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.

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.

The use and misuse of apparent resistivity in electromagnetic methods

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1462-1471 ◽  
Author(s):  
Brian R. Spies ◽  
Dwight E. Eggers
Keyword(s):  
Apparent Resistivity ◽  
Early Time ◽  
Asymptotic Formulas ◽  
Voltage Response ◽  
Late Time ◽  
Induced Voltage ◽  
Resistivity Curve ◽  
Transient Electromagnetic ◽  
Electromagnetic Methods ◽  
Tem Method

Problems and misunderstandings arise with the concept of apparent resistivity when the analogy between an apparent resistivity computed from geophysical observations and the true resistivity structure of the subsurface is drawn too tightly. Several definitions of apparent resistivity are available for use in electromagnetic methods; however, those most commonly used do not always exhibit the best behavior. Many of the features of the apparent resistivity curve which have been interpreted as physically significant with one definition disappear when alternative definitions are used. It is misleading to compare the detection or resolution capabilities of different field systems or configurations solely on the basis of the apparent resistivity curve. For the in‐loop transient electromagnetic (TEM) method, apparent resistivity computed from the magnetic field response displays much better behavior than that computed from the induced voltage response. A comparison of “exact” and “asymptotic” formulas for the TEM method reveals that automated schemes for distinguishing early‐time and late‐time branches are at best tenuous, and those schemes are doomed to failure for a certain class of resistivity structures (e.g., the loop size is large compared to the layer thickness). For the magnetotelluric (MT) method, apparent resistivity curves defined from the real part of the impedance exhibit much better behavior than curves based on the conventional definition that uses the magnitude of the impedance. Results of using this new definition have characteristics similar to apparent resistivity obtained from time‐domain processing.

scholarly journals Laplace Transform for Finite Element Analysis of Electromagnetic Interferences in Underground Metallic Structures

2022 ◽  
Vol 12 (2) ◽  
pp. 872
Author(s):  
Andrea Cristofolini ◽  
Arturo Popoli ◽  
Leonardo Sandrolini ◽  
Giacomo Pierotti ◽  
Mattia Simonazzi
Keyword(s):  
Finite Element ◽  
Laplace Transform ◽  
Electromagnetic Interference ◽  
Inverse Laplace Transform ◽  
Element Analysis ◽  
Metallic Structures ◽  
Numerical Inverse Laplace Transform ◽  
Transient Electromagnetic ◽  
The Time Domain ◽  
High Voltage Power Lines

A numerical methodology is proposed for the calculation of transient electromagnetic interference induced by overhead high-voltage power lines in metallic structures buried in soil—pipelines for oil or gas transportation. A series of 2D finite element simulations was employed to sample the harmonic response of a given geometry section. The numerical inverse Laplace transform of the results allowed obtaining the time domain evolution of the induced voltages and currents in the buried conductors, for any given condition of the power line.

scholarly journals INDUCTIVE SOURCE INDUCED POLARIZATION OF FROZEN ROCKS AND ITS RELATIONSHIP WITH DIELECTRIC RELAXATION OF ICE

2021 ◽  
Vol 2 (2) ◽  
pp. 67-73
Author(s):  
Nikolay O. Kozhevnikov
Keyword(s):  
Dielectric Relaxation ◽  
Decay Rate ◽  
Current Source ◽  
Induced Polarization ◽  
Voltage Source ◽  
Voltage Response ◽  
Current Response ◽  
Polarization Current ◽  
Polarization Voltage ◽  
Transient Electromagnetic

Fast decaying induced polarization in frozen rocks manifest itself as a not monotone induction transients. To account for induced polarization in the transient electromagnetic method, one usually uses the Pelton resistivity model. The relaxation time t, as found using the Pelton model, determines the decay rate of induced polarization voltage response to a current source. Conversion from t to the time constant t specifying the decay rate of the polarization current response to a voltage source, suggests that fast decaying induced polarization in frozen rocks is controlled by the dielectric relaxation of ice.

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.

scholarly journals Research and Fabrication of Broadband Ring Flextensional Underwater Transducer

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1548
Author(s):  
Jiuling Hu ◽  
Lianjin Hong ◽  
Lili Yin ◽  
Yu Lan ◽  
Hao Sun ◽  
...  
Keyword(s):  
High Speed ◽  
Structural Parameters ◽  
Low Frequency ◽  
Flexural Vibration ◽  
Underwater Acoustic Communication ◽  
Voltage Response ◽  
Water Tank ◽  
Spherical Cap ◽  
Finite Element Software ◽  
Underwater Transducer

At present, high-speed underwater acoustic communication requires underwater transducers with the characteristics of low frequency and broadband. The low-frequency transducers also are expected to be low-frequency directional for realization of point-to-point communication. In order to achieve the above targets, this paper proposes a new type of flextensional transducer which is constructed of double mosaic piezoelectric ceramic rings and spherical cap metal shells. The transducer realizes broadband transmission by means of the coupling between radial vibration of the piezoelectric rings and high-order flexural vibration of the spherical cap metal shells. The low-frequency directional transmission of the transducer is realized by using excitation signals with different amplitude and phase on two mosaic piezoelectric rings. The relationship between transmitting voltage response (TVR), resonance frequency and structural parameters of the transducer is analyzed by finite element software COMSOL. The broadband performance of the transducer is also optimized. On this basis, the low-frequency directivity of the transducer is further analyzed and the ratio of the excitation signals of the two piezoelectric rings is obtained. Finally, a prototype of the broadband ring flextensional underwater transducer is fabricated according to the results of simulation. The electroacoustic performance of the transducer is tested in an anechoic water tank. Experimental results show that the maximum TVR of the transducer is 147.2 dB and the operation bandwidth is 1.5–4 kHz, which means that the transducer has good low-frequency, broadband transmission capability. Meanwhile, cardioid directivity is obtained at 1.4 kHz and low-frequency directivity is realized.

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

scholarly journals Design and implementation of a jellyfish otolith-inspired MEMS vector hydrophone for low-frequency detection

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Renxin Wang ◽  
Wei Shen ◽  
Wenjun Zhang ◽  
Jinlong Song ◽  
Nansong Li ◽  
...  
Keyword(s):  
Structural Parameters ◽  
Low Frequency ◽  
Directivity Pattern ◽  
Stress Distributions ◽  
Strong Response ◽  
Underwater Acoustic ◽  
Frequency Detection ◽  
Vector Hydrophone ◽  
Shock Resistance ◽  
Marine Applications

AbstractDetecting low-frequency underwater acoustic signals can be a challenge for marine applications. Inspired by the notably strong response of the auditory organs of pectis jellyfish to ultralow frequencies, a kind of otolith-inspired vector hydrophone (OVH) is developed, enabled by hollow buoyant spheres atop cilia. Full parametric analysis is performed to optimize the cilium structure in order to balance the resonance frequency and sensitivity. After the structural parameters of the OVH are determined, the stress distributions of various vector hydrophones are simulated and analyzed. The shock resistance of the OVH is also investigated. Finally, the OVH is fabricated and calibrated. The receiving sensitivity of the OVH is measured to be as high as −202.1 dB@100 Hz (0 dB@1 V/μPa), and the average equivalent pressure sensitivity over the frequency range of interest of the OVH reaches −173.8 dB when the frequency ranges from 20 to 200 Hz. The 3 dB polar width of the directivity pattern for the OVH is measured as 87°. Moreover, the OVH is demonstrated to operate under 10 MPa hydrostatic pressure. These results show that the OVH is promising in low-frequency underwater acoustic detection.

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

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