Simultaneous Source Separation Research Articles

Simultaneous source separation and noise reduction with structure-oriented space-varying alpha-trimmed mean filter

Median filters are often used in simultaneous source data to remove sudden noise disturbances. Nonetheless, the median filter has a poor ability to process random noise, which can affect its performance in seismic data processing. This paper introduces a novel filtering method, a structure-oriented space-varying alpha-trimmed mean filter, which is an improvement of median filtering, and can deal with random noise better. The proposed filter's window length can be adaptively adjusted based on geological conditions, enabling the effective removal of spiky noise during simultaneous source acquisition and common random noise in geological exploration. This paper introduces the main differences between different types of median filtering methods and provides an overview of the principles and steps involved in our proposed approach. Our method's effectiveness is evaluated through its application to both simple synthetic examples and field data, alongside a comparative analysis against other existing approaches. The results of this research demonstrate that the approach we proposed here can efficiently make spike-like noise and random noise disappear while simultaneously maintaining vital signal characteristics.

Simultaneous source separation by shot collocation and strength variation

Simultaneous shooting offers opportunities for significant cost savings in seismic data acquisitions. The most common strategy uses random delay shots where source separation is achieved during the processing stage, thereby doubling source densities. We have determined that the creation of a collocated source survey, where shots are repeated simultaneously at multiple positions, is a viable alternative strategy, with the additional benefit that it may increase source density even further while keeping the acquisition duration unchanged. Source separation is achieved using overcomplete independent component analysis by first by applying a directional wavelet transform to separate source signals with different slowness, then estimating the mixing matrix, followed by solving an optimization problem with an energy constraint combined with a sparseness inducing prior and obtaining the required waveforms. Synthetic tests find average reconstruction quality on the order of 22.1, 15.4, and 8.4 dB if, respectively, three, four, or five shots are acquired in two mixtures. Examination of the true versus obtained zero-offset sections also demonstrates the robustness of our signal recovery strategy. The advantage of shot collocation over conventional acquisitions is that it may triple or even quadruple the source density for unchanged acquisition durations with superior reconstruction results compared with dithered acquisitions using similar blending factors.

Separation and Reconstruction of Nonuniform Simultaneous Source Data via a Robust and Sparse Radon Transform

In recent years, simultaneous source seismic data acquisition attracts much attenuation because of its higher efficiency and lower cost. However, the presence of blending noise reduces the accuracy of subsequent traditional seismic data processing steps, necessitating the separation of simultaneous source data. Conventional separation methods assume that seismic data is distributed on uniform grids, but in field cases, firing shots are always distributed on non-uniform grids. The binning strategy assigns a non-uniform sample onto its nearest uniform sample, introducing unavoidable errors and lowering the separation accuracy of simultaneous source data. As a result, irregularity influences must be taken into account during simultaneous source separation. To separate non-uniform simultaneous source data, a robust and sparse Radon transform (RSRT) is introduced because the Radon transform can deal with non-uniform grids along the space adaptively. The effectiveness of the proposed method in attenuating blending noise and reconstructing seismic data to uniform grids is demonstrated by synthetic and field data analysis.

Towed Streamer-Based Simultaneous Source Separation by Contourlet Transform

Simultaneous towed-streamer marine acquisition has the advantages of reducing the total time requirements and costs of surveys. However, the seismic records obtained are blended seismic data, so the successful deblending of such data is the key to this method. In this paper, we propose an effective deblending method with a new thresholding operator based on the shaping regularization framework in the contourlet domain. The new thresholding operator consists of an adaptive Bayesian threshold and a new thresholding function. Because of its multiresolution, locality, and directionality properties, the contourlet transform can effectively capture geometrical structures, which are the main features in natural images. To make the traditional Bayesian threshold adaptive in the contourlet domain, we propose a scale adjustment factor, a direction adjustment factor, and an attenuation factor to modify the threshold, and we also adopt local adaptive elliptic windows to estimate the standard deviations of useful signals; eventually, we obtain an adaptive Bayesian threshold. Furthermore, the new thresholding function can overcome the shortcomings of the existing soft and hard thresholding functions. Experimental results demonstrate that our method can effectively separate blended data.

Iterative Deblending of Simultaneous-Source Seismic Data via a Robust Singular Spectrum Analysis Filter

We solve the simultaneous source separation problem by adopting the projected gradient descent (PGD) method to iteratively estimate the data one would acquire via a conventional seismic acquisition. The projection operator is a windowed robust singular spectrum analysis (SSA) filter that suppresses source interferences in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f-x$ </tex-math></inline-formula> (frequency-space) domain. We reformulate the SSA filter as a robust optimization problem solved via a bifactored gradient descent (BFGD) algorithm. Robustness becomes achievable by adopting Tukey’s biweight loss function for the design of the robust SSA filter. The SSA filter requires breaking down common-receiver gathers or common offset gathers into small overlapping windows. The traditional SSA method needs the filter rank as an input parameter, which can vary from window to window. The latter has been a shortcoming for the application of classical SSA filtering to complex seismic data processing. The proposed robust SSA filter is less sensitive to rank-selection, making it appealing for deblending applications that require windowing. Additionally, the robust SSA projection provides an effective attenuation of random source interferences during the initial iterations of the PGD method. Comparing classical and robust SSA filters, we also report an acceleration of the PGD method convergence when we adopt the robust SSA filter. Finally, we provide synthetic and real data examples, and discuss heuristic strategies for parameter selection.

Regularization by denoising for simultaneous source separation

Denoisers can help solve inverse problems via a recently proposed framework known as regularization by denoising (RED). The RED approach defines the regularization term of the inverse problem via explicit denoising engines. Simultaneous source separation techniques, themselves being a combination of inversion and denoising methods, provide a formidable field to explore RED. We investigate the applicability of RED to simultaneous-source data processing and introduce a deblending algorithm called REDeblending (RDB). The formulation permits developing deblending algorithms in which the user can select any denoising engine that satisfies RED conditions. Two popular denoisers are tested, but the method is not limited to them: frequency-wavenumber thresholding and singular spectrum analysis. We offer synthetically blended data examples to showcase the performance of RDB.

Separation of simultaneous sources acquired with a high blending factor via coherence pass robust Radon operators

We have developed an iterative method for simultaneous source separation (deblending) suitable for data acquired with a high blending factor. Our technique adopts the robust sparse Radon transform to define a coherence pass operator that is used in conjunction with the steepest-descent method to guarantee solutions that honor simultaneous source records. We find that an important improvement in convergence is attainable when the coherence pass projection is derived from a robust sparse Radon transform. This is a consequence of having an iterative deblending algorithm that applies intense denoising to erratic blending noise in its initial iterations. The coherence pass robust Radon operator acts as a data projection operator that preserves coherent signals and annihilates incoherent blending noise right from the start of the iterative process. We compare the algorithm with its nonrobust version and find that a coherence pass nonrobust Radon operator will only achieve high-quality results for acquisitions with a moderate blending factor.

Acquisition and separation of coherent simultaneous sources: Theory and an application to data acquired in the Sultanate of Oman

In an effort to reduce acquisition costs or increase (source) sampling density, we have developed a coherent simultaneous-source scheme. Different from most existing simultaneous acquisition, our scheme enforces the received signal to remain coherent in all sorting domains, thus even in the common-receiver domain. A major benefit of the enforced signal coherency is that it enables multidomain preprocessing prior to source separation. At the same time, it poses a challenge to the source separation itself. Based on the observation that the proposed coherent simultaneous-source scheme is equivalent to the traditional source array, we have developed a novel source separation method that comprises (1) interpolating the observed signal in the space domain and (2) removing the source-array effect. In practice, the source-array effect cannot perfectly be removed in the presence of notches. This fact can, however, be deliberately leveraged for noise attenuation.

Iterative deblending of simultaneous-source data using smoothed singular spectrum analysis

Simultaneous-source acquisition helps the field crews obtain a faster seismic data recording by allowing multiple sources to be fired simultaneously. However, the simultaneous source ignition causes strong interferences in the recorded data, which greatly affects the subsequent seismic data processing and imaging workflows. An effective separation of simultaneous sources is considered as the key in successfully utilizing the simultaneous-source acquisition technology. In this paper, we propose a novel smoothed singular spectrum analysis (SSA) approach to remove blending noise in an iterative inversion manner. Compared with the traditional SSA approach, the smoothed SSA approach applies a Gaussian smoothing operator onto the Hankel matrix in the frequency domain, and can attenuate more blending noise than the traditional SSA method. We use both synthetic and field data examples to demonstrate the successful performance of the proposed method.

Source signature encoding of a vertical source array to separate the emitted direct wave from its ghost

Marine air-gun sources can be sequence-encoded by firing their individual elements independently over a short period of time. Using near-orthogonal firing sequences, whose crosscorrelation is minimal, as encoding sequences for multiple sets of air-gun sources, enables us to exploit their orthogonality as a separation feature. We find that, by distributing air guns over depths from 5 to 30 m, firing sequences can be designed whose direct, down-going wavefield is close to orthogonal to its source-ghost wavefield. The fundamentally new aspect of this approach is that the source-ghost signal is no longer just a time-delayed, opposite-polarity version of the down-going wavefield, but due to the different air-gun depths results in a different source sequence. This enables the consideration of the ghost wavefield as a separate source. We generate a set of such firing sequences by minimizing the crosscorrelation of these wavefields and optimizing their respective autocorrelations to achieve sharp peaks. The obtained, optimized firing sequences are then used for marine seismic source encoding. By adapting a multifrequency algorithm originally developed for simultaneous source separation, we determine that the ghost-source wavefield can be separated as a separate source from the direct, down-going wavefield.

Flawless diamond separation in simultaneous source acquisition by seismic apparition

Abstract In this paper we prove that the recently introduced method of signal apparition optimally separates signals from interfering sources recorded during simultaneous source seismic data acquisition. By utilizing a periodic sequence of source signatures along one source line, that wavefield becomes separately partially visible in the spectral domain where it can be isolated from interfering signals, processed, and subtracted from the original recordings, thereby separating the wavefields from each other. Whereas other methods for simultaneous source separation can recover data in a triangle-shaped region in the spectral domain, signal apparition allows for the exact separation of data in a diamond-shaped region that is twice as large thereby enabling superior reconstruction of separated wavefields throughout the entire data bandwidth.

An Improved Method for Blind Source Separation

In practical applications especially in biomedical signal processing, a large number of sensors is available but only one or a very few are desired. The simultaneous blind source separation (BSS) technique always introduces large computational load. A contrast function is formulated associated with normalized kurtosis. Furthermore, an improved learning algorithm is derived based on the standard gradient descent rule. In contrast to simultaneous BSS, the proposed method can provide more flexibility and has some potential advantages in terms of computational load. Computer simulations illustrate its performance.

Optimizing near-orthogonal air-gun firing sequences for marine simultaneous source separation

Air-gun arrays can be encoded by firing individual air guns sequentially over a range of time. This marine source encoding is shown to be particularly beneficial for simultaneous source separation, which can exploit the orthogonality of the encoding sequences to improve the source separation. We have developed a method to design encoding sequences for air-gun arrays having minimized crosscorrelation and optimized autocorrelation properties. By varying the firing times of the individual air-gun subelements, different encoding sequences are constructed using a simulated annealing approach so that their orthogonality properties are optimized. These optimized sequences are then used for time-dithered simultaneous source encoding. Realistic synthetic data examples show a significant improvement of simultaneous source separation. We have also determined the robustness of the method for take-off angle variations and possible errors in sequence estimation.

Exploiting the control of phase in marine vibrators

Marine seismic vibrators are considered to be more environmentally friendly than air guns and this has prompted a resurgence of interest in their use. However, these devices have novel features that are potentially of great benefit to seismic imaging and that have not yet been exploited - in particular, we can control the phase. With marine vibrators, the emitted waveform can be chosen freely, provided that it lies within the envelope of what the device can emit. Typically, the waveform is a swept-frequency sinusoid. In this paper, we show how the sweep phase can be used to suppress the residual shot noise (RSN) and to separate simultaneous sources of high multiplicity. This work is also described by Laws and Halliday (2013) and is closely related to that of Laws (2012). The control of phase is a benefit of marine vibrators that can be exploited to great effect. First, we look at the RSN situation. The conventional wisdom is that roughly a 10s shot-time interval is required in marine seismic data acquisition so that the RSN is acceptably small relative to the signal. Because both signal and RSN originate from the seismic source, the ratio of signal/RSN is not improved by using a larger source (pace Landro, 2008). We show a simple case of RSN attenuation using alternating sine and cosine sweeps. That is to say, the sequence of source phases goes, for successive shots, [0° 90° 0° 90° 0° 90° 0° 90°... and so on]. We show schematically how this ‘phase sequencing’ leads to a dramatic attenuation of the RSN. It does so by moving the RSN into parts of the frequency-wavenumber spectrum where there is no signal. We then use frequency-wavenumber filtering to remove the RSN. This can be done with simple filtering up to the limit imposed by spatial aliasing and beyond that limit by using wavefield reconstruction methods, such as generalized matching pursuit (Ozbek et al., 2010; Vassallo et al., 2010). Reconstruction methods decompose the seismic wavefield into a set of basis functions that allow the signal and RSN to be identified and separated. Then, we look at the simultaneous source situation. The RSN removal problem can be considered as a special case of the more general simultaneous source separation problem. As an example, in the case of two simultaneous sources, one source can be swept with consistent phase, while the other source is swept with alternating phase, i.e., the sequence of relative phases is [0° 180° 0° 180° 0° 180° 0° 180°... and so on]. The simultaneous source separation is demonstrated using the same type of reconstruction method as described above for the RSN. See also Moore et al. (2008) and Ji et al. (2012). The use of phase sequencing opens up possibilities for simultaneous source separation using large numbers of sources. By having complete control over the phases of all the sources it is possible, in certain domains, to make simultaneous source data look similar to aliased data from a single source. This opens the door to using many established wavefield interpolation and dealiasing-techniques to perform high-multiplicity simultaneous source separation.

High-productivity seabed time-lapse seismic data acquisition using simultaneous sources enabled by seismic apparition: A synthetic-data study

Seismic apparition is a recent signal-processing advance that trades signal interference and aliasing between different spatial (and temporal) dimensions. In particular, an important application of seismic apparition is for simultaneous-source separation to better exploit the available data space in the frequency-wavenumber (f-k) domain with energy from different simultaneous sources. The introduction of periodic modulation functions in seismic acquisition produces an effect where parts of the energy of one or more sources are partially shifted to different empty parts within the f-k domain. This so-called apparated energy then can be used to perfectly predict (at low frequencies) the remaining part of the signal in the regions of the f-k domain where the wavefields from the different sources overlap and to deterministically separate the sources at predetermined (repeated) positions — a prerequisite for 4D seismic processing. At higher frequencies, the apparition separation is dealiased using directional information, taking full advantage of the perfect separation at lower frequencies to achieve the required low-error separation. To apparate seismic energy to different portions within the f-k domain, we introduce a periodic modulation function, consisting for instance of a small time delay/advance or an amplitude scaling to every second shot. Our simultaneous-source approach is thus opposite to established industry practices of maximizing randomness using dithered sources. A deterministic simultaneous-source-separation approach in which shot points and simultaneous-source patterns are repeated accurately is a major advantage over industry-standard stochastic simultaneous-source-acquisition approaches, particularly for 4D applications. We demonstrate the suitability of the seismic-apparition simultaneous-source technique to time-lapse seismic, having a permanent-reservoir-monitoring context in mind, by investigating two operational scenarios of single-vessel acquisition where two sources are excited simultaneously. Single-vessel simultaneous-source acquisition represents the most challenging case for shot separation in general and for time-lapse seismic applications in particular. The quantitative and qualitative wavefield decomposition results analyzed pre- and poststack are highly encouraging on synthetic data and warrant further testing of seismic-apparition technology in a real 4D seismic test case.

Seismic Simultaneous Source Separation via Patchwise Sparse Representation

The concept of simultaneous source has recently become of interest in seismic exploration, due to its efficient or economic acquisition or both. The blended data overlapped between shot records are acquired in simultaneous source acquisition. Separating the blended data and recovering the single-shot seismic signals (the recovery) are of great importance in the scenario of current workflows, which can be called seismic simultaneous source separation. In the context of general random time-dithering firing, we propose an alternative method to separate the blended data by combining patchwise dictionary learning with sparse inversion, in which the dictionary is directly learned from the measured blended data. Apart from the sparse coding used for the coefficients, an additional regularization term on the dictionary is particularly designed to remove the severe interference noise. The efficient and flexible alternating direction method of multipliers (ADMM) is used to update the dictionary in the used alternating optimization scheme. The results obtained from the synthetic and real examples reasonably suggest that the separated seismic signals by using dictionary learning are more accurate and robust compared with that using the fixed transform basis, such as the local discrete cosine transform. The learned dictionary tailors for the recovery and is similar to the local seismic waveform, which improves the sparsity of the recovery substantially and is highly advantageous for producing the promised results.

Fast simultaneous seismic source separation using Stolt migration and demigration operators

Stolt migration is a Fourier-domain imaging operator that assumes a constant-velocity media. We have developed a multivelocity version of the Stolt migration and demigration operators to derive a transform that can decompose seismic data into a sparse collection of coefficients in the image space. This Stolt-based transform is similar to the apex-shifted hyperbolic Radon transform (ASHRT). However, the Stolt-based transform is considerably faster than the classical ASHRT because it uses two fast operators (forward and inverse fast Fourier transforms) to estimate the data coefficients in the image space. We used this Stolt-based transform as a tool for simultaneous seismic source separation by removing erratic interference noise in common receiver gathers. Estimating the coefficients of interference-free seismic data using the Stolt-based transform was posed as an inverse problem. The solution of this inverse problem was found by minimizing a cost function that included a sparsity-promoting regularization term. In addition, the cost function incorporated a robust misfit function that was not sensitive to erratic interferences. Our tests on synthetic and field data examples determined that this new transform can efficiently remove interference noise and achieve fast simultaneous seismic source separation.

Separation of simultaneous sources using a structural-oriented median filter in the flattened dimension

Simultaneous-source shooting can help tremendously shorten the acquisition period and improve the quality of seismic data for better subsalt seismic imaging, but at the expense of introducing strong interference (blending noise) to the acquired seismic data. We propose to use a structural-oriented median filter to attenuate the blending noise along the structural direction of seismic profiles. The principle of the proposed approach is to first flatten the seismic record in local spatial windows and then to apply a traditional median filter (MF) to the third flattened dimension. The key component of the proposed approach is the estimation of the local slope, which can be calculated by first scanning the NMO velocity and then transferring the velocity to the local slope. Both synthetic and field data examples show that the proposed approach can successfully separate the simultaneous-source data into individual sources. We provide an open-source toy example to better demonstratethe proposed methodology.

The benefit of encoded source sequences for simultaneous source separation

We have developed a method for simultaneous source separation using time dithering and encoded source sequences. The source sequences are designed so that they are close to orthogonal to each other, having minimized crosscorrelation and optimal autocorrelation properties. We found that this additional encoding of time-dithered sources could be exploited with a multifrequency separation method. The separation method relies on a coherency-based approach and is solved by a sparse Radon inversion. Realistic synthetic data examples confirmed the importance of using the multifrequency method to take advantage of the sequence orthogonality and to deal with spatially aliased data. Our results demonstrate that source sequence encoding can significantly improve simultaneous source separation compared with using time dithering only.

A cocktail party effect in the median plane?

Recent research has been conducted on the effects of spatialized audio on a listener’s ability to detect and identify a target speech signal when presented among nontarget speech signals in the horizontal plane [W. T. Nelson et al., Proceedings of the 1998 IMAGE Conference (1998), pp. 159–166]. However, the existence of a ‘‘cocktail party effect’’ in the median plane has not been addressed. The purpose of the present investigation was to determine whether or not the spatial separation of multiple simultaneous speech sources in the median plane leads to improved detection and intelligibility. Independent variables include the number and angular separation of the speech signals, the sex of the target talker, and the presence or absence of head motion cues. All speech signals—phrases from a modified Coordinate Response Measure [T. J. Moore, AGARD Conference Proceedings 311: Aural Communication in Aviation (1981), pp. 2.1–2.6]—were digitally filtered via nonindividualized HRTFs and presented over headphones. Results will be compared with those obtained in the horizontal plane. Inplications for the design of auditory displays will be discussed.