محمد رداد

Denoising is an important step in seismic data processing that can improve the results of other processing steps and, consequently, the interpretation of seismic sections. Both land and marine seismic data contain coherent and incoherent noise. Swell noise is one of the noises present in marine seismic data. It has a high amplitude and low frequency band and is observed as vertical bands in marine seismic data. Developing methods that can attenuate swell noise more while causing the least damage to the signal in marine seismic data seems necessary. There are various methods for attenuating swell noise, each with its advantages and limitations. The approach of most denoising methods is to maximize the separation of noise from the signal. Variational mode decomposition (VMD) has shown promising results in seismic denoising by separating different modes of signal and noise. The goal is to obtain a set of intrinsic mode functions (IMFs) and their corresponding center frequencies. The main approach of VMD is to decompose the input signal into a number of sub-signals (modes), which also have sparsity properties while recovering the input signal. Here, the sparsity of each mode is chosen as the bandwidth of that mode. In other words, it is assumed that each mode is more concentrated around the center frequency, which is determined in the decomposition. Another important issue in noise attenuation is that the denoising method should be able to perform the denoising process automatically with minimal user intervention. The proposed denoising algorithm in this paper consists of four steps: decomposition, identification, filtering, and reconstruction. In the first step, the seismic signal is decomposed into its constituent modes using the VMD method. In the second step, the modes contaminated with noise is identified according to the autocorrelation function of the modes, where the higher values of standard deviation of autocorrelation above a predefined measure present noisy modes. In the third step, the noise is removed through a filtering process based on a hard thresholding procedure. In the final step, the constituent modes, including the clean untouched modes, the denoised modes, and the residue, are summed together and the signal is denoised. The proposed algorithm's efficacy is demonstrated through its application to both synthetic and real seismic data. Notably, the method demonstrates superior performance compared to conventional high-pass filtering and time-frquency denoising (TFDN) method, effectively attenuating swell noise while preserving valuable low-frequency seismic information.

Identification of low-frequency shadows is very important in the sense that they are related to gas reservoirs. These low-frequency shadows, produced by gas attenuation on seismic waves, cause the low frequencies under the gas reservoirs to have stronger amplitudes compared to the amplitudes of the high frequencies. Therefore, if proper time accuracy is considered in the identification of this indicator, the gas reservoir, and consequently, its position will be identified with considerable accuracy. One of the methods of identifying low-frequency shadows is timefrequency transforms. Therefore, those time-frequency transforms that have good time and frequency resolution, can be of great help in identifying low-frequency shadows. In this research, a method called time-reassigned multisynchrosqueezing transform (TMSST) is used that acts better than common time-frequency transforms such as shorttime Fourier transform (STFT), reassignment method (RM), synchrosqueezing transform (SST) and multisynchrosqueezing transform (MSST) in terms of time and frequency resolution. Therefore, by applying this transform on a synthetic dataset and a real dataset, its performance has been demonstrated. As a seismic application, singlefrequency sections obtained from a hydrocarbon field were prepared in MATLAB environment and low-frequency shadow anomalies were detected using this time-frequency method with high resolution. In addition, in this study, the Rennie parameter, which is directly related to the sparsity, has been used to evaluate the energy concentration. The number obtained for the Rennie parameter using the method proposed in this paper is another reason for proving the remarkable performance of this method in obtaining time-frequency representation with high time and high frequency resolution at the same time.

Salt dome is a diapir shaped structure of salt that intrudes vertically through sediment layers and surrounding strata due to its low density. Salt area identification, determining its boundaries and its 3D modeling in seismic data is a crucial issue in the literature of the seismic data interpretation. Due to its high impermeability characteristic, it can form stratigraphic oil traps by sealing the hydrocarbon reservoirs and also could be used as underground storage for natural gas and disposal sites for hazardous waste such as isolation nuclear waste and creation of the compressed air reservoir. The steeply dipping complex-shaped structures related to the salt movement and significant difference in seismic wave propagation velocity inside the salt dome with the enclosed media, imposes significant challenges for seismic data processing and interpretation. Identification and delineation of salt body is a key step in seismic data processing and interpretation, which can help geophysicist to overcome aforementioned problems. In reflection seismic methods, salt boundaries are more often characterized by change of seismic character of the signal also called texture. There are several methods available for texture analysis in image processing that can be divided into seven classes which are statistical analysis, structural methods, transform based approaches, model-based methods, graph-based techniques, learning based strategies and entropy-based methods. Textural attributes characterize the spatial arrangement of neighboring amplitudes. Extraction of seismic texture attributes can be performed using spectral information of image such as Gabor filters and local 2D Fourier spectra. Dip, similarity and coherence are the common structural attributes which are used generally for textural analysis in seismic data. The most common rational approach to describe the texture in seismic image is to measure the statistical properties of the image. Gray Level Co-occurrence Matrix, chaos and variance are three conventional statistical seismic texture attributes used for this purpose. Due to the textural contrast of the salt dome with the surrounding layers and sediments, edge detection tools can also be used to determine the boundaries of textural changes and delineate the salt area. In this study, we used a new textural seismic attribute known as the gradient of texture to characterize the change of seismic character between the salt body and its surrounding geology. It calculates the texture gradient in two adjacent windows around a sample in different directions. It is supposed that different area in seismic image with different textural pattern will exhibit diverse gradient of texture. Thus, it will be appropriate for image segmentation for specific interpretation investigation. The gradient of texture attribute will differentiate desired area from the rest of the image through supervised classification and growth strategy in extending the selected classes. Efficiency of the introduced method for salt dome delineation and modeling in seismic data was investigated here by applying on a synthetic model and 3D seismic data from the Persian Gulf. Comparison between obtained results of the proposed method and conventional attributes revealed superiority of the 3D texture gradient in textural segmentation and salt dome modeling from seismic data.

Due to high cost of data gathering and in order to increase the quality of the data, the most important challenge in seismic data de-noising is maximum attenuation of seismic noise with minimum signal leakage to achieve maximum signal-to-noise ratio. Power line or fixed-frequency harmonic noise in the frequency range of 50 to 60 Hz is one of the factors that contributes to decrease seismic signal quality, and also, reduces signal-to-noise ratio. This occurs through a frequency interference of a harmonic in the natural frequency range of the power lines (50 to 60 Hz) with the seismic signal frequencies.

In this paper, the extended Euler deconvolution method is studied for interpreting magnetic and gravity anomalies. This method, overcoming some limitations of the conventional Euler deconvolution method, is utilized for simultaneous and automatic estimate of the depth, structural index and horizontal location of potential field sources. The main limitation of the conventional Euler deconvolution method is non-linear dependency of structural index and background field; hence a simultaneous estimation of these parameter is not possible. For overcoming this problem, a value of structural index is presumed and the obtained results are evaluated according to various criteria. A wrong structural index affects the final results. In the extended Euler deconvolution, the Euler differential equation is solved for Hilbert transform of the field and its derivatives. Since the Hilbert transform of a constant value is zero, the linear dependency of structural index and background filed will be removed, and therefore the automatic calculation of structural index will be possible and the presumption of structural index is not required anymore. Moreover, since Hilbert transform has two components of x and y, the number of equations to be solved at each point is increased, and consequently the solutions are more reliable. In this paper, firstly, a background theory of the extended Euler deconvolution is discussed in detail. Then the method is applied to a magnetic anomaly produced over eighteen magnetic sphere (dipole) having different magnetic properties. Finally, the method is used for interpreting a Bouguer gravity anomaly of Noranda in Quebec province of Canada and also a magnetic anomaly of an area located near Anar city of Kerman province of Iran.

Seismic facies analysis plays an important role in the studies of hydrocarbon reservoirs. Because in the beginning of exploration operations of hydrocarbon reservoirs, there is no or low number of wells in the area, the lateral changes and seismic facies analysis in a special horizon can be studied using pattern recognition algorithms and seismic attributes. Supervised and unsupervised methods have an important role in increasing the accuracy and the speed and decreasing the costs of data classification which a good analysis of seismic facies can be provided. The base of unsupervised methods, which is also the subject of this study, is the classification of all data in attribute space, and the result does not depend on prior information. In this method, the classification and interpretation of results are carried out by matching analysis between seismic facies, without using well data. There are several methods of unsupervised clustering. In this paper, the Gaussian Mixture Models (GMM) method has been employed which it uses some gaussian distributions and assigns membership probability to analysis samples in order to classify them. By using this method, seismic facies analysis is processed on a 3D seismic data set acquired in a hydrocarbon field in south of Iran. The analysis is carried out on two different horizons where the results show an acceptable facies classification by the GMM method, and the results are in a good agreement with reservoir quality analysis of electrofacies in some wells.

Assessing a time-frequency representation of signal with an acceptable timefrequency resolution, and for specific purposes in different applied studies, has always been a challenge for signal processing researchers. In case of seismic data, using a time-frequency representation with high resolution will yield a higher precision in processing and interpretational applications of timefrequency analysis of data. In the most of time-frequency analysis methods, a form of smoothing is used for generating time-frequency map, which it causes energy dissipation in time-frequency plane and decreasing the resolution. Reassignment is an efficient technique for compensating this issue and increasing the resolution. It can provide a high time-frequency resolution through moving and concentrating the energy distribution in the time-frequency plane to true location. Reassignment has been applied to various time-frequency analysis methods and its performance has been presented in different researches. In this paper, the reassigned Stransform as a new development on S-transform to provide higher time and frequency resolution is utilized to extract some seismic attributes. The performance of the method in providing an acceptable time-frequency resolution is shown by testing on synthetic non-stationary chirp and seismic signals. As a seismic application, the reassigned S-transform is utilized in studying low frequency shadows through time-frequency analysis of seismic data set acquired on a hydrocarbon reservoir. For this purpose, some time-frequency attributes including single-frequency, instantaneous amplitude, instantaneous dominant frequency and sweetness factor are extracted by this method. The results show that the reassigned S-transform can provide much higher energy concentration rather than standard S-transform, and the events and anomalies can be interpreted with more precision due to their better time and space resolution in attribute sections.

The time-frequency analysis methods are among the most common signal and image processing techniques in different applied fields of electric engineering, mechanical engineering, geoscience, etc. Time-frequency methods are employed in seismic data processing and interpretation applications for denoising, attenuation estimation, deconvolution, hydrocarbon detection, channels and faults visualization and so on.
There are several time-frequency analysis methods. One of the main reasons of developing new time-frequency methods is to reach higher time-frequency resolution. The reassignment is one of the successful approaches in this field. The mission of reassignment method (RM) is to move the energy distribution of the time-frequency plane to true location. Through this way, a precise distribution of instantaneous frequency has been provided for any time sample. Reassigning is also carried out in time direction. The RM has been applied in several time-frequency methods such as wavelet transform, Wigner-Ville distribution, Gabor transform and S-transform. In this paper, the reassigned Stransform has been studied in seismic data time-frequency analysis. The method has been utilized for detection of low frequency shadows in a seismic dataset to locate probable gas reservoir.

In this paper, the performance of reassigned S-transform has been studied by its application on synthetic chirp signal and seismic trace. The results show that the method is capable of providing a well-concentrated time-frequency maps. As an application in real seismic data, the method has been utilized for studying the low frequency shadows related to probable gas bearing zones. This approach extracts some attributes including single frequency, instantaneous amplitude, instantaneous dominant frequency and sweetness factor, through time-frequency analysis of the data. The results show that the reassigned S-transform can provide higher time and space resolution, and thus, the events and anomalies can be interpreted more precise compared to standard S-transform results.

Seismic attribute is a quantitative measure of an interested seismic characteristic. There are several seismic attributes. In recent years, time-frequency (TF) attributes have been developed which to reach them, TF analyzing of seismic data is required. A high resolution TF representation (TFR) can yield more accurate TF attributes. There are several TFR methods including short-time Fourier transform, wavelet transforms, S-transform, Wigner-Ville distribution, Hilbert-Huang transform and etc. In this paper, the S-transform is considered and an algorithm is proposed to improve its resolution. In the Fourier-based TFR methods, the width of the utilized window is the main factor affecting the resolution. The standard S-transform (SST) employs a Gaussian window which its standard deviation, controller the window width, changes inversely with frequency (Stockwell et al., 1996). It was an idea to use a frequency dependent window for TF decomposition. However, the TF resolution of SST is far from ideal; it demonstrates weak temporal resolution at low frequencies and weak spectral resolution at high frequency components. Later on, the generalized S-transform was proposed using an arbitrary window function whose shape is controlled by several free parameters (McFadden et a., 1999; Pinnegar and Mansinha, 2003). Another approach to improve the resolution of a TFR is based on energy concentration concept (Gholami, 2013; Djurovic et al., 2008). According this approach, in this paper, an algorithm is proposed to find the optimum windows for S-transform to get a TFR with maximum energy concentration. To reach this aim, an optimization problem is defined where an energy concentration measure (ECM) is employed to condition the windows so as the TFR would have the maximum energy concentration. Here, we utilize a Gaussian as the window function. Then different windows are constructed by a range of different values of standard deviations in a non-parametric form. Different TFRs are constructed by different windows. The optimum TFR is one with maximum energy concentration. The optimization is performed for each frequency component, individually, and hence, there would be an optimum window width for each frequency component. There are several ECMs which they are used in different applications (Hurley and Rickard, 2009). In this paper, we employ Modified Shannon Entropy as the ECM. As one knows, SST algorithm needs to be implemented in frequency domain (Stockwell et al., 1996). It is due to the dependency of the standard deviation of Gaussian window on the frequency. However, the proposed method of our paper can also be implemented in time domain where the optimum windows would be found, adaptively, for each time sample of the signal. We apply the proposed method to a synthetic signal to compare its performance with some other TF analysis methods in providing a well-concentrated TF map. The comparison of the results shows the superiority of the proposed method rather than STFT and SST. We also perform a quantitative experiment to evaluate the performance of the TFRs. The results confirm the best performance by the proposed method compared with STFT and SST. Then the proposed method is employed to detect gas bearing zones and low-frequency shadows on a seismic data set related to a gas reservoir of Iran. For this aim, some TF seismic attributes are extracted. The attributes include instantaneous amplitude, dominant instantaneous frequency, sweetness factor, single-frequency section and cumulative relative amplitude percentile (C80). The attributes are also extracted by SST to compare with those of the proposed method. The results show that the attributes obtained by the proposed method have more resolution; so that gas bearing zones and low-frequency shadows are better localized on the attribute sections obtained by the proposed method.

Most geologic changes have a seismic response but sometimes this is expressed only in certain spectral ranges hidden within the broadband data. Spectral decomposition is one of the methods which can be utilized to help interpreting such cases. There are several time-frequency methods including: short-time Fourier transform (STFT), continuous wavelet transform (CWT), Wigner-Ville distribution (WVD), S-transform, and matching pursuit decomposition (MPD). In this paper, we use the MPD method. This method is newer than the other time-frequency methods used in exploration seismology. Mallat and Zhang (1993) have improved time and frequency resolution simultaneously by using MPD method. In this method, a signal is decomposed into constructive wavelets. Time and frequency properties of wavelets are used locally for spectral decomposition. Pursuits are the algorithms which search the best time-frequency matching between the signal and a linear combination of selected wavelets from wavelet dictionary. Matching pursuit which is an iterative procedure optimizes signal estimation by each new wavelet chosen from a dictionary. These wavelets combined linearly to obtain the best match with the signal. A signal should expand to waveforms which their time-frequency properties could be matched to local structures. Such waveforms are called time-frequency atoms. There are many approaches to match wavelets of dictionary to a seismic signal and to obtain time-frequency spectrum in matching pursuit decomposition. The base of all approaches is the Mallat and Zhang’s algorithm. However, computing time of the original algorithm is very high due to many iterations and that is why particular conditions have been applied in different researches to limit the matching pursuit algorithm for obtaining the lower performing time. In this work, particular conditions are rather similar to Wang’s (2007) method. On seismic data, layer thickness is described on the basis of the seismic travel time. When a layer with different properties has a thickness by one-fourth wavelength, top and base reflections will interfere constructively. For thin layers less than tuning thickness, combined seismic amplitude decreases with thickness (when reflection coefficients of the top and of the base are opposite). Generally, spectral decomposition has many applications in interpretation of seismic sections and so there will be extra needs to study and develop them. Thin layers and many stratigraphic hydrocarbon reservoirs are beneath the threshold of the vertical seismic resolution (tuning thickness) and because of their low thicknesses, they are not resolvable. For this reason, mapping the small-scale geological structures is one of the important interpretational cases. When the thickness of a thin layer decreases pick frequency slightly increases. In this work, this issue has been used to detect thin layers by time-frequency spectrum and by single-frequency sections obtained from MPD. In this paper, we investigated the performance of the matching pursuit decomposition for time-frequency analysis of seismic sections to delineate and detect thin layers on synthetic data (including simple thin layer model and also wedge model) and real data. It is observed that the interpretation of thin layers is simpler by single-frequency sections. It is shown that for a simple thin layer if considerable frequency in single-frequency sections increases, ability in resolving layer interfaces would be increased. In the wedge model, as the frequency increases resolution threshold of layer interfaces moves to a lower thickness and therefore it would be possible to detect lower thickness layers. The tuning thickness has been decreased from 19 meters in original seismic section to 12 meters in 80 Hz frequency section. In the real data, it is shown that when a thin layer is not resolvable in a seismic section it might be detected using the MPD method. In this case, by providing 20, 40, 60, 80 and 100 Hz single-frequency sections when high frequency sections are studied, interfaces of thin layer are appeared gradually. It is concluded that time-frequency sections are useful instruments to detect and delineate thin layers.