutions was only competitive if the same factors are used to achieve a solution for multi right-hand sides. This aspect was also investigated using the presented methodology. We tested our proposed approach using 1D and 3D synthetic models, and they demonstrated that it is robust and suitable for 3D CSEM modeling using a distributed memory system. The codes could thus be used to help design new surveys, as well to estimate subsurface conductivities through the implementation of an appropriate inversion scheme.

Analytical Investigation of Non-Fourier Bio-Heat Transfer in the Axisymmetric Living Tissue Exposed to Pulsed Laser Heating Using Finite Integral Transform Technique

2021 ◽  
Author(s):  
Pankaj Kishore ◽  
Sumit Kumar
Keyword(s):  
Heat Transfer ◽  
Laser Heating ◽  
Integral Transform ◽  
Closed Form Solution ◽  
Pulsed Laser ◽  
Form Solution ◽  
Living Tissue ◽  
Finite Integral ◽  
Pulsed Laser Heating ◽  
Fourier Model

Abstract The present article proposed the closed-form solution of the generalized non-Fourier model-based bio-heat transfer equation (BHTE) in Cylindrical coordinates to understand the thermal behavior of living tissue heated by a pulsed laser. The axisymmetric living tissue exposed to the non-Gaussian temporal profile of laser heating has been considered to investigate the non-Fourier bio-heat transfer phenomena. The closed-form solution of the generalized non-Fourier model-based BHTE with time-dependent thermal energy generation has been obtained through the finite integral transform technique. The analytical solution was juxtaposed to the corresponding numerical solution in order to determine its reliability. The numerical solution of the aforementioned governing equation has been obtained by the finite volume method. The results of both analytical and numerical solutions have been verified using results given in published literature. Subsequently, the dual-phase-lag model's findings were juxtaposed to those obtained using the hyperbolic and traditional Fourier models. The effect of different parameters like relaxation times corresponding to the temperature gradient and heat flux, metabolic energy generation, and blood perfusion on the resultant temperature distribution inside the axisymmetric living tissue exposed to pulsed laser heating has been discussed. The importance of the present study might be found in various applications such as laser-based-photo-thermal therapy, melting of the surface of metal and alloys by laser heating, etc.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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