An application of regression M-estimation with the Hilbert transform to magnetotelluric data processing

1991 ◽  
Vol 22 (2) ◽  
pp. 383-390 ◽  
Author(s):  
D. Sutarno ◽  
K. Vozoff
Keyword(s):  
Data Processing ◽  
Hilbert Transform ◽  
Magnetotelluric Data ◽  
M Estimation ◽  
The Hilbert Transform

On: “Interpretation of magnetic bodies using Hilbert transforms” by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri Rao (GEOPHYSICS, 47, 376–387, March, 1982).

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 168-168
Author(s):  
Rob Pauls
Keyword(s):  
Data Processing ◽  
Hilbert Transform ◽  
Geophysical Data ◽  
Hilbert Transforms ◽  
Magnetic Interpretation ◽  
The Hilbert Transform

The Fourier and Hilbert transform techniques have played extremely important roles in geophysical data processing. We were naturally very interested to find the paper by Mohan et al. which described a possible application of the Hilbert transform approach in magnetic interpretation. However, we found some very serious problems in the paper.

scholarly journals Phase and the Hilbert transform

2014 ◽  
Vol 33 (10) ◽  
pp. 1164-1166 ◽  
Author(s):  
Steve Purves
Keyword(s):  
Signal Processing ◽  
Data Processing ◽  
Hilbert Transform ◽  
Seismic Data ◽  
Seismic Attributes ◽  
Seismic Data Processing ◽  
Data Set ◽  
The Hilbert Transform

The concept of phase permeates seismic data processing and signal processing in general, but it can be awkward to understand, and manipulating it directly can lead to surprising results. It doesn't help that the word phase is used to mean a variety of things, depending on whether we refer to the propagating wavelet, the observed wavelet, poststack seismic attributes, or an entire seismic data set. Several publications have discussed the concepts and ambiguities (e.g., Roden and Sepúlveda, 1999 ; Liner, 2002 ; Simm and White, 2002 ).

scholarly journals New approaches for automated data processing of annually laminated sediments

2004 ◽  
Vol 11 (5/6) ◽  
pp. 599-607 ◽  
Author(s):  
I. Rupf ◽  
G. Radons
Keyword(s):  
Data Processing ◽  
Hilbert Transform ◽  
Signal To Noise Ratio ◽  
Laminated Sediments ◽  
Frequency Noise ◽  
Detection And Counting ◽  
Actual Signal ◽  
Annually Laminated Sediments ◽  
The Hilbert Transform ◽  
Local Trend

Abstract. Laminated sediments, like evaporites and biogenic lake sediments, provide high-resolution paleo-climate records. Yet detection and counting of laminae causes still problems because sedimentary structures are often disturbed. In the past laminated rocks often were analysed manually - a tedious and subjective work. The present study describes four automated approaches for lamina detection based on 1d grey-scale vectors. Best results are obtained with a newly developed algorithm, called Adaptive Template Method (ATM) in combination with the Hilbert transform. ATM improves the signal to noise ratio of the grey-value signal. Its basic idea is to extract first a characteristic waveform, the template, which describes the typical grey-value variation transverse to the laminae. This is a kind of "template learning" process, which in practice is done by an appropriate averaging method. This template is in a second step used for processing the whole sample. One calculates the overlap of the template with the actual signal, the grey-value variation along the core, as function of position in core direction. This method generates a new signal with maxima at positions, where the template optimally matches the original signal. The new time-series is called AT-transform. It is smoother than the initial data sequence. High frequency noise and local trend effects are suppressed. Afterwards, the AT-transform can be analysed with the Hilbert transformation for extracting phase information. The data processing methods are tested both on artificial data sequences and on a seasonally laminated sedimentary record of the Oligocene Baruth Maar (Germany). Although ATM is no panacea for highly disturbed signals, our comparison with other approaches shows that it provides the best results. The combination of ATM and the Hilbert transform allows to detect clearly long-term oscillations in the sedimentation patterns and thus cycles in climatic variations.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci
Keyword(s):  
Power Generation ◽  
Electrochemical Impedance Spectroscopy ◽  
Hilbert Transform ◽  
Electrochemical Impedance ◽  
The Self ◽  
Impedance Data ◽  
The Hilbert Transform ◽  
Validation Tests ◽  
Self Consistency ◽  
Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

scholarly journals A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger
Keyword(s):  
Radial Basis Function ◽  
Hilbert Transform ◽  
Basis Function ◽  
Differential Operators ◽  
Convergence Rates ◽  
Traveling Wave Solutions ◽  
Algebraic Decay ◽  
Pseudo Differential Operators ◽  
Radial Basis ◽  
The Hilbert Transform

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

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