scholarly journals The Effect of Signal-to-Noise Ratio on the Study of Sea Level Trends

2011 ◽  
Vol 24 (5) ◽  
pp. 1396-1408 ◽  
Author(s):  
B. D. Hamlington ◽  
R. R. Leben ◽  
R. S. Nerem ◽  
K.-Y. Kim
Keyword(s):  
Least Squares ◽  
Sea Level ◽  
Least Squares Method ◽  
Secular Trend ◽  
Signal To Noise Ratio ◽  
Empirical Orthogonal Functions ◽  
Signal To Noise ◽  
Orthogonal Functions ◽  
Geophysical Processes ◽  
Noise Ratio

Abstract Extracting secular sea level trends from the background ocean variability is limited by how well one can correct for the time-varying and oscillating signals in the record. Many geophysical processes contribute time-dependent signals to the data, making the sea level trend difficult to detect. In this paper, cyclostationary empirical orthogonal functions (CSEOFs) are used to quantify and improve the signal-to-noise ratio (SNR) between the secular trend and the background variability, obscuring this trend in the altimetric sea level record by identifying and removing signals that are physically interpretable. Over the 16-yr altimetric record the SNR arising from the traditional least squares method for estimating trends can be improved from 4.0% of the ocean having an SNR greater than one to 9.9% when using a more sophisticated statistical method based on CSEOFs. From a standpoint of signal detection, this implies that the secular trend in a greater portion of the ocean can be estimated with a higher degree of confidence. Furthermore, the CSEOF method improves the standard error on the least squares estimates of the secular trend in 97% of the ocean. The convergence of the SNR as the record length is increased is used to estimate the SNR of sea level trends in the near future as more measurements become available from near-global altimetric sampling.

scholarly journals Least Squares Reconstruction of Doppler Radar Spectra for Irregular PRT

2012 ◽  
Vol 29 (12) ◽  
pp. 1744-1756 ◽  
Author(s):  
John Kalogiros
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Irregular Sampling ◽  
Filter Method ◽  
Reconstruction Method ◽  
Signal To Noise ◽  
Mean Velocity ◽  
Noise Ratio

Abstract A least squares method for the reconstruction of Doppler spectra of weather radars with irregular pulse repetition time used to increase the range of unambiguous velocity is presented and evaluated. This method is a robust spectral method that is based on the least squares minimum norm principle and reconstructs both the magnitude and the phase of the discrete Fourier transform of the signal. The phase spectrum is useful in the estimation of the differential phase in dual-polarization radars with staggered sampling schemes, which is a case of irregular sampling. A computationally efficient iterative algorithm for estimating the mean frequency of the signal, which is required for the reconstruction of the spectrum, is described for possible real-time applications. A clutter filter method based on spectral interpolation, which can be applied to echoes with generally nonzero mean velocity, is also described and combined with the spectrum reconstruction method. Using simulated data it is shown that the least squares reconstruction method with or without the presence of clutter gives results with small bias and standard error and can be applied to wide spectra. The application of the method to real X-band radar data with a low signal-to-noise ratio and a high stagger ratio value of ⅚ showed that the least squares method has low sensitivity to the stagger ratio and satisfactorily gives spectral reconstruction for signal-to-noise ratio values as low as 10 dB.

Application of frequency-dependent multichannel Wiener filters to detect events in 2D three-component seismometer arrays

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. V133-V141 ◽  
Author(s):  
J. Wang ◽  
F. Tilmann ◽  
R. S. White ◽  
P. Bordoni
Keyword(s):  
Least Squares Method ◽  
Signal To Noise Ratio ◽  
Noise Levels ◽  
Signal To Noise ◽  
Coherent Noise ◽  
Gas Field ◽  
Frequency Dependent ◽  
Wiener Filters ◽  
Noise Ratio

Hydraulic fracture-induced microseismic events in producing oil and gas fields are usually small, and noise levels are high at the surface as a result of the heavy equipment in use. Similarly, in nonhydrocarbon settings, arrays for detecting local earthquakes will benefit from reduced noise levels and the ability to detect smaller events will be increased. We propose a frequency-dependent multichannel Wiener filtering technique with linear constraints that uses an adaptive least-squares method to remove coherent noise in seismic array data. The noise records on several reference channels are used to predict the noise on a primary channel and then can be subtracted from the observed data. On a test with an unconstrained version of this filter, maximal noise suppression leads to signal distortion. Two methods of im-posing constraints then achieve signal preservation. In one case study, synthetic signals are added to noise from a pilot deployment of a hexagonal array (nine three-component seismometers, approximately [Formula: see text]) above a gas field; noise levels are suppressed by up to [Formula: see text] (at [Formula: see text]). In a second case study, natural seismicity recorded at a dense array ([Formula: see text] spacing) in Italy is used, where the application of the filter improves the signal-to-noise ratio (S/N) more than [Formula: see text] (at [Formula: see text]) using 35 stations. In both cases, the performance of the multichannel Wiener filters is significantly better than stacking, espe-cially at lower frequencies where stacking does not help to suppress the coherent noise. The unconstrained version of the filter yields the best improvement in signal-to-noise ratio, but the constrained filter is useful when waveform distortion is unacceptable.

A Least-Squares Strain Estimator for Elastography

1997 ◽  
Vol 19 (3) ◽  
pp. 195-208 ◽  
Author(s):  
Faouzi Kallel ◽  
Jonathan Ophir
Keyword(s):  
Least Squares ◽  
Spatial Resolution ◽  
Dynamic Range ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Gel Phantom

A least-squares strain estimator (LSQSE) for elastography is proposed. It is shown that with such an estimator, the signal-to-noise ratio in an elastogram ( SNRe) is significantly improved. This improvement is illustrated theoretically using a modified strain filter and experimentally using a homogeneous gel phantom. It is demonstrated that the LSQSE results in an increase of the elastographic sensitivity (smallest strain that could be detected), thereby increasing the strain dynamic range. Using simulated data, it is shown that a tradeoff exists between the improvement in SNRe and the reduction of strain contrast and spatial resolution.

scholarly journals Towards improved analysis of short mesoscale sea level signals from satellite altimetry

2021 ◽  
Author(s):  
Yves Quilfen ◽  
Jean-François Piolle ◽  
Bertrand Chapron
Keyword(s):  
Sea Level ◽  
Signal To Noise Ratio ◽  
Ocean Dynamics ◽  
Small Scale ◽  
Noise Filtering ◽  
Signal To Noise ◽  
Data Set ◽  
Noise Ratio ◽  
Filter Noise ◽  
Along Track

Abstract. Satellite altimeters routinely supply sea surface height (SSH) measurements, which are key observations for monitoring ocean dynamics. However, below a wavelength of about 70 km, along-track altimeter measurements are often characterized by a dramatic drop in signal-to-noise ratio, making it very challenging to fully exploit the available altimeter observations to precisely analyze small mesoscale variations in SSH. Although various approaches have been proposed and applied to identify and filter noise from measurements, no distinct methodology has emerged for systematic application in operational products. To best address this unresolved issue, the Copernicus Marine Environment Monitoring Service (CMEMS) actually provides simple band-pass filtered data to mitigate noise contamination of along-track SSH signals. More innovative and suitable noise filtering methods are thus left to users seeking to unveil small-scale altimeter signals. As demonstrated here, a fully data-driven approach is developed and applied successfully to provide robust estimates of noise-free Sea Level Anomaly (SLA) signals. The method combines Empirical Mode Decomposition (EMD), to help analyze non-stationary and non-linear processes, and an adaptive noise filtering technique inspired by Discrete Wavelet Transform (DWT) decompositions. It is found to best resolve the distribution of SLA variability in the 30–120 km mesoscale wavelength band. A practical uncertainty variable is attached to the denoised SLA estimates that accounts for errors related to the local signal-to-noise ratio, but also for uncertainties in the denoising process, which assumes that the SLA variability results in part from a stochastic process. For the available period, measurements from the Jason-3, Sentinel-3 and Saral/AltiKa missions are processed and analyzed, and their energy spectral and seasonal distributions characterized in the small mesoscale domain. In anticipation of the upcoming SWOT (Surface Water and Ocean Topography) mission data, the SASSA data set (Satellite Altimeter Short-scale Signals Analysis, Quilfen and Piolle, 2021) of denoised SLA measurements for three reference altimeter missions already yields valuable opportunities to evaluate global small mesoscale kinetic energy distributions.

Signal-to-Noise Ratio Enhancement by Least-Squares Polynomial Smoothing

1976 ◽  
Vol 48 (8) ◽  
pp. 705A-712A ◽  
Author(s):  
C. G. Enke ◽  
Timothy A. Nieman
Keyword(s):  
Least Squares ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Polynomial Smoothing

The value of constrained conjugate-gradient least-squares migration in seismic inversion: Application to a fractured-basement play, Texas Panhandle

2017 ◽  
Vol 5 (3) ◽  
pp. SN13-SN23 ◽  
Author(s):  
Thang Ha ◽  
Kurt Marfurt
Keyword(s):  
Least Squares ◽  
Signal To Noise Ratio ◽  
Seismic Inversion ◽  
High Signal ◽  
Radon Transforms ◽  
Signal To Noise ◽  
Data Set ◽  
Texas Panhandle ◽  
Noise Ratio ◽  
Least Squares Migration

Seismic inversion has become almost routine in quantitative 3D seismic interpretation. To ensure the quality of the seismic inversion, the input seismic data need to have a high signal-to-noise ratio. With the current low oil price environment, seismic reprocessing is often preferred over reacquisition to improve data quality. Common filter pairs include forward and inverse [Formula: see text]-[Formula: see text] and Radon transforms. Forward and inverse migrations (i.e., migration and demigration) are a more recently introduced transform pair that, when used together in an iterative workflow, results in a least-squares migration algorithm. Least-squares migration compensates for surface variation in data density and, when combined with a filter applied to prestack migrated images, suppresses the operator and data aliasing. We apply a least-squares migration workflow to a fractured-basement data set from the Texas Panhandle to demonstrate the enhancement in signal-to-noise ratio, the reduction in acquisition footprint and migration artifacts, and the improvement in the P-impedance inversion result.

Determination of the Best Emulsion for the Microscopy of Crystals

1981 ◽  
Vol 39 ◽  
pp. 32-33
Author(s):  
David A. Grano ◽  
Kenneth H. Downing
Keyword(s):  
Spatial Frequency ◽  
Information Transfer ◽  
Signal To Noise Ratio ◽  
Experimental Situation ◽  
Photographic Emulsion ◽  
Modulation Transfer ◽  
Signal To Noise ◽  
Frequency Space ◽  
Noise Ratio

The retrieval of high-resolution information from images of biological crystals depends, in part, on the use of the correct photographic emulsion. We have been investigating the information transfer properties of twelve emulsions with a view toward 1) characterizing the emulsions by a few, measurable quantities, and 2) identifying the “best” emulsion of those we have studied for use in any given experimental situation. Because our interests lie in the examination of crystalline specimens, we've chosen to evaluate an emulsion's signal-to-noise ratio (SNR) as a function of spatial frequency and use this as our critereon for determining the best emulsion.The signal-to-noise ratio in frequency space depends on several factors. First, the signal depends on the speed of the emulsion and its modulation transfer function (MTF). By procedures outlined in, MTF's have been found for all the emulsions tested and can be fit by an analytic expression 1/(1+(S/S0)2). Figure 1 shows the experimental data and fitted curve for an emulsion with a better than average MTF. A single parameter, the spatial frequency at which the transfer falls to 50% (S0), characterizes this curve.

Experiments in Bright-Field Imaging with Hollow-Cone Illumination

1981 ◽  
Vol 39 ◽  
pp. 226-227
Author(s):  
W. Kunath ◽  
K. Weiss ◽  
E. Zeitler
Keyword(s):  
Signal To Noise Ratio ◽  
Carbon Support ◽  
Electronic System ◽  
Optic Axis ◽  
Hollow Cone ◽  
Signal To Noise ◽  
Bright Field ◽  
Noise Ratio ◽  
Single Field ◽  
Field Imaging

Bright-field images taken with axial illumination show spurious high contrast patterns which obscure details smaller than 15 ° Hollow-cone illumination (HCI), however, reduces this disturbing granulation by statistical superposition and thus improves the signal-to-noise ratio. In this presentation we report on experiments aimed at selecting the proper amount of tilt and defocus for improvement of the signal-to-noise ratio by means of direct observation of the electron images on a TV monitor.Hollow-cone illumination is implemented in our microscope (single field condenser objective, Cs = .5 mm) by an electronic system which rotates the tilted beam about the optic axis. At low rates of revolution (one turn per second or so) a circular motion of the usual granulation in the image of a carbon support film can be observed on the TV monitor. The size of the granular structures and the radius of their orbits depend on both the conical tilt and defocus.

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