From time domain to Laplace domain

2016 ◽  
pp. 21-38
Author(s):  
Francisco-Javier Sayas
Keyword(s):  
Time Domain ◽  
Laplace Domain

Time domain modelling of concurrent insertion and capacitive storage using Laplace domain representations of impedance

2019 ◽  
Vol 850 ◽  
pp. 113379 ◽  
Author(s):  
Charles A. Hall ◽  
Aleksandar Ignjatovic ◽  
Yu Jiang ◽  
Patrick A. Burr ◽  
Alison Lennon
Keyword(s):  
Time Domain ◽  
Capacitive Storage ◽  
Laplace Domain ◽  
Domain Modelling

scholarly journals Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data

2019 ◽  
Vol 11 (16) ◽  
pp. 1839
Author(s):  
Xu Meng ◽  
Sixin Liu ◽  
Yi Xu ◽  
Lei Fu
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Radar Data ◽  
Dominant Frequency ◽  
Data Set ◽  
Laplace Domain ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
The Time Domain ◽  
Ground Penetrating

Full waveform inversion (FWI) can yield high resolution images and has been applied in Ground Penetrating Radar (GPR) for around 20 years. However, appropriate selection of the initial models is important in FWI because such an inversion is highly nonlinear. The conventional way to obtain the initial models for GPR FWI is ray-based tomogram inversion which suffers from several inherent shortcomings. In this paper, we develop a Laplace domain waveform inversion to obtain initial models for the time domain FWI. The gradient expression of the Laplace domain waveform inversion is deduced via the derivation of a logarithmic object function. Permittivity and conductivity are updated by using the conjugate gradient method. Using synthetic examples, we found that the value of the damping constant in the inversion cannot be too large or too small compared to the dominant frequency of the radar data. The synthetic examples demonstrate that the Laplace domain waveform inversion provide slightly better initial models for the time domain FWI than the ray-based inversion. Finally, we successfully applied the algorithm to one field data set, and the inverted results of the Laplace-based FWI show more details than that of the ray-based FWI.

A Numerical Method for Representing Retardation Functions With Complex Exponentials

2017 ◽  
Author(s):  
Fushun Liu ◽  
Lei Jin ◽  
Jiefeng Chen ◽  
Wei Li
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Memory Effects ◽  
Floating Structure ◽  
Frequency Dependent ◽  
Laplace Domain ◽  
The Time Domain ◽  
Frequency Domain Techniques

Numerical time- or frequency-domain techniques can be used to analyze motion responses of a floating structure in waves. Time-domain simulations of a linear transient or nonlinear system usually involve a convolution terms and are computationally demanding, and frequency-domain models are usually limited to steady-state responses. Recent research efforts have focused on improving model efficiency by approximating and replacing the convolution term in the time domain simulation. Contrary to existed techniques, this paper will utilize and extend a more novel method to the frequency response estimation of floating structures. This approach represents the convolution terms, which are associated with fluid memory effects, with a series of poles and corresponding residues in Laplace domain, based on the estimated frequency-dependent added mass and damping of the structure. The advantage of this approach is that the frequency-dependent motion equations in the time domain can then be transformed into Laplace domain without requiring Laplace-domain expressions of the added mass and damping. Two examples are employed to investigate the approach: The first is an analytical added mass and damping, which satisfies all the properties of convolution terms in time and frequency domains simultaneously. This demonstrates the accuracy of the new form of the retardation functions; secondly, a numerical six degrees of freedom model is employed to study its application to estimate the response of a floating structure. The key conclusions are: (1) the proposed pole-residue form can be used to consider the fluid memory effects; and (2) responses are in good agreement with traditional frequency-domain techniques.

Well Testing Applications of Numerical Laplace Transformation of Sampled-Data

1998 ◽  
Vol 1 (03) ◽  
pp. 268-277 ◽  
Author(s):  
M. Onur ◽  
A.C. Reynolds
Keyword(s):  
Parameter Estimation ◽  
Flow Rate ◽  
Time Domain ◽  
Laplace Transformation ◽  
Numerical Inversion ◽  
Rate Data ◽  
Sampled Data ◽  
Laplace Domain ◽  
The Time Domain ◽  
Measured Pressure

Abstract In recent years, the numerical Laplace transformation of sampled-data has proven to be useful for well test analysis applications. However, the success of this approach is highly dependent on the algorithms used to transform sampled-data into Laplace space and to perform the numerical inversion. In this work, we investigate several functional approximations (piecewise linear, quadratic, and log-linear) for sampled-data to achieve the "forward" Laplace transformation and present new methods to deal with the "tail" effects associated with transforming sampled-data. New algorithms that provide accurate transformation of sampled-data into Laplace space are provided. The algorithms presented can be applied to generate accurate pressure-derivatives in the time domain. Three different algorithms investigated for the numerical inversion of sampled-data. Applications of the algorithms to convolution, deconvolution, and parameter estimation in Laplace space are also presented. By using the algorithms presented here, it is shown that performing curve-fitting in the Laplace domain without numerical inversion is computationally more efficient than performing it in the time domain. Both synthetic and field examples are considered to illustrate the applicability of the proposed algorithms. Introduction Due to its efficiency, the Stehfest algorithm for the numerical inversion of the Laplace transform is now a well established tool in pressure transient analysis research and applications. Roumboutsos and Stewart showed that convolution and deconvolution in Laplace domain with the aid of the numerical Laplace transformation of measured pressure and/or rate data is more efficient and stable than techniques based on the discretized form of convolution integral in the time domain. Use of the numerical Laplace transformation of tabulated (pressure and/or rate) data has become increasingly popular in recent years for other well testing analysis purposes in a variety of applications; see for example, Refs. 3-10. Guillot and Horne were the first to use piecewise constant and cubic spline interpolations to represent measured flow rate data in Laplace space for the purpose of analyzing pressure tests under variable (downhole or surface) flow rate history by nonlinear regression. Roumboutsos and Stewart were the first to introduce the idea of using the numerical Laplace transformation of measured data for convolution and deconvolution purposes. They presented an algorithm based on piecewise linear interpolation of sampled-data, which can be used to transform measured pressure or rate data into Laplace space. Mendes et al. presented a Laplace domain deconvolution algorithm based on cubic spline interpolation of sampled-data. By considering deconvolution of DST data, they showed that Laplace domain deconvolution is fast and more stable than deconvolution methods based on the discretized forms of the convolution integral in the time domain. However, they noted that noise in pressure and flow rate measurements can also cause instability in Laplace space deconvolution methods, but they did not present any specific results on this issue. Both Corre and Thompson et al. showed that the convolution methods based on a representation of the linear interpolation of the tabulated unit-rate response solution and numerical inversion to the time domain are far more computationally efficient for generating variable rate solutions for complex well/reservoir systems (e.g., partially penetrating wells and horizontal wells) than convolution methods based on the direct use of analytical solutions in Laplace space. Using the numerical Laplace transformation of measured pressure data, Bourgeois and Horne introduced the so-called Laplace pressure and its derivative, and presented Laplace type curves based on these functions for model recognition and parameter estimation purposes. They also deconvolved data using these Laplace pressure functions in the Laplace domain without inversion to the time domain. Wilkinson investigated the applicability of performing nonlinear regression based on the Laplace pressure as suggested in Ref. 7 for parameter estimation purposes.

scholarly journals Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 101
Author(s):  
George C. Hsiao ◽  
Tonatiuh Sánchez-Vizuet
Keyword(s):  
Field Equation ◽  
Time Domain ◽  
Wave Structure ◽  
Scaling Factor ◽  
Time Dependent ◽  
Laplace Domain ◽  
Boundary Field ◽  
Structure Interaction ◽  
The Time Domain ◽  
Wave Structure Interaction

In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body that is immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided that an appropriate scaling factor is employed. As usual, based on estimates for solutions in the Laplace-transformed domain, we may obtain properties of corresponding solutions in the time-domain without having to perform the inversion of the Laplace-domain solutions.

Time‐domain solution for horizontal coaxial dipoles on a half‐space

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1850-1852 ◽  
Author(s):  
David C. Bartel
Keyword(s):  
Frequency Domain ◽  
Half Space ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
Direct Solution ◽  
Current Waveform ◽  
Laplace Domain ◽  
Homogeneous Half Space ◽  
The Time Domain ◽  
The Magnetic Field

The practice of transforming frequency‐domain results into the time domain is fairly common in electromagnetics. For certain classes of problems, it is possible to obtain a direct solution in the time domain. A summary of these solutions is given in Hohmann and Ward (1986). Presented here is another problem which can be solved directly in the time domain—the magnetic field of horizontal coaxial dipoles on the surface of a homogeneous half‐space. Solutions are presented for both an impulse transmitter current and a step turnon in the transmitter current. The solution in the time domain is obtained by taking the inverse Laplace transform of the product of the frequency‐domain solution and the Laplace‐domain representation of the current waveform.

scholarly journals Analysis of models for viscoelastic wave propagation

2018 ◽  
Vol 3 (1) ◽  
pp. 55-96 ◽  
Author(s):  
Thomas S. Brown ◽  
Shukai Du ◽  
Hasan Eruslu ◽  
Francisco-Javier Sayas
Keyword(s):  
Time Domain ◽  
Numerical Experiments ◽  
Semigroup Theory ◽  
Fractional Differentiation ◽  
Viscoelastic Solid ◽  
Laplace Domain ◽  
Viscoelastic Wave Propagation ◽  
Viscoelastic Wave ◽  
The Laplace Transform ◽  
The Time Domain

AbstractWe consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the coupling of different models within the same solid are covered as well. Stability of each model is investigated in the Laplace domain, and these are then translated to time-domain estimates. With the use of semigroup theory, some time-domain results are also given which avoid using the Laplace transform and give sharper estimates. We take the time to develop and explain the theory necessary to understand the relation between the equations we solve in the Laplace domain and those in the time-domain which are written using the language of causal tempered distributions. Finally we offer some numerical experiments that highlight some of the differences between the models and how different parameters effect the results.

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