Algorithms for time–frequency imaging and analysis: introduction to mixed-model spectral decomposition

Delineating the extend of a producing reservoir is one of the main challenge of exploration and development interpreters. Our approach to address this challenge is to use ?spectral decomposition? of pre-stack data couple with an AVA/AVO studies (Amplitude Versus Angle/Offset). Seismic spectral decomposition is a known method to determine more accurately the lithology of an area of interest. AVO effect are used to identify and quantify the extend of a fluid anomaly in a potential reservoir. Combine together, the aim of this method is to provide a better delineation of the producing area. A shared earth approach will be used in order to perform cross validation of the results at each step. The first step is a 1D study well bore centred: Using well logs information: Vp (compressional velocity), Vs (Shear velocity) and the density to compute a first set of synthetic gather that will constitute our reference. The chosen well has an AVO effect and should be visible on this reference set. A real set of pre-stack gather at the well bore will then go through a series of tests to identify the best frequency bandwidth that identify more accurately the AVO effect. In a second phase, this frequency bandwidth will be used to produce two results: A 3d set of gather with this optimum bandwidth. Producing Gradient and the Intercept of this set, a cross plot of those attributes should confirm the result of the 1D study and will help to delineate the AVO effect spatial extent. An inversion based on this spectral decomposition should help to delineate more accurately the reservoir lithology Those results unified well bore information, seismic pre and post stack data, frequency analysis and inversion results. The analysis will tend to demonstrate that lithology and gas anomaly can be better mapped using combined methodology, compare to a juxtaposition of methods.

Peter Dallas Auditory Physiology Laboratory (The Hugh Knowles Center) and Department of Neurobiology and Physiology, Northwestern University, Evanston, Illinois 60208 The cochlea is a hydromechanical frequency analyzer located in the inner ear (Fig. 1 a). Its principal role is to perform a real- time spectral decomposition of the acoustic signal in producing a spatial frequency map. The frequency analysis may be un- derstood with the aid of Figure 1 b, which shows a straightened cochlea with a snapshot of its basilar membrane displaced in response to a single-frequency sound (pure tone). Upon delivery of an acoustic signal into the fluid-filled cochlea, the basilar membrane undergoes an oscillatory motion at the frequency of the sound, resulting in a wave traveling toward its distal end. The drawing shows an instantaneous view ofthis traveling wave. The wave is spatially confined along the length of the basilar membrane, and the location of its maximum amplitude is re- lated to the frequency of the sound. The higher the frequency, the more restricted the disturbance to the proximal end. The vibrating membrane supports the sense organ of hearing, the spiral organ of Corti (Fig. 2) which is deformed maximally in the region of the peak of the traveling wave. In this location, the sensory receptor cells of the organ of Corti receive maximal mechanical stimulation, transduce it into maximal electrical signals, and thus produce maximal afferent sensory outflow from the cochlea. Thus, mechanical frequency analysis is performed by matching particular frequencies with particular groups of auditory receptor cells and their nerve fibers. Understanding of frequency analysis in the inner ear pro- gressed through three main epochs. The first was dominated by Helmholtz’s suggestions that lightly damped, spatially ordered, mechanically resonant elements in the cochlea perform the spec- tral analysis (this period was reviewed by Wever, 1949). The second epoch, lasting from the late 1940s to the early 1970s was dominated by von Bekesy’s description of the traveling wave (von BtkCsy, 1960). We are now in the third epoch (an overview of its evolution is given in Dallos, 1988) during which a fundamentally different paradigm has emerged. According to this paradigm, von Btktsy’s traveling wave is boosted by a local electromechanical amplification process in which one of the mammalian ear’s sensory cell groups, outer hair cells, function as both sensors and mechanical feedback elements. The ideas that the operation of a sense organ is dependent upon local mechanical feedback modification by what resembles a sensory receptor cell, that such mechanical feedback may operate at audio frequencies utilizing some novel cellular motor, and that

Summary Conventional seismic sections cannot display most of the important events in reservoir studies. The study of frequency content of seismic sections can provide better understanding to geoscientists, as well as interpreters in the field of petroleum engineering studies. An isofrequency process is a powerful tool in terms of reservoir imaging. One of the methods that provides isofrequency slice is Spectral Decomposition (SD). SD is a comprehensive method that eliminates most of limitations encountered in seismic data to reveal geological information. SD provides continuous analysis of amplitude, frequency, phase, and energy spectrum. Therefore, SD is applied to obtain an amplitude spectrum of frequency content of seismic trace which is attributed to the temporal center of the sample trace. So higher frequency resolution is obtained at lower frequencies and higher time resolution at higher frequencies. In this paper, Short Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) as SD methods were used in order to detect sand channel at one of the Iranian Southwest oil fields for which it has the potential to be considered as a reservoir.

Editorial

Asymmetric windows in digital signal processing

Classical time-frequency analysis is based on the amplitude responses of bandpass filters, discarding phase information. Instantaneous frequency analysis, in contrast, is based on the derivatives of these phases. This method of frequency calculation is of interest for its high precision and for reasons of similarity to cochlear encoding of sound. This article describes a methodology for high resolution analysis of sparse sounds, based on instantaneous frequencies. In this method, a comparison between tonotopic and instantaneous frequency information is introduced to select filter positions that are well matched to the signal. Second, a cross-check that compares frequency estimates from neighboring channels is used to optimize filter bandwidth, and to signal the quality of the analysis. These cross-checks lead to an optimal time-frequency representation without requiring any prior information about the signal. When applied to a signal that is sufficiently sparse, the method decomposes the signal into separate time-frequency contours that are tracked with high precision. Alternatively, if the signal is spectrally too dense, neighboring channels generate inconsistent estimates-a feature that allows the method to assess its own validity in particular contexts. Similar optimization principles may be present in cochlear encoding.

Face milling is among the processes that can produce a high-precision surface finish. Tool condition monitoring and signal processing algorithms are under extensive research to improve production quality and productivity in machining processes. In the present research, the time–frequency analysis technique was applied to the signal obtained from a sensor integrated into the primary AC power circuitry during the milling of steel bars to evaluate its applicability in detecting the current variations associated with the cutting force. The signal acquired from the sensor was processed in the time–frequency domain using wavelet analysis, and the results were compared with the traditional time and frequency analyses. The results showed that the signal variations produced by the cutting force were well localized in the frequency spectra with both approaches. However, the wavelet processing method yielded a poorly defined cutting force signal shape due to the limited resolution inherent in the sub-bands containing the frequencies of interest.

Comparison of different spectral decompositions for non-marine deep water sandstone reservoir prediction in the Xingma area

Time–frequency (TF) analysis is a powerful tool to describe the frequency response of subsurface rocks and hydrocarbon reservoirs. In this letter, the matching demodulation synchrosqueezing S transform (MDSST) that achieves a highly concentrated TF representation was introduced to seismic TF analysis. The MDSST includes two steps: the matching demodulation technique is preprocessing that provides a rough estimation of instantaneous frequency (IF) of the analyzed signal, and the synchrosqueezing transform (SST) is postprocessing that produces an accurate IF. Numerical experiments on synthetic and real signals demonstrate the superiority of the MDSST in seismic TF analysis.

The analysis of spectroscopic optical coherence tomography (SOCT) signals suffers the trade-off between time resolution and frequency resolution. Various joint time-frequency distributions (TFDs) can optimize this trade-off. Synthesized signals were generated and experimentally acquired data were obtained to compare and validate several different TFDs under different SOCT imaging schemes. Specific criteria were designed to quantify the TFD performance. We found that different SOCT imaging schemes require different optimal TFDs. Cohen's class TFDs generate the most compact time-frequency (TF) analysis, while linear TFDs offer the most reliable TF analysis. In both cases, if some prior information is known, model-based TF analysis can improve the performance.

Third order time and frequency analysis has exhibited great potential for correlation analysis of multi-sensor datasets, but is usually presented as separate time domain and frequency domain approaches. A combined framework of both frequency domain and time domain has rarely been used. This paper proposes a non-parametric third order time and frequency domain framework which used two dimensional Fourier transforms to bridge the gap between time domain and frequency domain. A unified framework offers flexibility and efficiency to apply to data. In this paper we study neural spike train data treated as stochastic point processes. In time domain direct analysis, third order cumulant densities of spike trains are applied, which need all first-, secondand third order product densities to be calculated before constructing the third order cumulant density, which brings additional challenges. The novelty in this study is that a new framework is proposed which can offer an alternative approach without calculating lower order quantities and can reveal nonlinear relationship between neural recordings. The results show that the present framework provides a novel non-parametric method to estimate both time and frequency domain measurements which is applicable to neural spike trains.

Due to the complicated and distributed characters of DDoS attack, a novel detection DDoS method based on global network is presented in this paper. Our method detects DDoS by analyzing network-wide traffic, whereas the traditional methods detect it on single link or victim network, they can only detect the DDoS which show large scope. Our method was carried out as follows: First, we get network traffic matrix. Then we diagnose DDoS in time domain and frequency domain by K-L transformation and computing correlation coefficient. K-L divides time domain and frequency domain sequence into normal space and abnormal space and then we compute the abnormal space's correlation coefficient. Finally, we set threshold to detect DDoS attack. The simulation result shows that some DDoS could be detected in time domain but others could only be detected in frequency domain. This method is more accurate and faster than traditional ones. It is well suited for detecting earlier DDoS attack.

Decomposing delta, theta, and alpha time–frequency ERP activity from a visual oddball task using PCA

In terms of today, one may argue, throughout observations from energy literature papers, that (i) one of the main contributors of the global warming is carbon dioxide emissions, (ii) the fossil fuel energy usage greatly contributes to the carbon dioxide emissions, and (iii) the simulations from energy models attract the attention of policy makers to renewable energy as alternative energy source to mitigate the carbon dioxide emissions. Although there appears to be intensive renewable energy works in the related literature regarding renewables' efficiency/impact on environmental quality, a researcher might still need to follow further studies to review the significance of renewables in the environment since (i) the existing seminal papers employ time series models and/or panel data models or some other statistical observation to detect the role of renewables in the environment and (ii) existing papers consider mostly aggregated renewable energy source rather than examining the major component(s) of aggregated renewables. This paper attempted to examine clearly the impact of biomass on carbon dioxide emissions in detail through time series and frequency analyses. Hence, the paper follows wavelet coherence analyses. The data covers the US monthly observations ranging from 1984:1 to 2015 for the variables of total energy carbon dioxide emissions, biomass energy consumption, coal consumption, petroleum consumption, and natural gas consumption. The paper thus, throughout wavelet coherence and wavelet partial coherence analyses, observes frequency properties as well as time series properties of relevant variables to reveal the possible significant influence of biomass usage on the emissions in the USA in both the short-term and the long-term cycles. The paper also reveals, finally, that the biomass consumption mitigates CO2 emissions in the long run cycles after the year 2005 in the USA.

Corona-generated audible noise is induced by the collisions between space charges and air molecules. It has been proven that there is a close correlation between audible noise and corona current from DC corona discharge. Analysis on the correlation between audible noise and corona current can promote the cognition of the generation mechanism of corona discharge. In this paper, time-domain waveforms of AC corona-generated audible noise and corona current are measured simultaneously. The one-to-one relationship between sound pressure pulses and corona current pulses can be found and is used to remove the interferences from background noise. After the interferences are removed, the linear correlated relationships between sound pressure pulse amplitude and corona current pulse amplitude are obtained through statistical analysis. Besides, frequency components at the harmonics of power frequency (50 Hz) can be found both in the frequency spectrums of audible noise and corona current through frequency analysis. Furthermore, the self-correlation relationships between harmonic components below 400 Hz with the 50 Hz component are analyzed for audible noise and corona current and corresponding empirical formulas are proposed to calculate the harmonic components based on the 50 Hz component. Finally, based on the AC corona discharge process and generation mechanism of audible noise and corona current, the correlation between audible noise and corona current in time domain and frequency domain are interpreted qualitatively. Besides, with the aid of analytical expressions of periodic square waves, sound pressure pulses, and corona current pulses, the modulation effects from the AC voltage on the pulse trains are used to interpret the generation of the harmonic components of audible noise and corona current.