scholarly journals SPECTRAL DECOMPOSITION TECHNIQUE BASED ON STFT AND CWT FOR IDENTIFYING THE HYDROCARBON RESERVOIR

2018 ◽  
Vol 40 (3) ◽  
pp. 125-131
Author(s):  
Abdul Haris ◽  
Haryono Haryono ◽  
Agus Riyanto
Keyword(s):  
Fourier Transform ◽  
Spectral Decomposition ◽  
Real Data ◽  
Seismic Signal ◽  
Frequency Resolution ◽  
Decomposition Technique ◽  
Window Length ◽  
Data Set ◽  
Time Frequency ◽  
Hydrocarbon Reservoir

The spectral decomposition is one of the advanced interpretation techniques such as seismic inversion, amplitude versus offset analysis, and seismic attribute that helpful in direct interpretative approach in seismic exploration. This technique is a transformation algorithm, thus a signal can be transformed into its varying frequency contained in the seismic signal. There are a variety of spectral decomposition algorithms in the decomposing seismic signal from time domain into frequency domain. These algorithms include Short Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT). The STFT algorithm is a conventional and simple technique for computing a time-frequency spectrum, which is based on the application of Fourier transform. However, the STFT algorithm has a problem related to the frequency resolution. In its implementation, this algorithm is limited by predefi ned window length. In contrast, the CWT algorithm is believed to be able to overcome the limitation of window length. The CWT threats wavelet at certain window length, which is defi ned by the characteristics of the wavelet. In this study, the comparison between spectral decomposition technique based on STFT and CWT method was performed, particularly in its application to the synthetic and real data set. Each algorithm has its own advantages and disadvantages in decomposing the seismic signal. Further, this analysis can be used as a reference to select one of two algorithms for the specifi c application. The synthetic data set application shows that CWT algorithm produces better frequency resolution compared to STFT algorithm. In addition, the real data set application shows that time frequency section of the seismic line provides a spectral feature, which is useful to identify the hydrocarbon reservoir, which is associated with low-frequency shadow zone.

Seismic spectral decomposition using deconvolutive short-time Fourier transform spectrogram

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. V43-V51 ◽  
Author(s):  
Wenkai Lu ◽  
Fangyu Li
Keyword(s):  
Fourier Transform ◽  
Spectral Decomposition ◽  
Reservoir Characterization ◽  
Low Frequency ◽  
Seismic Signal ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Distribution Method ◽  
Time Frequency ◽  
Short Time

The spectral decomposition technique plays an important role in reservoir characterization, for which the time-frequency distribution method is essential. The deconvolutive short-time Fourier transform (DSTFT) method achieves a superior time-frequency resolution by applying a 2D deconvolution operation on the short-time Fourier transform (STFT) spectrogram. For seismic spectral decomposition, to reduce the computation burden caused by the 2D deconvolution operation in the DSTFT, the 2D STFT spectrogram is cropped into a smaller area, which includes the positive frequencies fallen in the seismic signal bandwidth only. In general, because the low-frequency components of a seismic signal are dominant, the removal of the negative frequencies may introduce a sharp edge at the zero frequency, which would produce artifacts in the DSTFT spectrogram. To avoid this problem, we used the analytic signal, which is obtained by applying the Hilbert transform on the original real seismic signal, to calculate the STFT spectrogram in our method. Synthetic and real seismic data examples were evaluated to demonstrate the performance of the proposed method.

Spectral decomposition of seismic data with continuous-wavelet transform

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. P19-P25 ◽  
Author(s):  
Satish Sinha ◽  
Partha S. Routh ◽  
Phil D. Anno ◽  
John P. Castagna
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Scale ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Map

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

scholarly journals Low Latency Convolutive Blind Source Separation

2021 ◽  
Author(s):  
◽  
Jiawen Chua
Keyword(s):  
Frequency Domain ◽  
Real Time ◽  
Impulse Response ◽  
Source Separation ◽  
Frequency Resolution ◽  
Separation Performance ◽  
Window Length ◽  
Time Frequency ◽  
Time Systems ◽  
Separation Parameters

<p>In most real-time systems, particularly for applications involving system identification, latency is a critical issue. These applications include, but are not limited to, blind source separation (BSS), beamforming, speech dereverberation, acoustic echo cancellation and channel equalization. The system latency consists of an algorithmic delay and an estimation computational time. The latter can be avoided by using a multi-thread system, which runs the estimation process and the processing procedure simultaneously. The former, which consists of a delay of one window length, is usually unavoidable for the frequency-domain approaches. For frequency-domain approaches, a block of data is acquired by using a window, transformed and processed in the frequency domain, and recovered back to the time domain by using an overlap-add technique.  In the frequency domain, the convolutive model, which is usually used to describe the process of a linear time-invariant (LTI) system, can be represented by a series of multiplicative models to facilitate estimation. To implement frequency-domain approaches in real-time applications, the short-time Fourier transform (STFT) is commonly used. The window used in the STFT must be at least twice the room impulse response which is long, so that the multiplicative model is sufficiently accurate. The delay constraint caused by the associated blockwise processing window length makes most the frequency-domain approaches inapplicable for real-time systems.  This thesis aims to design a BSS system that can be used in a real-time scenario with minimal latency. Existing BSS approaches can be integrated into our system to perform source separation with low delay without affecting the separation performance. The second goal is to design a BSS system that can perform source separation in a non-stationary environment.  We first introduce a subspace approach to directly estimate the separation parameters in the low-frequency-resolution time-frequency (LFRTF) domain. In the LFRTF domain, a shorter window is used to reduce the algorithmic delay of the system during the signal acquisition, e.g., the window length is shorter than the room impulse response. The subspace method facilitates the deconvolution of a convolutive mixture to a new instantaneous mixture and simplifies the estimation process.  Second, we propose an alternative approach to address the algorithmic latency problem. The alternative method enables us to obtain the separation parameters in the LFRTF domain based on parameters estimated in the high-frequency-resolution time-frequency (HFRTF) domain, where the window length is longer than the room impulse response, without affecting the separation performance.  The thesis also provides a solution to address the BSS problem in a non-stationary environment. We utilize the ``meta-information" that is obtained from previous BSS operations to facilitate the separation in the future without performing the entire BSS process again. Repeating a BSS process can be computationally expensive. Most conventional BSS algorithms require sufficient signal samples to perform analysis and this prolongs the estimation delay. By utilizing information from the entire spectrum, our method enables us to update the separation parameters with only a single snapshot of observation data. Hence, our method minimizes the estimation period, reduces the redundancy and improves the efficacy of the system.  The final contribution of the thesis is a non-iterative method for impulse response shortening. This method allows us to use a shorter representation to approximate the long impulse response. It further improves the computational efficiency of the algorithm and yet achieves satisfactory performance.</p>

scholarly journals An Efficient Adaptive Window Size Selection Method for Improving Spectrogram Visualization

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shibli Nisar ◽  
Omar Usman Khan ◽  
Muhammad Tariq
Keyword(s):  
Fourier Transform ◽  
Filter Bank ◽  
Window Size ◽  
Fixed Time ◽  
Frequency Resolution ◽  
High Spectral Resolution ◽  
Background Information ◽  
High Temporal Resolution ◽  
Low Frequencies ◽  
Time Frequency

Short Time Fourier Transform (STFT) is an important technique for the time-frequency analysis of a time varying signal. The basic approach behind it involves the application of a Fast Fourier Transform (FFT) to a signal multiplied with an appropriate window function with fixed resolution. The selection of an appropriate window size is difficult when no background information about the input signal is known. In this paper, a novel empirical model is proposed that adaptively adjusts the window size for a narrow band-signal using spectrum sensing technique. For wide-band signals, where a fixed time-frequency resolution is undesirable, the approach adapts the constant Q transform (CQT). Unlike the STFT, the CQT provides a varying time-frequency resolution. This results in a high spectral resolution at low frequencies and high temporal resolution at high frequencies. In this paper, a simple but effective switching framework is provided between both STFT and CQT. The proposed method also allows for the dynamic construction of a filter bank according to user-defined parameters. This helps in reducing redundant entries in the filter bank. Results obtained from the proposed method not only improve the spectrogram visualization but also reduce the computation cost and achieves 87.71% of the appropriate window length selection.

scholarly journals Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170254 ◽  
Author(s):  
Jean Baptiste Tary ◽  
Roberto Henry Herrera ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Signal ◽  
American Football ◽  
Frequency Resolution ◽  
Time Varying ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Frequency Information ◽  
Synchrosqueezing Transform

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a ‘FanQuake’ signal displaying observed vibrations during an American football game, a seismic recording of the M w 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

scholarly journals Inverse spectral decomposition using an lp-norm constraint for the detection of close geological anomalies

2020 ◽  
Vol 17 (6) ◽  
pp. 1463-1477 ◽  
Author(s):  
San-Yi Yuan ◽  
Shan Yang ◽  
Tie-Yi Wang ◽  
Jie Qi ◽  
Shang-Xu Wang
Keyword(s):  
Spectral Decomposition ◽  
Frequency Resolution ◽  
Space Resolution ◽  
Time Frequency ◽  
Lp Norm ◽  
Geological Features ◽  
Full Band ◽  
Spectral Coefficients ◽  
Norm Constraint ◽  
Compact Spectrum

AbstractAn important application of spectral decomposition (SD) is to identify subsurface geological anomalies such as channels and karst caves, which may be buried in full-band seismic data. However, the classical SD methods including the wavelet transform (WT) are often limited by relatively low time–frequency resolution, which is responsible for false high horizon-associated space resolution probably indicating more geological structures, especially when close geological anomalies exist. To address this issue, we impose a constraint of minimizing an lp (0 < p < 1) norm of time–frequency spectral coefficients on the misfit derived by using the inverse WT and apply the generalized iterated shrinkage algorithm to invert for the optimal coefficients. Compared with the WT and inverse SD (ISD) using a typical l1-norm constraint, the modified ISD (MISD) using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features. We design a 3D synthetic dataset involving frequency-close thin geological anomalies and the other 3D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD. The application of 4D spectrum on a 3D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.

Gaussian Window of Optimal Time-Frequency Resolution in Numerical Implementation of Short-Time Fourier Transform

2011 ◽  
Vol 48-49 ◽  
pp. 555-560 ◽  
Author(s):  
Yang Jin ◽  
Zhi Yong Hao
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Gaussian Function ◽  
Frequency Resolution ◽  
Optimal Time ◽  
Numerical Implementation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Gaussian Window ◽  
Short Time

In this paper, we report the condition to keep the optimal time-frequency resolution of the Gaussian window in the numerical implementation of the short-time Fourier transform. Because of truncation and discretization, the time-frequency resolution of the discrete Gaussian window is different from that of the proper Gaussian function. We compared the time-frequency resolution performance of the discrete Gaussian window and Hanning window based on that they have the same continuous-time domain standard deviation, and generalized the condition under which the time-frequency resolution of the Gaussian window will prevail over that of the Hanning window.

The Time-Frequency Resolution of Short Time Fourier Transform Based on Multi-Window Functions

2011 ◽  
Vol 214 ◽  
pp. 122-127 ◽  
Author(s):  
Li Hua Wang ◽  
Qi Dong Zhang ◽  
Yong Hong Zhang ◽  
Kai Zhang
Keyword(s):  
Fourier Transform ◽  
Time Resolution ◽  
High Performance ◽  
Frequency Resolution ◽  
Good Time ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Window Functions ◽  
Short Time ◽  
Good Time Resolution

The short-time Fourier transform has the disadvantage that is does not localize time and frequency phenomena very well. Instead the time-frequency information is scattered which depends on the length of the window. It is not possible to have arbitrarily good time resolution simultaneously with good frequency resolution. In this paper, a new method that uses the short-time Fourier transform based on multi-window functions to enhance time-frequency resolution of signals has been proposed. Simulation and experimental results present the high performance of the proposed method.

scholarly journals A Study of Parameters Setting of the STADZT

10.14311/1654 ◽  
2012 ◽  
Vol 52 (5) ◽  
Author(s):  
Václav Turoň
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Stationary Signals ◽  
Zolotarev Polynomials ◽  
Non Stationary Signal ◽  
Short Time ◽  
Main Influence

This paper deals with the new time-frequency Short-Time Approximated Discrete Zolotarev Transform (STADZT), which is based on symmetrical Zolotarev polynomials. Due to the special properties of these polynomials, STADZT can be used for spectral analysis of stationary and non-stationary signals with the better time and frequency resolution than the widely used Short-Time Fourier Transform (STFT). This paper describes the parameters of STADZT that have the main influence on its properties and behaviour. The selected parameters include the shape and length of the segmentation window, and the segmentation overlap. Because STADZT is very similar to STFT, the paper includes a comparison of the spectral analysis of a non-stationary signal created by STADZT and by STFT with various settings of the parameters.

High-resolution seismic complex trace analysis by adaptive fast sparse S-transform

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. V51-V67 ◽  
Author(s):  
Hamid Sattari
Keyword(s):  
High Resolution ◽  
Hilbert Transform ◽  
Trace Analysis ◽  
Spectral Decomposition ◽  
Decomposition Method ◽  
Random Noise ◽  
Real Data ◽  
Mixed Norm ◽  
Time Frequency ◽  
S Transform

Complex trace analysis provides seismic interpreters with a view to identify the nature of challenging subsurface geologic features. However, the conventional procedure based on the Hilbert transform (HT) is highly sensitive to random noise and sudden frequency variations in seismic data. Generally, conventional filtering methods reduce the spectral bandwidth while stabilizing complex trace analysis, whereas obtaining high-resolution images of multiple thin-bed layers requires wideband data. It is thus a challenging problem to reconcile the conflict between the two purposes, and a powerful signal processing device is required. To overcome the issue, I first introduced the fast sparse S-transform (ST) as a powerful time-frequency decomposition method to improve the windowed Hilbert transform (WHT). Then, in addition to the mixed-norm higher resolution provided by the fast sparse ST, I have developed a novel sparsity-based optimization for window parameters. The process adaptively regularizes sudden changes in frequency content of nonstationary signals with the same computational complexity of the nonoptimized algorithm. The performance of the proposed windowing optimization is compared with those of available methods that have so far been used for adaptivity enhancement of Fourier-based spectral decomposition methods. The final adaptive and sparse version of WHT is used to achieve high-resolution complex trace analysis and address the above-mentioned conflict. The instantaneous complex attributes obtained by the proposed method for several synthetic and real data sets of which multiple thin-bed layers contain wedges, trapped gas reservoirs, and faults are superior to those obtained by WHT via adaptive sparse STFT, robust adaptive WHT, and conventional HT. Potential applications of the adaptive double-sparse ST as a new spectral decomposition method were also evaluated.

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