THE COEFFICIENT OF COHERENCE: ITS ESTIMATION AND USE IN GEOPHYSICAL DATA PROCESSING

Geophysics ◽  
1967 ◽  
Vol 32 (4) ◽  
pp. 602-616 ◽  
Author(s):  
M. R. Foster ◽  
N. J. Guinzy
Keyword(s):  
Time Series ◽  
Signal To Noise Ratio ◽  
Power Spectra ◽  
Stationary Time Series ◽  
Signal To Noise ◽  
Spectral Window ◽  
Data Window ◽  
Approximate Distribution ◽  
Noise Ratio ◽  
Gaussian Data

The coefficient of coherence between two stationary time series was introduced by Wiener in 1930. It is related to the signal‐to‐noise ratio, to the minimum prediction error, and has important invariance properties. As an estimate of this parameter, most geophysicists have used the so‐called “sample coherence.” An approximate distribution of the sample coherence for Gaussian data has been derived by N. R. Goodman. We have tested this distribution by means of Monte Carlo experiments for validity and robustness (insensitivity to the Gaussian assumption). It has passed the tests. The Goodman distribution provides a means of constructing estimates of the true coherence which are better than the widely used sample coherence. It can also be used to calculate confidence intervals. Finally, it forms a basis for choosing the lag window and data window necessary for best estimation of the true coherence. For good estimates of the true coherence, two precautions must be observed: 1. The cross‐spectrum and power spectra of the two time series must be smoothly varying over the width of the spectral window. 2. The ratio of the length of the data window to the lag window must be large. For most seismic work the second requirement severely limits the spectral resolution. Examples show that large errors can result if this resolution is not sufficient to satisfy the first requirement. In many geophysical studies the parameter of interest is the signal‐to‐noise ratio. Because of its relation to the coherence, the Goodman distribution provides a basis for its estimation as well.

The Noise Analysis of Fluid Systemsin Solid-State Nanopore Sensors

2013 ◽  
Vol 419 ◽  
pp. 517-520 ◽  
Author(s):  
Song Ying ◽  
Lei Wang ◽  
Wen Yuan Zhao
Keyword(s):  
Solid State ◽  
Signal To Noise Ratio ◽  
Noise Analysis ◽  
Power Spectra ◽  
Noise Power ◽  
Label Free ◽  
Signal To Noise ◽  
Fluid Systems ◽  
Noise Ratio ◽  
Nanopore Sensors

The solid-state nanopore sensor offers a versatile platform for the rapid, label-free electrical detection and analysis of single molecules, especially on DNA sequencing. However, the overall signal-to-noise ratio (SNA) is a major challenge in sequencing applications. In our work, two different fluid systems made by metal and plexiglass have been designed to improve the signal to noise ratio of the solid-state nanopore sensor. From the measurements on the noise power spectra with a variety of conditions, it is found that plexiglass fluid system coupled with shielding box produces a good quality of electric signals on nanopore sensors.

Ground surface elevation changes estimated using multiple GNSS signal-to-noise ratio observations over permafrost area

2020 ◽  
Author(s):  
Yufeng Hu
Keyword(s):  
Time Series ◽  
Signal To Noise Ratio ◽  
Model Fitting ◽  
Ground Surface ◽  
Composite Model ◽  
Surface Elevation ◽  
Signal To Noise ◽  
Frozen Ground ◽  
Elevation Changes ◽  
Noise Ratio

<p>The ground surface over permafrost area subsides and uplifts annually due to the seasonal thawing and freezing of active layer. GPS Interferometric Reflectometry (GPS-IR) has been successfully applied to the signal-to-noise ratio (SNR) observations to retrieve elevation changes of frozen ground surface at Barrow, Alaska. In this study, the method is extended to include GLONASS and Galileo SNR observations. Based on the multiple SNR observations collected by SG27 in Barrow, the multiple GNSS-IR time series of ground surface elevation changes during snow-free days from late June to middle October in year 2018 are obtained at daily intervals. All the three time series show a similar pattern that the ground subsided in thaw season followed by uplifts in freezing season, which is well characterized by the previous composite physical model using thermal indexes. Fitted with the composite model, the amplitude of the GPS-derived elevation changes during the snow-free days is suggested to be 3.3 ± 0.2 cm. However, the time series of GLONASS-IR and Galileo-IR measurements are much noisier than that of GPS-IR due to their inconsistent daily satellite tracks. Applied with a specific strategy in the composite model fitting, the amplitudes of GLONASS- and Galileo-derived elevation changes are estimated to be 4.0 ± 0.3 cm and 3.9 ± 0.5 cm, respectively. Then, GLONASS-IR and Galileo-IR time series are reconstructed in turn with the fitting coefficients. Moreover, the occurrences of the short-term variations in time series of GNSS-IR measurements are found to coincidence with the precipitation events, indicating the hydrologic control on the movements of frozen ground surface. The results presented in this study show the feasibility to combine multiple GNSS to densely monitor frozen ground surface deformations, and provide an insight to understand the impacts of both thermal and hydrologic forces on the frozen ground dynamics.</p>

Brain activity detection by estimating the signal-to-noise ratio of fMRI time series using dynamic linear models

2015 ◽  
Vol 47 ◽  
pp. 205-211
Author(s):  
Alicia Quirós ◽  
Simon P. Wilson ◽  
Raquel Montes Diez ◽  
Ana Beatriz Solana ◽  
Juan Antonio Hernández Tamames
Keyword(s):  
Time Series ◽  
Linear Models ◽  
Signal To Noise Ratio ◽  
Brain Activity ◽  
Activity Detection ◽  
Signal To Noise ◽  
Dynamic Linear Models ◽  
Fmri Time Series ◽  
Noise Ratio

scholarly journals Multitaper spectral analysis of atmospheric radar signals

2004 ◽  
Vol 22 (11) ◽  
pp. 3995-4003 ◽  
Author(s):  
V. K. Anandan ◽  
C. J. Pan ◽  
T. Rajalakshmi ◽  
G. Ramachandra Reddy
Keyword(s):  
Spectral Analysis ◽  
Lower Stratosphere ◽  
Signal To Noise Ratio ◽  
Power Spectra ◽  
Estimation Accuracy ◽  
Doppler Width ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Width Measurements ◽  
Backscattered Signals

Abstract. Multitaper spectral analysis using sinusoidal taper has been carried out on the backscattered signals received from the troposphere and lower stratosphere by the Gadanki Mesosphere-Stratosphere-Troposphere (MST) radar under various conditions of the signal-to-noise ratio. Comparison of study is made with sinusoidal taper of the order of three and single tapers of Hanning and rectangular tapers, to understand the relative merits of processing under the scheme. Power spectra plots show that echoes are better identified in the case of multitaper estimation, especially in the region of a weak signal-to-noise ratio. Further analysis is carried out to obtain three lower order moments from three estimation techniques. The results show that multitaper analysis gives a better signal-to-noise ratio or higher detectability. The spectral analysis through multitaper and single tapers is subjected to study of consistency in measurements. Results show that the multitaper estimate is better consistent in Doppler measurements compared to single taper estimates. Doppler width measurements with different approaches were studied and the results show that the estimation was better in the multitaper technique in terms of temporal resolution and estimation accuracy.

scholarly journals Temporal Behavior of Solar P-Modes from Gong and Golf Experiments

1998 ◽  
Vol 185 ◽  
pp. 227-228
Author(s):  
V.G. Gavryusev ◽  
E.A. Gavryuseva
Keyword(s):  
Time Series ◽  
Signal To Noise Ratio ◽  
Temporal Behavior ◽  
The Sun ◽  
Solar Oscillations ◽  
Signal To Noise ◽  
Data Set ◽  
Noise Ratio

We used the measurements of solar oscillations taken by GONG and GOLF experiments. The first set of data are the integrated images obtained from the complex GONG observations taken from June 10 of 1995 to January 7 of 1997, 578 days in total, referenced below as ts0 time series. Radial, dipole and quadrupole modes are well visible in this time series. The second data set is the GOLF time series obtained on-board SOHO mission from April 11, 1996 to June 22, 1997. GOLF observes the “Sun as a star”. This time series is similar to ts0 of GONG but of a better quality (better signal-to-noise ratio; uniform, practically uninterrupted data). Both experiments are significantly overlapped in time. Because of this the direct comparison between them is possible, and the effects visible in both observations support each other.

scholarly journals Estimations of uncertainties of frequencies

2015 ◽  
Vol 11 (A29A) ◽  
pp. 201-201
Author(s):  
Laurent Eyer ◽  
Jean-Marc Nicoletti ◽  
Stephan Morgenthaler
Keyword(s):  
Time Series ◽  
Light Curve ◽  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Signal To Noise ◽  
Periodic Signals ◽  
Noise Ratio ◽  
The Universe

AbstractDiverse variable phenomena in the Universe are periodic. Astonishingly many of the periodic signals present in stars have timescales coinciding with human ones (from minutes to years). The periods of signals often have to be deduced from time series which are irregularly sampled and sparse, furthermore correlations between the brightness measurements and their estimated uncertainties are common. The uncertainty on the frequency estimation is reviewed. We explore the astronomical and statistical literature, in both cases of regular and irregular samplings. The frequency uncertainty is depending on signal to noise ratio, the frequency, the observational timespan. The shape of the light curve should also intervene, since sharp features such as exoplanet transits, stellar eclipses, raising branches of pulsation stars give stringent constraints. We propose several procedures (parametric and nonparametric) to estimate the uncertainty on the frequency which are subsequently tested against simulated data to assess their performances.

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