A signal-to-noise model for ELF propagation in subsurface regions

1994 ◽  
Vol 19 (3) ◽  
pp. 353-359 ◽  
Author(s):  
C.P. Burke ◽  
D.L. Jones
Keyword(s):  
Noise Model ◽  
Signal To Noise

Frequency limits for seismometers as determined from signal-to-noise ratios. Part 1. The electromagnetic seismometer

1992 ◽  
Vol 82 (2) ◽  
pp. 1071-1098 ◽  
Author(s):  
Peter W. Rodgers
Keyword(s):  
Operational Amplifier ◽  
Seismic Noise ◽  
Low Noise ◽  
Noise Model ◽  
Noise Voltage ◽  
Signal To Noise ◽  
Noise Current ◽  
System Noise ◽  
Large Gain ◽  
Total Noise

Abstract The range of frequencies that a seismometer can record is nominally set by the corner frequencies of its amplitude frequency response. In recording pre-event noise in very quiet seismic sites, the internally generated self-noise of the seismometer can put further limits on the range of frequencies that can be recorded. Some examples of such low seismic noise sites are Lajitas, Texas; Deep Springs, California; and Karkaralinsk, U.S.S.R. In such sites, the seismometer self-noise can be large enough to degrade the signal-to-noise ratio (SNR) of the recorded pre-event data. The widely used low seismic noise model (LNM) (due to Peterson, 1982; Peterson and Hutt, 1982; Peterson and Tilgner, 1985; Peterson and Hutt, 1989) is used as representative of the input ground motion acceleration power density spectrum (pds) at such very low noise sites. This study determines the range of frequencies for which the SNR of an electromagnetic seismometer exceeds 3 db (a factor of 2 in power and 1.414 in amplitude). In order to do this, an analytic expression is developed for the SNR of a generalized electromagnetic seismometer. The signal pds using Peterson's LNM as an input is developed for an electromagnetic seismometer. Suspension noise is modeled following Usher (1973). In order to determine the electronically caused component of the self-noise, noise properties are compared among three commonly used amplifiers. The advantages and disadvantages of the inverting and noninverting configurations in terms of their SNR are discussed. In most cases, the noninverting configuration is to be preferred as it avoids the use of the large gain setting resistances required in the inverting configuration to avoid loading the seismometer output. A noise model is developed for a typical low noise operational amplifier (Precision Monolithics OP-27). This noise model is used to numerically compute the SNRs for the three electromagnetic seismometers used as examples. The degradation in SNR caused by large gain setting resistances is shown. Numerical examples are given using the Mark Products L-4C and L-22D and the Teledyne Geotech GS-13 electromagnetic seismometers. For each of the example seismometers, the calculated range of frequencies for which their SNR exceeds 3 db is as follows: the GS-13, 0.078 to 56.1 Hz; the L-4C, 0.113 to 7.2 Hz; and the L-22D, 0.175 to 0.6 Hz. For the GS-13, the calculated lower and upper frequencies at which the SNR is 3 db are 0.078 and 56.1 Hz. This compares with the values 0.073 and 59 Hz measured in the noise tests on the vertical GS-13. Expressions for the total noise voltage referred to the input of an operational amplifier are developed in Appendix A. It is shown that in the inverting configuration, although no noise current flows in the input resistor, the noise current appears in the expression for the total noise voltage as if it did. In Appendix B, it is shown that any noise current flowing through an electromagnetic seismometer having a generator greater than several hundred V/m/sec generates a back emf that adds significantly to the noise of the system. This implies that system noise tests that substitute a resistor at the noninverting input of the preamplifier or clamp the seismometer mass will tend to underestimate the system noise.

Frequency limits for seismometers as determined from signal-to-noise ratios. Part 2. The feedback seismometer

1992 ◽  
Vol 82 (2) ◽  
pp. 1099-1123
Author(s):  
Peter W. Rodgers
Keyword(s):  
Seismic Noise ◽  
Transfer Functions ◽  
Low Noise ◽  
Noise Model ◽  
Power Density Spectrum ◽  
Signal To Noise ◽  
Density Spectrum ◽  
Velocity Feedback ◽  
Noise Models ◽  
Feedback Seismometer

Abstract The range of frequencies that a seismometer can record is nominally set by the corner frequencies of its amplitude frequency response. In recording pre-event noise in very quiet seismic sites, the internally generated self-noise of the seismometer can put further limits on the range of frequencies that can be recorded. Some examples of such low seismic noise sites are Lajitas, Texas; Deep Springs, California; and Karkaralinsk, U.S.S.R. In such sites, the seismometer self-noise can be large enough to degrade the signal-to-noise ratio (SNR) of the recorded pre-event data. The widely used low seismic noise model (LNM) (due to Peterson, 1982; Peterson and Hutt, 1982; Peterson and Tilgner, 1985; Peterson and Hutt, 1989) is used as representative of the input ground motion acceleration power density spectrum (pds) at such very low noise sites. This study determines the range of frequencies for which the SNR of a feedback seismometer exceeds 3 db (a factor of 2 in power and 1.414 in amplitude). Analytic expressions for the SNR are developed for three types of feedback seismometers. These are the displacement feedback, velocity feedback, and coil-to-coil velocity feedback seismometers. It was found that the analytic SNRs of the displacement and velocity feedback seismometers are identical and that the SNRs for the coil-coil feedback seismometer and the electromagnetic seismometer are also the same. The signal pds using Peterson's LNM as an input is developed for each of the three types of feedback seismometers. Suspension noise is modeled following Aki and Richards (1980). In order to model the electronically caused component of the self-noise, the electronic noise properties of two commonly used operational amplifiers (Precision Monolithics OP-27 and the Burr-Brown OPA2111 FET) are described. Using these, noise models are developed for a synchronous demodulator and a chopper-stabilized amplifier. These noise models are used to numerically compute the SNRs for the two feedback seismometers used as examples, which are the Guralp Systems CMG-3ESP and Sprengnether Instruments SBX-1000 feedback seismometers. For each of the example seismometers, the calculated range of frequencies for which their SNR exceeds 3 db is as follows: the CMG-3ESP, 0.025 to 13.3 Hz; the SBX-1000, 0.098 to 11.3 Hz. The calculated and measured SNRs for the CMG-3ESP are compared. The calculated upper frequency for a SNR of 3 db was 13.3 Hz compared with 18.4 Hz measured in the noise tests. The calculated lower frequency for a SNR of 3 db was 0.025 Hz, whereas the measured value was 0.047 Hz. The difference is most likely due to the fact the CMG-3ESP is cut off at 0.1 Hz. Formulas are developed in Appendix A for calculating the SNR and self-noise of identical, colocated seismometers from their recorded outputs. The analytic transfer functions, midband gain, upper and lower corner frequencies, and bandwidths for the three types of feedback seismometers are given in Appendix B for comparison with the frequency limits set by the SNR.

Error Analysis for Estimation of Trace Vapor Concentration Pathlength in Stack Plumes

2003 ◽  
Vol 57 (6) ◽  
pp. 614-621 ◽  
Author(s):  
Neal B. Gallagher ◽  
Barry M. Wise ◽  
David M. Sheen
Keyword(s):  
Remote Sensing ◽  
Error Analysis ◽  
Near Infrared ◽  
Signal To Noise Ratio ◽  
Chemical Vapor ◽  
Noise Model ◽  
Vapor Concentration ◽  
Signal To Noise ◽  
Sensing Applications ◽  
Noise Ratio

Near-infrared hyperspectral imaging is finding utility in remote sensing applications such as detection and quantification of chemical vapor effluents in stack plumes. Optimizing the sensing system or quantification algorithms is difficult because reference images are rarely well characterized. The present work uses a radiance model for a down-looking scene and a detailed noise model for dispersive and Fourier transform spectrometers to generate well-characterized synthetic data. These data were used with a classical least-squares-based estimator in an error analysis to obtain estimates of different sources of concentration-pathlength quantification error in the remote sensing problem. Contributions to the overall quantification error were the sum of individual error terms related to estimating the background, atmospheric corrections, plume temperature, and instrument signal-to-noise ratio. It was found that the quantification error depended strongly on errors in the background estimate and second-most on instrument signal-to-noise ratio. Decreases in net analyte signal (e.g., due to low analyte absorbance or increasing the number of analytes in the plume) led to increases in the quantification error as expected. These observations have implications on instrument design and strategies for quantification. The outlined approach could be used to estimate detection limits or perform variable selection for given sensing problems.

Secrets of image denoising cuisine

Acta Numerica ◽  
2012 ◽  
Vol 21 ◽  
pp. 475-576 ◽  
Author(s):  
M. Lebrun ◽  
M. Colom ◽  
A. Buades ◽  
J. M. Morel
Keyword(s):  
Stochastic Process ◽  
Numerical Methods ◽  
Image Denoising ◽  
Digital Images ◽  
Signal To Noise Ratio ◽  
Noise Model ◽  
Noisy Image ◽  
Image Model ◽  
Signal To Noise ◽  
Photon Count

Digital images are matrices of equally spaced pixels, each containing a photon count. This photon count is a stochastic process due to the quantum nature of light. It follows that all images are noisy. Ever since digital images have existed, numerical methods have been proposed to improve the signal-to-noise ratio. Such ‘denoising’ methods require a noise model and an image model. It is relatively easy to obtain a noise model. As will be explained in the present paper, it is even possible to estimate it from a single noisy image.

Signal-to-noise estimates of time-reverse images

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. MA1-MA10 ◽  
Author(s):  
Ben Witten ◽  
Brad Artman
Keyword(s):  
Energy Content ◽  
Signal To Noise Ratio ◽  
Imaging Techniques ◽  
Low Frequency ◽  
Velocity Model ◽  
Noise Model ◽  
Signal To Noise ◽  
Image Domain ◽  
Velocity Models ◽  
Confidence Threshold

Locating subsurface sources from passive seismic recordings is difficult when attempted with data that have no observable arrivals and/or a low signal-to-noise ratio (S/N). Energy can be focused at its source using time-reversal techniques. However, when a focus cannot be matched to a particular event, it can be difficult to distinguish true focusing from artifacts. Artificial focusing can arise from numerous causes, including noise contamination, acquisition geometry, and velocity model effects. We present a method that reduces the ambiguity of the results by creating an estimate of the (S/N) in the image domain and defining a statistical confidence threshold for features in the images. To do so, time-reverse imaging techniques are implemented on both recorded data and a noise model. In the data domain, the noise model approximates the energy of local noise sources. After imaging, the result also captures the effects of acquisition geometry and the velocity model. The signal image is then divided by the noise image to produce an estimate of the (S/N). The distribution of image (S/N) values due to purely stochastic noise provides a means by which to calculate a confidence threshold. This threshold is used to set the minimum displayed value of images to a statistically significant limit. Two-dimensional synthetic examples show the effectiveness of this technique under varying amounts of noise and despite challenging velocity models. Using this method, we collocate anomalous low-frequency energy content, measured over oil reservoirs in Africa and Europe, with the subsurface location of the productive intervals through 2D and 3D implementations.

scholarly journals Structured illumination microscopy with noise-controlled image reconstructions

2021 ◽  
Author(s):  
Carlas S. Smith ◽  
Johan A. Slotman ◽  
Lothar Schermelleh ◽  
Nadya Chakrova ◽  
Sangeetha Hari ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Resolving Power ◽  
Noise Model ◽  
Physical Parameters ◽  
Structured Illumination ◽  
Reconstruction Algorithms ◽  
Structured Illumination Microscopy ◽  
Signal To Noise ◽  
Trade Off ◽  
Noise Ratio

AbstractSuper-resolution structured illumination microscopy (SIM) has become a widely used method for biological imaging. Standard reconstruction algorithms, however, are prone to generate noise-specific artefacts that limit their applicability for lower signal-to-noise data. Here, we present a physically realistic noise model that explains the structured noise artefact and that is used to motivate new complementary reconstruction approaches. True Wiener-filtered SIM optimizes contrast given the available signal-to-noise ratio, flat-noise SIM fully overcomes the structured noise artefact while maintaining resolving power. Both methods eliminate ad-hoc user adjustable reconstruction parameters in favour of physical parameters, enhancing objectivity. The new reconstructions point to a trade-off between contrast and a natural noise appearance. This trade-off can be partly overcome by additional notch filtering, but at the expense of a decrease in signal-to-noise ratio. The benefits of the proposed approaches are demonstrated on focal adhesion and tubulin samples in 2D and 3D, and on nano-fabricated fluorescent test patterns.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

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.

Ultra-spatially resolved synchrotron powered FT-IR microspectroscopy of individual cells of biological material

1995 ◽  
Vol 53 ◽  
pp. 884-885
Author(s):  
David L. Wetzel ◽  
John A. Reffner ◽  
Gwyn P. Williams
Keyword(s):  
Thermal Noise ◽  
Spot Size ◽  
Acquisition Time ◽  
Thermal Source ◽  
Signal To Noise ◽  
Spatially Resolved ◽  
Good Spatial Resolution ◽  
Small Spot ◽  
Ft Ir ◽  
Ir Microspectroscopy

Synchrotron radiation is 100 to 1000 times brighter than a thermal source such as a globar. It is not accompanied with thermal noise and it is highly directional and nondivergent. For these reasons, it is well suited for ultra-spatially resolved FT-IR microspectroscopy. In efforts to attain good spatial resolution in FT-IR microspectroscopy with a thermal source, a considerable fraction of the infrared beam focused onto the specimen is lost when projected remote apertures are used to achieve a small spot size. This is the case because of divergence in the beam from that source. Also the brightness is limited and it is necessary to compromise on the signal-to-noise or to expect a long acquisition time from coadding many scans. A synchrotron powered FT-IR Microspectrometer does not suffer from this effect. Since most of the unaperatured beam’s energy makes it through even a 12 × 12 μm aperture, that is a starting place for aperture dimension reduction.

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