Simple interpretation of time‐domain electromagnetic sounding using similarities between wave and diffusion propagation

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 763-774 ◽  
Author(s):  
Mier Gershenson
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Synthetic Data ◽  
Time Base ◽  
Time Interval ◽  
Exponential Time ◽  
The Laplace Transform ◽  
Image Function ◽  
The Time Domain ◽  
Conductive Media

By using similarities between EM sounding in dielectric and conductive media, it is shown that one can transform between solutions in one type of propagation to the other. The method is based on the similarities of the Laplace transform between diffusive and nondiffusive cases. In the diffusive case, the equation involves the Laplace variable s in the first power, while for the nondiffusive cases, similar equations occur with [Formula: see text]. Three alternative implementations are developed, and their use is demonstrated. The first implementation is based on substituting [Formula: see text] for the Laplace transform variable s using forward and inverse numerical Laplace transforms. The second implementation is based on expanding the diffusive time response on an exponential time base and replacing it with its image function in the wave case, namely, a sinusoidal function. The third implementation is based on direct transformation in the time domain using exponential time interval sampling. The performance of the techniques on synthetic data is demonstrated. Besides the advantage of simple implementation of these techniques, other advantages and limitations of the method and each of the implementations are discussed. A case history is presented. The application of common techniques used in the processing of seismic and radar for processing and EM sounding in conductive media is discussed. The use of the Poynting vector as a means of determining distance and direction is demonstrated.

scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

A generalization of the Laplace transform

1967 ◽  
Vol 63 (1) ◽  
pp. 155-160 ◽  
Author(s):  
H. S. Dunn
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Finite Interval ◽  
Integral Transformation ◽  
System Response ◽  
Simple Scheme ◽  
Exponential Order ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Determine System

AbstractAn integral transformation is denned over a finite interval of the time domain. When the Laplace transform exists, the finite transform yields identical results. However, the finite transform is found to be considerably more general than the Laplace transform. It permits consideration of functions which are not of exponential order, leads to a simple scheme to determine system response, and is applicable to boundary-value problems.

scholarly journals Rigorous time domain responses of polarizable media II

1998 ◽  
Vol 41 (3) ◽  
Author(s):  
M. Caputo ◽  
W. Plastino
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Time Domain ◽  
Input Data ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Discharge Data ◽  
Time Domain Data ◽  
Previous Note ◽  
The Laplace Transform

We present and test in detail with synthetic data a method which may be used to retrieve the parameters describing the induced polarization properties of media which fit the generally accepted frequency dependent formula of Cole and Cole (1941) (CC model). We use time domain data and rigorous formulae obtained from the exact solution of the problem found in a previous note (Caputo, 1996). The observed data considered here are the theoretical responses of the medium to box inputs of given duration in media defined with different parameters; however, as is usually done, only the discharge data are used (Patella >F2<et al.>F1<, 1987). The curve at the beginning of the discharge is studied in some detail. The method is successful in identifying the parameters when the data fit the CC model; if the medium is not exactly of the CC type the method may also help identify how the medium departs from the CC model. The Laplace Transform of the discharge for a box type input data is also given.

scholarly journals Last Exit Before an Exponential Time for Spectrally Negative Lévy Processes

2009 ◽  
Vol 46 (02) ◽  
pp. 542-558 ◽  
Author(s):  
E. J. Baurdoux
Keyword(s):  
Laplace Transform ◽  
Lévy Process ◽  
Risk Process ◽  
Levy Process ◽  
Risk Theory ◽  
Exponential Time ◽  
Main Motivation ◽  
Spectrally Negative Lévy Process ◽  
The Laplace Transform ◽  
Spectrally Negative Lévy Processes

Chiu and Yin (2005) found the Laplace transform of the last time a spectrally negative Lévy process, which drifts to ∞, is below some level. The main motivation for the study of this random time stems from risk theory: what is the last time the risk process, modeled by a spectrally negative Lévy process drifting to ∞, is 0? In this paper we extend the result of Chiu and Yin, and we derive the Laplace transform of the last time, before an independent, exponentially distributed time, that a spectrally negative Lévy process (without any further conditions) exceeds (upwards or downwards) or hits a certain level. As an application, we extend a result found in Doney (1991).

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

Estimating interannual variability arising from weather events

2001 ◽  
Vol 38 (A) ◽  
pp. 274-288 ◽  
Author(s):  
Xiaogu Zheng ◽  
James Renwick
Keyword(s):  
Frequency Domain ◽  
Interannual Variability ◽  
Time Domain ◽  
Synthetic Data ◽  
Estimation Procedure ◽  
Frequency Domain Method ◽  
Domain Method ◽  
Weather Events ◽  
Long Time ◽  
The Time Domain

The advantages and limitations of frequency domain and time domain methods for estimating the interannual variability arising from day-to-day weather events are summarized. A modification of the time domain method is developed and its application in examining a precondition for the frequency domain method is demonstrated. A combined estimation procedure is proposed: it takes advantage of the strengths of both methods. The estimation procedures are tested with sets of synthetic data and are applied to long time series of three meteorological parameters. The impacts of the different methods on tests of potential long-range predictability for seasonal means are also discussed.

Spar Platform Installation: Tank Flooding Simulation

2014 ◽  
Author(s):  
Abel Medellin ◽  
Michelle Arango-Turner ◽  
Curtis Fuhr
Keyword(s):  
Hydrostatic Pressure ◽  
Modeling And Simulation ◽  
Time Domain ◽  
Time Interval ◽  
Design Phase ◽  
Time Domain Simulation ◽  
Spar Platform ◽  
Software Suite ◽  
Dynamic Time ◽  
The Time Domain

Spars are towed to installation site horizontally and upended by progressive flooding of tanks. It is common practice to perform a dynamic time domain simulation for a self upending classic spar to determine hydrostatic pressures on compartments. There are many different flooding scenarios that create challenges in modeling and simulation during the design phase. In one particular scenario, the spar upending is initiated by opening valves that allow water to flood into the skirt tank. The skirt tank will progressively fill, based on the differential hydrostatic pressure at valves, and cause the spar to upend. Flooding into keel tanks will commence once respective openings become submerged. Several openings from the skirt tank into the keel tanks reduce the differential pressure experienced in the keel tanks during upending. Simulation of the transfer of water between tanks cannot be modeled with ease using the standard tank flooding options available within the software suite. This particular compartment flooding problem is solved by utilizing a scheme in which the time domain simulation was performed iteratively for a specified time interval. For every iteration the amount of water transferred between the skirt and keel tanks are calculated. The amount of water transferred is calculated using a custom modeling technique. The openings from the skirt tank into the keel tanks are not modeled as a typical hole or valve into a compartment, but the location of these holes are modeled. The amount of water flowing through these openings is determined by the water level in the skirt tank, friction through the opening, and pressure inside the keel tanks. This paper will describe in detail the scheme developed, the tank modeling requirements, and the results obtained.

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