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

Seismic data reconstruction plays an important role in the whole seismic data processing and imaging workflow, especially for those data that are acquired from severe field environment and are missing a large portion of the reflection signals. The rank-reduction method is considered to be a very effective method for interpolating data that are of small curvature, e.g. the post-stack data. However, when the data are more complicated, the rank-reduction method may fail to achieve acceptable performance. A useful strategy is to use local windows to process the data so that the data in each local window satisfy the plane-wave assumption of the rank-reduction method. However, the rank in each window requires a careful selection. Traditional methods select a global rank for all windows. We have proposed an automatic algorithm to select the rank in each processing window. The energy ratio between two consecutive singular values is chosen as the criterion to define the optimal rank. We apply this strategy to seismic data interpolation and use both synthetic and field data examples to demonstrate its potential in practical applications.

High-resolution seismic imaging requires noise attenuation to achieve signal-to-noise ratio (S/N) improvements without compromising data bandwidth. Amplitude versus offset analysis requires good amplitude fidelity in premigration processes. Any nonreflected wavefield energy in the data will degrade the seismic image quality. Despite significant progress over the years, preserving low-frequency signals without compromising the S/N and avoiding the smearing of aliased signal are still a challenge for conventional methods. This problem is compounded when additional interference noise is added with simultaneous source acquisition. Because noise characteristics vary from shot to shot and receiver to receiver, we need a method that is robust and effective. In addition, we also want the method to be efficient and easy to use from a practical perspective. We have recently developed an approach using a wavelet transform to deterministically separate the primary signal from the noise, including simultaneous source interference. The goals are (1) improving the S/N without compromising bandwidth, (2) preserving the low-frequency and near-offset primaries without compromising the S/N, and (3) preserving the local primary wavefield while attenuating noise. For distance-separated simultaneous source acquisition, the goal is preserving long-offset primaries while removing interference. This wavelet denoising flow consists of a linear transformation and filtering using the complex wavelet transform (CWT). For reflection signals, normal moveout (NMO) is used. NMO transforms the low-velocity surface waves and the interference noise to where it is easily identified and rejected with a dip filter in the multidimensional CWT domain. Land field data examples have demonstrated significantly improved S/Ns and low-frequency signal preservation in migrated images after wavelet denoising. Since the numerical implementation of the CWT is as fast as a fast Fourier transform, this flow is able to suppress noise and interference simultaneously on the 3D land data much faster than the other inversion methods.

In this paper, we propose an iterative method combining the rank-reduction and thresholding constraints, to separate the simultaneous source data. In the common receiver domain, the incoherent interference generated by simultaneous source acquisition increases the rank of the Hankel matrix. Thus, rank-reduction can effectively suppress the incoherent interference. When the rank is small, the incoherent interference can get well attenuated, but it will introduce unexpected artifacts. We use the threshold function further to attenuate the unexpected artifacts. In the next iteration, we enlarge the rank and reduce the threshold value. More accurate deblended results are then recovered. The proposed algorithm is tested via two synthetic and one field data examples.

Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually misses along various spatial axes and always mix with random noise. In order to obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. Nonsubsampled contourlet transform is an effective transform to obtain multi-scale and multi-direction sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the nonsubsampled contourlet transform framework. First, we use nonsubsampled contourlet transform to convert the seismic missing data with random noise to sparse domain. Then, we apply two-step iterative log thresholding algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse nonsubsampled contourlet transform to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

This paper proposes a heuristic singular spectrum analysis (SSA) approach to extract signals from suspended sediment concentration (SSC) time series contaminated by multiplicative noise, in which multiplicative noise is converted to approximate additive noise by multiplying with the signal estimate of the time series. Therefore both the signal and noise components need to be recursively estimated. Since the converted additive noise is heterogeneous, a weight factor is introduced according to the variance of additive noise. The proposed heuristic SSA approach is employed to process the SSC series in San Francisco Bay compared to the traditional SSA and homomorphic log-transformation SSA approach. By using our heuristic SSA approach, the first 10 principal components derived can capture 96.49% of the total variance with the fitting error of 6.17 mg/L, better than those derived by traditional SSA approach and homomorphic log-transformation SSA approach that catch 88.97% and 87.35% of the total variance with the fitting errors of 14.47 mg/L and 15.03 mg/L, respectively. Therefore, our heuristic SSA approach can extract more signals than traditional SSA and homomorphic log-transformation SSA approach. Furthermore, the results from the simulation cases show that all the mean root mean squared errors and mean absolute errors derived by our heuristic SSA are smaller than the traditional and homomorphic log-transformation SSA, which indicate that the extracted signals by heuristic SSA approach are much closer to the real signals than those by the other two approaches. Therefore it can be conclude that our heuristic SSA approach performs better in extracting signals from SSC time series contaminated with multiplicative noise.

Multiscale frequency-domain seismic inversion for fracture weakness

Summary Wavefield separation is an important processing step to remove the interfering receiver ghost in seismic data. For ocean-bottom surveys, where typically both the pressure P (hydrophone) and particle velocity Vz (geophone) is measured, PZ-summation is a commonly used wavefield separation method. Although this method delivers excellent results, the required wavefield calibration makes it user-intensive to apply and QC. Supervised machine learning (ML) can offer a robust and user-friendly alternative to the industry-standard PZ-summation method. The convolutional neural network used in the proposed approach automatically calibrates the multi-component recordings and performs the wavefield separation without any user interaction required. A comparison study is conducted where the ML method is compared to the industry-standard PZ-summation method for a controlled shallow water data experiment and an OBN field data example with water depths ranging between 25m and 40m. After an easy to execute network training phase, the method delivers excellent wavefield separation results for both the complex synthetic and the shallow water field data example.

ABSTRACTSeismic blended source acquisition, also referred to as simultaneous source acquisition, is a cost‐effective technology that achieves a significant reduction in acquisition cycle time and increases seismic crew field productivity. The dispersed source array is a blended acquisition field technique that simultaneously employs sources emitting different types of sweeps (i.e. multi‐sweep), in terms of frequency bandwidth and length, which ultimately will result in a full broadband seismic data. In this paper, deblending of 3D multi‐sweep seismic blended data and the subsequent merging of the data volumes having different frequency bandwidths will be discussed. In specific data domains where the signal component is coherent, interference shots (i.e. blending noise) are randomly distributed in the data space according to its own shot firing time. Therefore, the deblending process, which separates interference shots from a signal component, becomes a noise attenuation problem. A sparse inversion methodology is applied in the frequency–wavenumber–wavenumber (f–kx–ky) domain to attenuate blending noise. By applying this deblending methodology to both dispersed source array's low‐ and mid‐high‐frequency bandwidths, we obtained high‐quality deblending results. For both frequency bandwidths of the deblended dispersed source array data, additional effort was made to combine the two datasets to a single broadband data volume. Consequently, deblending and merging of the dispersed source array blended data generated a broadband, deblended and well‐balanced seismic volume suitable for further processing and reservoir characterization applications.

The goal of simultaneous shooting is to acquire better seismic data more quickly at lower total cost. Effective source deblending techniques provide us with one of the tools for accomplishing this goal. The use of compressive sensing theory gives us another tool by helping to increase the effective spatial bandwidth of our acquired data. Seismic surveys designed to collect both optimally sampled and blended data can reduce acquisition costs and significantly improve image quality. In this paper, we consider a joint deblending and reconstruction problem using the framework of a synthesis-based basis pursuit denoising model. The combination of a “deblending” operator together with a “restriction” operator leads to a joint inversion in which the data are both deblended and reconstructed at regular sampling intervals. Our inversion model can be further constrained by down-weighting the evanescent portion of the wavefield. We illustrate our method using both synthetic and real data examples simulating continuous-time recording under ocean bottom node (OBN) settings.

Summary We have developed a novel random noise attenuation method for seismic data based on inversion in the frequency-space (f-x) domain. The method regards ‘clean’ seismic data in f-x domain as model parameters, and the noise attenuation is equivalent to inverting these parameters from the noisy data. The prediction error filter (PEF) in the f-x prediction method is used as lateral continuity constraints of the inversion. Since the PEF is calculated from the noisy data, it should be recalculated from the denoised seismic data. The process of calculating signal, then getting a new PEF should be iterated a few times. The choice of trade-off parameters also influences the performance of this method. The proposed method overcame the problem of the generation of spurious events and reduction of the signal amplitudes in the conventional f-x prediction method. Tests on synthetic and field data examples demonstrated that, compared with f-x domain prediction, the proposed method has a better performance in noise attenuation and signal-preserving.

Event detection is an essential component of microseismic data analysis. This process is typically carried out using a short- and long-term-average-ratio (STA/LTA) method, which is simple and computationally efficient but often yields inconsistent results for noisy data sets. We have aimed to optimize the performance of the STA/LTA method by testing different input forms of 3C waveform data and different characteristic functions (CFs), including a proposed [Formula: see text]-mean CF. These tests are evaluated using receiver operating characteristic (ROC) analysis and are compared based on synthetic and field data examples. Our analysis indicates that the STA/LTA method using a [Formula: see text]-mean CF improves the detection sensitivity and yields more robust event detection on noisy data sets than some previous approaches. In addition, microseismic events are detected efficiently on field data examples using the same detection threshold obtained from the ROC analysis on synthetic data examples. We recommend the use of the Youden index based on ROC analysis using a training subset, extracted from the continuous data, to further improve the detection threshold for field microseismic data.

Production through wellbores in petroleum industry involves multi-phase flow of oil, gas and water. It is necessary to capture the effects of varying composition of phases to represent wellbore hydraulics accurately. However, a majority of current wellbore simulators prefer a ‘black-oil’ formulation due to its higher speed as compared to a compositional approach. In this work, a neuro-simulation protocol is developed for fast and accurate simulation of wellbore hydraulics in vertical non-isothermal systems. The proposed toolbox is capable of predicting the pressure profile along a production tubing containing flow of pure hydrocarbons (C1 through C45) and water. The tool can operate within a range of flow rates, well depths, pipe diameters, inlet fluid compositions, wellhead pressures and geothermal gradients. The data for training the expert system is generated from a numerical simulator that computes wellbore hydraulics. The numerical simulator is a compositional model, which uses a two-phase equilibrium flash calculation for determining the distribution of hydrocarbon components in oil and gas phases. A two-phase drift flux model accounts for the variation in gas and liquid velocities under various flow regimes. The compositional mass balance and momentum equations are simultaneously solved using a fully implicit scheme, while the temperature profile of the well is taken into consideration in computations. The results provided by both the numerical simulator and the tool described in this paper are compared against field data as well as numerical simulation results reported in the literature. It is observed that the average relative deviation of the results generated in this study from the field data example is 2.2 %. The average relative deviation between the numerical simulator developed and field data example is 2.4 %, showing that the expert system is capable of capturing the related physics and thermodynamics of the wellbore hydraulics phenomena. The average relative deviation between the results generated by the proposed tool and numerical simulation examples from literature data is observed to be between 3.3 and 7.1 %. The average relative deviations between results from the numerical simulator developed in the current work and simulation results reported in literature are found to be between 2.3 and 8.1 %. The variation between predictions provided by various models for wellbore hydraulics in the literature lie within the ranges mentioned above. It is observed that the tool discussed in this paper is a fast, accurate and robust model for predicting wellbore hydraulics for compositional systems. The proposed tool also overcomes the stability issues associated with compositional numerical wellbore simulation models. Such a versatile tool can also be used for generating tubing intake curves for an unrestricted set of scenarios and for quick selection of optimal gas lift design parameters.

Shallow-seismic Rayleigh waves are attractive for geotechnical site investigations. They exhibit a high signal to noise ratio in field data recordings and have a high sensitivity to the S-wave velocity, an important lithological and geotechnical parameter to characterize the very shallow subsurface. In recent years we studied the applicability of the two-dimensional elastic FWI method using numerous synthetic reconstruction tests and two field data examples. Some important challenges are reported here: (1) the accurate correction of the geometrical spreading, (2) the estimation of the source wavelet, (3) the importance of an-elastic attenuation in the forward simulations. We found that Important pre-processing steps for the application of 2-D elastic FWI to shallow-seismic field data are the 3D to 2D correction of geometrical spreading and the estimation of a priori Q-values that must be used as a passive medium parameter during the FWI. Furthermore, a source-wavelet correction filter should be applied during the FWI process. Smooth initial models obtained from the analysis of the first arrivals of body waves are important and seem to be sufficient. Our field data examples indicate that FWI is able to resolve lateral variations of S-wave velocities in the very shallow subsurface.

Seismic data suffer from under-sampling along spatial dimensions due to physical and economic limitations during acquisition, which can adversely impact subsequent imaging processes. Various approaches have been proposed to address this issue, including rank-reduction, transform, and deep learning (DL) methods for reconstructing missing traces in observed seismic data. While many DL-based reconstruction methods employ convolutional neural networks (CNNs) as their core components in supervised or unsupervised settings, the accuracy of CNN-based DL reconstruction methods can still be enhanced due to the inherent localization of convolutional operators. In this study, we present an innovative method, termed Attentive CNN (ACNet), that incorporates a transformer model with a multi-head self-attention mechanism into the CNN framework for unsupervised seismic data reconstruction. ACNet consists of an encoder built with the transformer model and a CNN decoder, enabling an iterative reconstruction process within the proposed unsupervised DL-based approach. We compare the performance of our method with that of the damped rank-reduction (DRR) method using synthetic and field data examples. The results demonstrate that our proposed method exhibits superior signal reconstruction and random noise suppression capabilities compared to the DRR method.

Azimuthally variation of elastic impedances for fracture estimation