Time-Reassigned Synchro squeezing Transform and low-frequency shadows associated with gas detection.

Time-frequency representation, which has been widely used in seismic data inquiry, can reveal a parcel of useful data hidden inside the seismic data. We've introduced a previously unexplored seismic application of the high-resolution Time-Reassigned Synchrosqueezing Transform (TRSST), which can provide significantly sparser time-frequency representation than other methods. One of the most appealing aspects of the proposed technique is its ability to be entirely adaptable. For the flag examination representation and deterioration, various approaches have been presented. This paper used the TRSST to provide the time-frequency contour and stimulate the depiction of low-frequency shadows associated with hydrocarbons. It was also compared to the Short Time Fourier Transform (STFT), both of which are STFT-based time-frequency transforms.

1. 1 INTRODUCTION Time-frequency analysis converts a 1D flag in time into a 2D image in the time-frequency domain, describing both time-frequency highlights and instantaneous frequency.Timefrequency decomposition in seismic data processing and interpretation has lately grown in popularity.TheSynchrosqueezing Wavelet Change [1], [2] which was originally based on audio signal analysis, could be a wavelet-based time-frequency representation, although it has a more rigid conceptual foundation than EMD.Compared to wavelet-based techniques, this transform appeared to have superior time-frequency resolution [3].
Unfortunately, the HeisenbergGabor uncertainty principle limits these methods.As a result, the generated representations are hazy and have low energy concentration, necessitating a trade-off between time and frequency localization accuracy.Another method, the reassignment method [4], [5], was introduced to increase the readability of a time-frequency representation in a mathematically elegant and efficient way (TFR).The drawback is that reassignment produces non-invertible TFRs, limiting its utility for analysis and modelling.
Synchrosqueezing has recently been developed as a version of the reassignment approach because of its potential to create crisp and reversible TFRs [6], [7].Because of its capacity to reconstruct, this technology continues to gain popularity because it opens the door to an unlimited number of synchrosqueezing-based applications, such asnoise removal [12], signal components extraction or separation [1], [8], [9].
DOI: http://doi.org/10.24086/cocos2022/paper.767 Seismic signals with a low-frequency content contain information about reservoir fluid mobility [10].We derive the computational implementation of reservoir fluid mobility and determinethe optimal frequency in the implementation using

Methodology
The equation determination is presented by developing the STFT method's analysis approach to better execute the strategy.
The following equations are used to represent a recorded seismic flag in the time domain [11], [12], [13]: In any case, it appears that its gather delay may be a frequency function with single time esteem.In this way, using the frequency-domain signal display to represent impulsive-like signals is appropriate: equation and concept, as well as the developed TSST method [14], [15], [11].
A recorded seismic signal in the time domain ) ( yt can easily be transformed into the frequency domain by [14], [11]: Where the signal's FT is denoted by () Y  .In addition, the original signal is reconstructed using the inverse FT concept, which is as follows: The complex conjugate is denoted by an asterisk (*).The STFT form in the frequency domain can be calculated using Parseval's theorem: Where ( )  is an instantaneous frequency estimator [9].In the STFT instance, both time-frequency reassignment operators t and  can be computed as follows [16]: Finally, a reallocated spectrogram can be calculated using the formula:

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Due to the loss of phase information, the resultant reassigned spectrogram ( ) RSTFT t  is a sharpened but non-reversible TFR.Synchrosqueezing offers moving the signal transform rather than its energy to avoid the problem of nonreversibility while preserving the phase information of the original transform.As a result, time-assigned synchrosqueezed STFT is defined as [17], [18], [11]: The marginalization of the resulting change over time leads to: As a result, Eq. ( 13) can be used to derive an exact signal reconstruction from its synchrosqueezed STFT [7], [11]:  respectively.As can be seen from figure 2, the STFTT's performance in identifying wave frequencies in accurate time sections, on the other hand, should not be overlooked.In compared to STFTT, it is also clear that proposed method has produced a higher quality map with a considerably sparser map, allowing all components to be clearly seen.The Renyi entropies for STFT and the proposed method are 5.23 and 0.238, respectively.This paper has used this method to directly detect hydrocarbons time.Accurate estimation of the in case results in increased determination of the TFR of the seismic signal along the frequency direction inside the synchrosqueezing technique.On the off event that the seismic data acquired within the time-space works, the signal should have a single-valued time-dependent signal.The typical STFT method, in addition, does not provide enough information to represent the seismic signal.The seismic flag's immediate frequency could be a time-varying, multivalued task.

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When considering the norm-1 window function ( ) f t , the STFT of the signal ( ) analysis with a synthetic seismic signal.The synthetic trace is made up of three zero-phase Ricker wavelets with dominant frequencies of 35, 30, and 25 Hz, respectively, at 0.065, 0.193, and 0.321 s, as shown in Figure.
1 (a).The STFT and the Time-Reassigned SynchrosqueezingTransform magnitude spectrum of the indicated signals are shown in Figures1b and 1c, respectively.We see sparser TFR of a seismic trace can be achieved using the Time-Reassigned Synchrosqueezing Transform.In order to show the performance of proposed transform, a real seismic signal was showed[see Figure2(a)].The time-frequencyrepresentation of the signal by theSTFT and theTime-Reassigned Synchrosqueezing Transform areshown in figure 2(b)and 2(c),

Figure 1 .
Figure 1.Sparse TFR of a seismic trace using STFT

Figure 2 (
Figure 2 (a) A real seismic signal, (b) Time-frequency representation by (b) STFT and (c) the Time-Reassigned Synchrosqueezing Transform method with window length 0.01.

Figure. 4
Figure. 4 displays the findings of both methodologies' time-frequency maps in the position of the low-frequency shadow where the hydrocarbon is found, followed by the detection of frequency slices of 10 Hz and 50 Hz.The window duration parameter is set to 0.008.The presence of lowfrequency anomalies (10 Hz) with high amplitude and its attenuation at high frequency (50 Hz), which is known as the low-frequency shadow phenomenon, indicates the presence of gas.The location of the low-frequency ellipse shadow phenomenon is shown in Figure 4. On the other hand, the high resolution of the spectral decomposition method is indicated better performance of the proposed method.
this paper, we have used the TRSST method to enhance timefrequency representation.Although the signal's instantaneous frequency is a multivalued time-dependent function, the signal's group delay is a single-valued frequency function.This spectral analysis method has a high resolution in terms of time and frequency.The results of applying this method of spectral analysis and comparing it with conventional methods show the properties and benefits of this new method of spectral analysis compared to other spectral analysis methods such as STFT.
However, the TSST is capable of efficient frequency domain performance.The overall goal of this research is to resolve this deficiency by using a frequency domain signal model.This goal is supposed to be accomplished using the Gaussian-modulated linear group delay (GLGD) Y  .The group delay (GD) is calculated by ()  deriving the relevant frequency.The TSST can be performed as a practical method by estimating the GD DOI: http://doi.org/10.24086/cocos2022/paper.767 (citehe2019time).
t is the function that was used to window the signal in order to derive the signal's Fourier Transform.It's ˆ, xtt  is a group-delay estimator and