Research on Efficient Seismic Data Acquisition Methods Based on Sparsity Constraint

In actual exploration,the demand for 3D seismic data collection is increasing,and the requirements for data are becoming higher and higher.Accordingly,the collection cost and data volume also increase.Aiming at this problem,we make use of the nature of data sparse expression,based on the theory of compressed sensing,to carry out the research on the efficient collection method of seismic data.It combines the collection of seismic data and the compression in data processing in practical work,breaking through the limitation of the traditional sampling frequency,and the sparse characteristics of the seismic signal are utilized to reconstruct the missing data.We focus on the key elements of the sampling matrix in the theory of compressed sensing,and study the methods of seismic data acquisition.According to the conditions that the compressed sensing sampling matrix needs to meet,we introduce a new random acquisition scheme,which introduces the widely used Low-density Parity-check(LDPC)sampling matrix in image processing into seismic exploration acquisition.Firstly,its properties are discussed and its conditions for satisfying the sampling matrix in compressed sensing are verified.Then the LDPC sampling method and the conventional data acquisition method are used to synthesize seismic data reconstruction experiments.The reconstruction results,signal-to-noise ratio and reconstruction error are compared to verify the seismic data based on sparse constraints.The LDPC sampling method improves the current seismic data reconstruction efficiency,reduces the exploration cost and the effectiveness and feasibility of the method.

Multiple wave prediction and suppression based on LO-norm sparsity constraint

Multiple wave is one of the important factors affecting the signal-to-noise ratio of marine seismic data.The model-driven-method(MDM)can effectively predict and suppress water-related multiple waves,while the quality of the multiple wave contribution gathers(MCG)can affect the prediction accuracy of multiple waves.Based on the compressed sensing framework,this study used the sparse constraint under LO norm to optimize MCG,which can not only reduce the false in the prediction and improve the image accuracy,but also saves computing time.At the same time,the MDM-type method for multiple wave suppression can be improved.The unified prediction of multiple types of water-related multiple waves weakens the dependence of conventional MDM on the adaptive subtraction process in suppressing water-related multiple waves,improves the stability of the method,and simultaneously,reduces the computational load.Finally,both theoretical model and practical data prove the effectiveness of the present method.

Simultaneous receiver-side deghosting and denoising method based on the sparsity constraint

In marine seismic exploration,the sea surface ghost causes frequency notches and low-frequency loss,which aff ects the signal-to-noise ratio(SNR)and resolution of seismic records.This paper presents a simultaneous receiver-side deghosting and denoising method based on the sparsity constraint.First,considering the influence of propagation direction and sea surface reflection coefficient,the ghost time delay is calculated accurately,and then the accurate ghost operator is constructed in the frequency–slowness domain.Finally,the ghost-free data are obtained using the sparse constraint algorithm that can effectively suppress the ghost along with the noise energy.This method can remove the ghost and noise simultaneously,achieving quick convergence and with few iterations.It is applied to synthetic data and actual streamer fi eld data.Test results prove that the ghost and notches are suppressed eff ectively,the SNR is improved,and the band is well broadened.

Nonstationary sparsity-constrained seismic deconvolution

The Robinson convolution model is mainly restricted by three inappropriate assumptions, i.e., statistically white reflectivity, minimum-phase wavelet, and stationarity. Modern reflectivity inversion methods（e.g., sparsity-constrained deconvolution） generally attempt to suppress the problems associated with the first two assumptions but often ignore that seismic traces are nonstationary signals, which undermines the basic assumption of unchanging wavelet in reflectivity inversion. Through tests on reflectivity series, we confirm the effects of nonstationarity on reflectivity estimation and the loss of significant information, especially in deep layers. To overcome the problems caused by nonstationarity, we propose a nonstationary convolutional model, and then use the attenuation curve in log spectra to detect and correct the influences of nonstationarity. We use Gabor deconvolution to handle nonstationarity and sparsity-constrained deconvolution to separating reflectivity and wavelet. The combination of the two deconvolution methods effectively handles nonstationarity and greatly reduces the problems associated with the unreasonable assumptions regarding reflectivity and wavelet. Using marine seismic data, we show that correcting nonstationarity helps recover subtle reflectivity information and enhances the characterization of details with respect to the geological record.

Sparse constrained encoding multi-source full waveform inversion method based on K-SVD dictionary learning

Full waveform inversion(FWI)is an extremely important velocity-model-building method.However,it involves a large amount of calculation,which hindsers its practical application.The multi-source technology can reduce the number of forward modeling shots during the inversion process,thereby improving the efficiency.However,it introduces crossnoise problems.In this paper,we propose a sparse constrained encoding multi-source FWI method based on K-SVD dictionary learning.The phase encoding technology is introduced to reduce crosstalk noise,whereas the K-SVD dictionary learning method is used to obtain the basis of the transformation according to the characteristics of the inversion results.The multiscale inversion method is adopted to further enhance the stability of FWI.Finally,the synthetic subsag model and the Marmousi model are set to test the effectiveness of the newly proposed method.Analysis of the results suggest the following:(1)The new method can effectively reduce the computational complexity of FWI while ensuring inversion accuracy and stability;(2)The proposed method can be combined with the time-domain multi-scale FWI strategy flexibly to further avoid the local minimum and to improve the stability of inversion,which is of significant importance for the inversion of the complex model.

Recent Advances in Mathematical Programming with Semi-continuous Variables and Cardinality Constraint

Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.