Inapplicability of pulse train time‐domain measurements to spectral induced polarization

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 826-827 ◽  
Author(s):  
Heikki Soininen
Keyword(s):  
Time Domain ◽  
Pulse Train ◽  
Apparent Resistivity ◽  
Single Pulse ◽  
Induced Polarization ◽  
Spectral Measurements ◽  
Frequency Spectra ◽  
Voltage Transient ◽  
The Fourier Transform ◽  
The Time Domain

The method of induced polarization (IP) is based on the frequency dependence of resistivity of rocks. In spectral IP the apparent resistivity is measured at a wide‐frequency band (e.g., 1/1024…4096 Hz). The apparent resistivity depends upon the distribution of the resistivity of the earth according to the laws of electromagnetism. On the basis of their spectral measurements Pelton et al. (1978) proposed that variations in mineral texture give rise to variations in the frequency spectra of resistivity. It should thus be feasible to use these spectra to discriminate between, say, graphite and sulfides. The frequency domain and the time domain are equivalent in a linear and causal system, the domains being interrelated through the Fourier transform. The time domain is attractive in that the whole transient can be recorded in a single measurement. Hence, there are devices in commercial use that record spectra in the time domain by measuring the voltage transient at a number of instances after the current pulse has been switched off. The primary current signal in these devices is generally a pulse train composed of pulses of finite duration. The pulse train has advantages over the single pulse because it permits the measurements to be repeated and thus improves the signal‐to‐noise (S/N) ratio of the measurements.

A Deep Neural Network Model for Learning Runtime Frequency Response Function Using Sensor Measurements

2021 ◽  
Author(s):  
Yongzhi Qu ◽  
Gregory W. Vogl ◽  
Zechao Wang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fourier Transform ◽  
Time Domain ◽  
Frequency Response Function ◽  
Frequency Component ◽  
Operating Conditions ◽  
Input Output ◽  
The Fourier Transform ◽  
The Time Domain

Abstract The frequency response function (FRF), defined as the ratio between the Fourier transform of the time-domain output and the Fourier transform of the time-domain input, is a common tool to analyze the relationships between inputs and outputs of a mechanical system. Learning the FRF for mechanical systems can facilitate system identification, condition-based health monitoring, and improve performance metrics, by providing an input-output model that describes the system dynamics. Existing FRF identification assumes there is a one-to-one mapping between each input frequency component and output frequency component. However, during dynamic operations, the FRF can present complex dependencies with frequency cross-correlations due to modulation effects, nonlinearities, and mechanical noise. Furthermore, existing FRFs assume linearity between input-output spectrums with varying mechanical loads, while in practice FRFs can depend on the operating conditions and show high nonlinearities. Outputs of existing neural networks are typically low-dimensional labels rather than real-time high-dimensional measurements. This paper proposes a vector regression method based on deep neural networks for the learning of runtime FRFs from measurement data under different operating conditions. More specifically, a neural network based on an encoder-decoder with a symmetric compression structure is proposed. The deep encoder-decoder network features simultaneous learning of the regression relationship between input and output embeddings, as well as a discriminative model for output spectrum classification under different operating conditions. The learning model is validated using experimental data from a high-pressure hydraulic test rig. The results show that the proposed model can learn the FRF between sensor measurements under different operating conditions with high accuracy and denoising capability. The learned FRF model provides an estimation for sensor measurements when a physical sensor is not feasible and can be used for operating condition recognition.

scholarly journals Tailoring of multi-pulse dynamics in mode-locked laser via optoacoustic manipulation of quasi-continuous-wave background

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Ki Sang Lee ◽  
Chang Kyun Ha ◽  
Kyoung Jun Moon ◽  
Dae Seok Han ◽  
Myeong Soo Kang
Keyword(s):  
Information Processing ◽  
Time Domain ◽  
Continuous Wave ◽  
Single Pulse ◽  
Laser Cavity ◽  
Temporal Position ◽  
Optical Information ◽  
Pulse Dynamics ◽  
Mode Locked Laser ◽  
The Time Domain

Abstract Various nonequilibrium multi-pulse states can emerge in a mode-locked laser through interactions between the quasi-continuous-wave background (qCWB) and pulses inside the laser cavity. While they have been regarded as unpredictable and hardly controllable due to the noise-like nature of qCWB, we here demonstrate that the qCWB landscape can be manipulated via optoacoustically mediated pulse-to-qCWB interactions, which alters the behaviors of multi-pulse dynamics. In this process, impulsive qCWB modulations are created at well-defined temporal locations, which act as the point emitters and attractive potentials for drifting pulse bunches and soliton rains. Hence, we can transport a single pulse bunch from a certain temporal position to another, and also make soliton rains created and collided exclusively at specific temporal locations. Our study opens up possibilities to control the nonequilibrium multi-pulse phenomena precisely in the time domain, which would offer a practical means of advanced optical information processing.

Spectral induced polarization parameters as determined through time‐domain measurements

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1993-2003 ◽  
Author(s):  
Ian M. Johnson
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Field Trials ◽  
Induced Polarization ◽  
Polarization Data ◽  
Forward Solution ◽  
Spectral Parameters ◽  
Impedance Model ◽  
Measurement And Analysis ◽  
The Time Domain

A method for the extraction of Cole-Cole spectral parameters from time‐domain induced polarization data is demonstrated. The instrumentation required to effect the measurement and analysis is described. The Cole-Cole impedance model is shown to work equally well in the time domain as in the frequency domain. Field trials show the time‐domain method to generate spectral parameters consistent with those generated by frequency‐domain surveys. This is shown to be possible without significant alteration to field procedures. Cole-Cole time constants of up to 100 s are shown to be resolvable given a transmitted current of a 2 s pulse‐time. The process proves to have added usefulness as the Cole-Cole forward solution proves an excellent basis for quantifying noise in the measured decay.

scholarly journals Clustering revisited: A spectral analysis of microseismic events

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. KS41-KS49 ◽  
Author(s):  
Deborah Fagan ◽  
Kasper van Wijk ◽  
James Rutledge
Keyword(s):  
Oil Recovery ◽  
Time Domain ◽  
Power Spectra ◽  
Fault System ◽  
Microseismic Events ◽  
The Fourier Transform ◽  
The Time Domain ◽  
The Relationship ◽  
Single Cluster ◽  
Full Body

Identifying individual subsurface faults in a larger fault system is important to characterize and understand the relationship between microseismicity and subsurface processes. This information can potentially help drive reservoir management and mitigate the risks of natural or induced seismicity. We have evaluated a method of statistically clustering power spectra from microseismic events associated with an enhanced oil recovery operation in southeast Utah. Specifically, we were able to provide a clear distinction within a set of events originally designated in the time domain as a single cluster and to identify evidence of en echelon faulting. Subtle time-domain differences between events were accentuated in the frequency domain. Power spectra based on the Fourier transform of the time-domain autocorrelation function were used, as this formulation results in statistically independent intensities and is supported by a full body of statistical theory upon which decision frameworks can be developed.

Discrete Time, Discrete Frequency

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Continuous Time ◽  
Time Varying ◽  
Discrete Frequency ◽  
The Fourier Transform ◽  
Definition Of ◽  
The Time Domain

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. T117-T123 ◽  
Author(s):  
Chunlei Chu ◽  
Paul L. Stoffa
Keyword(s):  
Fourier Transform ◽  
Frequency Response ◽  
Time Domain ◽  
Wave Equations ◽  
Time Integration ◽  
Expansion Method ◽  
Rapid Expansion ◽  
The Fourier Transform ◽  
The Time Domain ◽  
Response Modeling

Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency.

scholarly journals Induced capacitance in the squid giant axon. Lipophilic ion displacement currents.

1983 ◽  
Vol 82 (3) ◽  
pp. 331-346 ◽  
Author(s):  
J M Fernández ◽  
R E Taylor ◽  
F Bezanilla
Keyword(s):  
Action Potential ◽  
Frequency Domain ◽  
Time Domain ◽  
Numerical Solutions ◽  
Ionic Current ◽  
Induced Polarization ◽  
Resting Potential ◽  
Axonal Membrane ◽  
Cable Properties ◽  
The Time Domain

Voltage-clamped squid giant axons, perfused internally and externally with solutions containing 10(-5) M dipicrylamine (DpA-), show very large polarization currents (greater than or equal to 1 mA/cm2) in response to voltage steps. The induced polarization currents are shown in the frequency domain as a very large voltage-and frequency-dependent capacitance that can be fit by single Debye-type relaxations. In the time domain, the decay phase of the induced currents can be fit by single exponentials. The induced polarization currents can also be observed in the presence of large sodium and potassium currents. The presence of the DpA- molecules does not affect the resting potential of the axons, but the action potentials appear graded, with a much-reduced rate of rise. The data in the time domain as well as the frequency domain can be explained by a single-barrier model where the DpA- molecules translocate for an equivalent fraction of the electric field of 0.63, and the forward and backward rate constants are equal at -15 mV. When the induced polarization currents described here are added to the total ionic current expression given by Hodgkin and Huxley (1952), numerical solutions of the membrane action potential reproduce qualitatively our experimental data. Numerical solutions of the propagated action potential predict that large changes in the speed of conduction are possible when polarization currents are induced in the axonal membrane. We speculate that either naturally occurring substances or drugs could alter the cable properties of cells in a similar manner.

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