Frequency estimates of seismic traces

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 370-380 ◽  
Author(s):  
H. H. Hardy ◽  
Richard A. Beier ◽  
Jonathan D. Gaston
Keyword(s):  
Seismic Data ◽  
Time Window ◽  
Time Windows ◽  
Average Frequency ◽  
Frequency Method ◽  
Zero Crossings ◽  
Time Frequency ◽  
Shale Volume ◽  
True Frequency ◽  
Short Time

Local estimates of amplitude, frequency, and phase have been used in the past to characterize seismic data. In particular, these attributes have sometimes been successfully related to well attributes at the reservoir scale (net pay thickness, sand fraction, etc.). This paper introduces a method called SINFIT for computing local amplitude, frequency, and phase estimates of seismic traces over short‐time windows. The SINFIT method uses a sine‐curve fitting approach. The method is shown to give more accurate and robust frequency estimates than four other common methods on a set of test traces where the true frequency components are known. The four methods compared with SINFIT are instantaneous frequency, zero‐crossings, short‐time Fourier analysis, and a more recent time‐frequency method called AOK. In a field case with fluvial sands, an average frequency over a 30‐ms time window of seismic data correlates with estimated shale volume from well logs. The SINFIT method gives an average frequency attribute that more strongly correlates with shale volume than corresponding attributes from any of the other four methods.

Parameters of Spike Trains Observed in a Short Time Window

2008 ◽  
Vol 20 (5) ◽  
pp. 1325-1343 ◽  
Author(s):  
Zbyněk Pawlas ◽  
Lev B. Klebanov ◽  
Martin Prokop ◽  
Petr Lansky
Keyword(s):  
Coefficient Of Variation ◽  
Point Processes ◽  
Interspike Interval ◽  
Time Window ◽  
Time Windows ◽  
Time Interval ◽  
Short Time Interval ◽  
Target Neuron ◽  
Short Time Window ◽  
Short Time

We study the estimation of statistical moments of interspike intervals based on observation of spike counts in many independent short time windows. This scenario corresponds to the situation in which a target neuron occurs. It receives information from many neurons and has to respond within a short time interval. The precision of the estimation procedures is examined. As the model for neuronal activity, two examples of stationary point processes are considered: renewal process and doubly stochastic Poisson process. Both moment and maximum likelihood estimators are investigated. Not only the mean but also the coefficient of variation is estimated. In accordance with our expectations, numerical studies confirm that the estimation of mean interspike interval is more reliable than the estimation of coefficient of variation. The error of estimation increases with increasing mean interspike interval, which is equivalent to decreasing the size of window (less events are observed in a window) and with decreasing the number of neurons (lower number of windows).

Doppler Radio Fuze Signal Processing Method Based on the Extraction of Instantaneous Frequency

2013 ◽  
Vol 411-414 ◽  
pp. 1033-1039
Author(s):  
Lian Jie Li ◽  
Jia Hao Deng ◽  
Jin Liu
Keyword(s):  
Time Window ◽  
Doppler Frequency ◽  
Signal Amplitude ◽  
Doppler Signal ◽  
Test Results ◽  
Time Frequency ◽  
Frequency Information ◽  
Short Time Window ◽  
Short Time ◽  
System Time

To get accurate frequency information from doppler signal is very difficult. In order to improve accuracy of doppler radio fuze, a design scheme which is not only using doppler signal amplitude information but also using doppler frequency information, and comprehensive and these two aspects of information give out the fuze work distance. The solution we give out in this paper is that we realize the STFT by application of parallel process mass on FPGA and together with quick frequency selection mechanism. Then we could get the frequency information from the doppler signal. Test results show that by using short time window Fourier transform, we could realize time-frequency analysis of doppler signal in allow system time delay.

The robustness of seismic attenuation measurements using fixed- and variable-window time-frequency transforms

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA123-WA135 ◽  
Author(s):  
Carl Reine ◽  
Mirko van der Baan ◽  
Roger Clark
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Window ◽  
Time Windows ◽  
Seismic Attenuation ◽  
Continuous Wavelet ◽  
Transmission Experiment ◽  
Time Frequency ◽  
S Transform ◽  
Variable Window

Frequency-based methods for measuring seismic attenuation are used commonly in exploration geophysics. To measure the spectrum of a nonstationary seismic signal, different methods are available, including transforms with time windows that are either fixed or systematically varying with the frequency being analyzed. We compare four time-frequency transforms and show that the choice of a fixed- or variable-window transform affects the robustness and accuracy of the resulting attenuation measurements. For fixed-window transforms, we use the short-time Fourier transform and Gabor transform. The S-transform and continuous wavelet transform are analyzed as the variable-length transforms. First we conduct a synthetic transmission experiment, and compare the frequency-dependent scattering attenuation to the theoretically predicted values. From this procedure, we find that variable-window transforms reduce the uncertainty and biasof the resulting attenuation estimate, specifically at the upper and lower ends of the signal bandwidth. Our second experiment measures attenuation from a zero-offset reflection synthetic using a linear regression of spectral ratios. Estimates for constant-[Formula: see text] attenuation obtained with the variable-window transforms depend less on the choice of regression bandwidth, resulting in a more precise attenuation estimate. These results are repeated in our analysis of surface seismic data, whereby we also find that the attenuation measurements made by variable-window transforms have a stronger match to their expected trend with offset. We conclude that time-frequency transforms with a systematically varying time window, such as the S-transform and continuous wavelet transform, allow for more robust estimates of seismic attenuation. Peaks and notches in the measured spectrum are reduced because the analyzed primary signal is better isolated from the coda, and because of high-frequency spectral smoothing implicit in the use of short-analysis windows.

QUANTUM COHERENCE IN NEUTRON SCATTERING ON PROTONS

2004 ◽  
Vol 18 (07n08) ◽  
pp. 247-268 ◽  
Author(s):  
ERIK B. KARLSSON
Keyword(s):  
Quantum Coherence ◽  
Time Window ◽  
Condensed Matter ◽  
Time Windows ◽  
Phase Relations ◽  
Time Intervals ◽  
Quantum Objects ◽  
Quantum Coherence Effects ◽  
Short Time ◽  
Small Clusters

Several recent observations of closely spaced hydrogen nuclei in condensed matter systems — water, polymers and metal hydrides — indicate that they cannot be considered as independent quantum objects when observed over very short time intervals. According to these measurements, pairs (or possibly small clusters) of protons or deuterons seem to be quantum correlated, and are able to preserve their mutual quantum phase relations over times of the order of femtoseconds even in strongly perturbing liquid or solid environments. These new experimental results are mainly based on scattering of neutrons with time windows in the atto- and femtosecond range, but there also exists corroborating evidence from other spectroscopies. When the width of the observational time window is increased above a characteristic value, the quantum coherence effects are seen to disappear. This time limit marks the onset of decoherence as the mutual phase relations between the particles are gradually lost. Possible reasons for short-time entanglement of nuclei in condensed matter systems, as well as mechanisms for its decoherence will be discussed.

scholarly journals Identification of ship wake structures by a time–frequency method

2015 ◽  
Vol 765 ◽  
pp. 229-251 ◽  
Author(s):  
T. Torsvik ◽  
T. Soomere ◽  
I. Didenkulova ◽  
A. Sheremet
Keyword(s):  
High Frequency ◽  
Individual Component ◽  
Energy Content ◽  
Low Frequency ◽  
Frequency Method ◽  
Ship Wake ◽  
Time Frequency ◽  
Time Space ◽  
Short Time ◽  
Ship Speed

AbstractThe wake of a ship that sails at relatively large Froude numbers usually contains a number of components of different nature and with different heights, lengths, timings and propagation directions. We explore the possibilities of the spectrogram representation of one-point measurements of the ship wake to identify these components and to quantify their main properties. This representation, based on the short-time Fourier transform, facilitates a reliable decomposition of the wake into constituent components and makes it possible to quantify their variations in the time–space domain and the energy content of each component, from very low-frequency precursor waves up to high-frequency signals within the frequency range of typical wind-generated waves. A method for estimation of the ship speed and the distance of its sailing line from the measurement site is proposed, which only uses information available within the record of the ship wake surface elevation, but where it is assumed that the wake pattern does not deviate significantly from the classical Kelvin wake structure. The wake decomposition using the spectrogram method allows investigation of the energy content that can be attributed to each individual component of the wake. We demonstrate that the majority (60–80 %) of wake energy from strongly powered large ferries that sail at depth Froude numbers ${\sim}0.7$ is concentrated in components that are located near the edge of the wake wedge. Finally, we demonstrate that the spectrogram representation offers a convenient way to identify a specific signature of single types of ships.

scholarly journals Event-related EEG oscillatory responses elicited by dynamic facial expression

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Tuba Aktürk ◽  
Tom A. de Graaf ◽  
Yasemin Abra ◽  
Sevilay Şahoğlu-Göktaş ◽  
Dilek Özkan ◽  
...  
Keyword(s):  
Facial Expressions ◽  
Face Processing ◽  
Time Window ◽  
Phase Locking ◽  
Time Windows ◽  
Real Life ◽  
Emotion Expression ◽  
Expression Recognition ◽  
Time Frequency ◽  
Recognition Of Facial Expressions

Abstract Background Recognition of facial expressions (FEs) plays a crucial role in social interactions. Most studies on FE recognition use static (image) stimuli, even though real-life FEs are dynamic. FE processing is complex and multifaceted, and its neural correlates remain unclear. Transitioning from static to dynamic FE stimuli might help disentangle the neural oscillatory mechanisms underlying face processing and recognition of emotion expression. To our knowledge, we here present the first time–frequency exploration of oscillatory brain mechanisms underlying the processing of dynamic FEs. Results Videos of joyful, fearful, and neutral dynamic facial expressions were presented to 18 included healthy young adults. We analyzed event-related activity in electroencephalography (EEG) data, focusing on the delta, theta, and alpha-band oscillations. Since the videos involved a transition from neutral to emotional expressions (onset around 500 ms), we identified time windows that might correspond to face perception initially (time window 1; first TW), and emotion expression recognition subsequently (around 1000 ms; second TW). First TW showed increased power and phase-locking values for all frequency bands. In the first TW, power and phase-locking values were higher in the delta and theta bands for emotional FEs as compared to neutral FEs, thus potentially serving as a marker for emotion recognition in dynamic face processing. Conclusions Our time–frequency exploration revealed consistent oscillatory responses to complex, dynamic, ecologically meaningful FE stimuli. We conclude that while dynamic FE processing involves complex network dynamics, dynamic FEs were successfully used to reveal temporally separate oscillation responses related to face processing and subsequently emotion expression recognition.

Constrained least-squares spectral analysis: Application to seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. V143-V167 ◽  
Author(s):  
Charles I. Puryear ◽  
Oleg N. Portniaguine ◽  
Carlos M. Cobos ◽  
John P. Castagna
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Continuous Wavelet ◽  
Window Length ◽  
Short Time Fourier Transform ◽  
Constrained Least Squares ◽  
Time Frequency ◽  
Short Time

An inversion-based algorithm for computing the time-frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method resulted in spectra that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases. As compared with the continuous wavelet transform, the method has greatly improved temporal resolution, particularly at low frequencies.

scholarly journals Exploration of the data space via trans-dimensional sampling: the case study of seismic double difference data

2021 ◽  
Author(s):  
Nicola Piana Agostinetti ◽  
Giulia Sgattoni
Keyword(s):  
Seismic Data ◽  
Time Window ◽  
Time Windows ◽  
Correlation Coefficients ◽  
Double Difference ◽  
Seismicity Rate ◽  
Data Space ◽  
Double Differences ◽  
Time Invariant

Abstract. Double differences (DD) seismic data are widely used to define elasticity distribution in the Earth's interior, and its variation in time. DD data are often pre-processed from earthquakes recordings through expert-opinion, where couples of earthquakes are selected based on some user-defined criteria, and DD data are computed from the selected couples. We develop a novel methodology for preparing DD seismic data based on a trans-dimensional algorithm, without imposing pre-defined criteria on the selection of couples of events. We apply it to a seismic database recorded on the flank of Katla volcano (Iceland), where elasticity variations in time has been indicated. Our approach quantitatively defines the presence of changepoints that separate the seismic events in time-windows. Within each time-window, the DD data are consistent with the hypothesis of time-invariant elasticity in the subsurface, and DD data can be safely used in subsequent analysis. Due to the parsimonious behavior of the trans-dimensional algorithm, only changepoints supported by the data are retrieved. Our results indicate that: (a) retrieved changepoints are consistent with first-order variations in the data (i.e. most striking changes in the DD data are correctly reproduced in the changepoint distribution in time); (b) changepoint locations in time do correlate neither with changes in seismicity rate, nor with changes in waveforms similarity (measured through the cross-correlation coefficients); and (c) noteworthy, the changepoint distribution in time seems to be insensitive to variations in the seismic network geometry during the experiment. Our results proofs that trans-dimensional algorithms can be positively applied to pre-processing of geophysical data before the application of standard routines (i.e. before using them to solve standard geophysical inverse problems) in the so called exploration of the data space.

Time-frequency analysis of seismic data using local attributes

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. P23-P34 ◽  
Author(s):  
Guochang Liu ◽  
Sergey Fomel ◽  
Xiaohong Chen
Keyword(s):  
Frequency Analysis ◽  
Seismic Data ◽  
Low Frequency ◽  
Average Frequency ◽  
Time Varying ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Frequency Map

Time-frequency analysis is an important technology in seismic data processing and interpretation. To localize frequency content in time, we have developed a novel method for computing a time-frequency map for nonstationary signals using an iterative inversion framework. We calculated time-varying Fourier coefficients by solving a least-squares problem that uses regularized nonstationary regression. We defined the time-frequency map as the norm of time-varying coefficients. Time-varying average frequency of the seismic data can also be estimated from the time-frequency map calculated by our method. We tested the method on benchmark synthetic signals and compared it with the well-known S-transform. Two field data examples showed applications of the proposed method for delineation of sand channels and for detection of low-frequency anomalies.

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