Nonlinear Radon Transform Algorithm For Multiple Attenuation

Multiple is a kind of regular interference wave,which is abundant in marine seismic exploration.It is generated when secondary downward reflections occur upon encountering strong reflecting interfaces,such as the sea level,during seismic wave propagation.Multiples are received by the receiver point as well as primaries.The presence of multiples distorts the frequency,amplitude,phase,and other attributes of effective waves,rendering it challenging to identify primaries.This distortion leads to a reduction in the signal-to-noise ratio of seismic sections.And the presence of multiples amplifies the complexities of velocity modeling.These problems can interfere with small features and changes within the target layer,thus undermining the reliability of primary imaging by interfering.Radon transform filtering method is one of the common multiple attenuation methods,which can suppress multiple according to the difference of time difference between primary and multiple,and it has the advantages of remarkable efficiency and low cost.Nevertheless,the conventional Radon transform method encounters difficulties in achieving complete multiple attenuation and exhibits limitations in terms of data reconstruction.As exploration requirements intensify and technology evolves,the demand for high-resolution data becomes increasingly pronounced.In this paper,the high-resolution Radon transform multiple attenuation method and velocity analysis method are studied.The potential of machine learning algorithms combined with the Radon transform is studied.Then,according to the sparsity of the data,the parabolic Radon transform multiple attenuation method based on L1/2 regularization is studied,and considering the problem of weak signal loss caused by the regularization parameter settings,the nonlinear Radon transform method based on mixed regularization of Lq1-Lq2 is developed.The proposed nonconvex mixed regularization nonlinear Radon transform method is applied to multiple attenuation and velocity analysis.the parabolic Radon transform multiple attenuation method based on mixed regularization of Lq1-Lq2(q1=q2=1/2)and the hyperbolic Radon transform velocity analysis and multiple attenuation method based on mixed regularization of Lq1-Lq2(0<q1,q2<1)are studied respectively.Firstly,this paper studies the generation,classification and characteristics of multiples,and analyzes the difference of time difference between primary and multiple,which is the theoretical basis of Radon transform multiple attenuation method.Then,several methods of multiple attenuation are reviewed,and two methods based on mathematical transform(traditionalf-ktransform and traditional Radon transform)are compared.Considering the problems of incomplete multiples suppression and loss of primary caused by the low resolution and poor reconstruction ability of traditional methods,the mathematical transform method combined with machine learning algorithm is applied to multiple attenuation.Since the sparse constrained Radon transform method is solved by iterative method,the calculation time is long.Therefore,considering the Radon domain data resolution and computing efficiency comprehensively,the Radon transform multiple suppression method based on support vector machine is proposed.According to the theory of support vector machine,Radon domain data is divided into effective signal and illusion with "1" and "0" respectively to remove Radon domain illusion and improve resolution.This method is suitable for training models with fewer training sets.At the same time,the problem of picking up effective signal points and false points in training set data of support vector machine is analyzed,and the method of selecting effective signal points centrally and distributing false points uniformly is given.The model data and real data verify that the proposed method can suppress multiple more efficiency than the traditional method,and the computational efficiency is much higher than that of the sparse constraint method.In addition,the training results can be generalized to other data.Secondly,two Radon transform multiple attenuation methods based on sparse inversion are proposed.In the first method,L1/2 regularization is introduced into the traditional parabolic Radon transform to improve the separation effect of signal and noise,and improve the consistency of reconstructed data and original data.The model data and the actual data show that the proposed method can suppress multiples more efficiently than the least square method and the L1 regularization method.In the second method,is to constrain the sparsity of multiple and primary data respectively,and further,the mixed regularization of Lq1-Lq2(q1=q2=1/2)is introduced into the traditional parabolic Radon transform.The method restricts the sparsity of multiple and primary data,sets different regularization parameters to highlight the weak signal energy and constrain the strong enery signal,and directly invert the primary energy cluster to improve the multiple attenuation.As the same time,it can effectively protect the primary and ensure the continuity of primary event.Finally,this paper applies hyperbolic Radon transform to velocity analysis,and introduces the traditional velocity analysis method.If seismic data contains multiples,high resolution velocity spectrum is needed to pick up the velocity information of primary.Mixed regularization of Lq1-Lq2(0<q1,q2<1)is introduced to highlight the weak signal energy.Effectively constrain the strong signal energy,improve the hyperbolic Radon domain resolution,and improve the accuracy of the velocity spectrum.At the same time,the multi-task inversion framework is used to directly invert the primary energy,and finally get the velocity spectrum after suppressing the multiples,eliminating the influence of multiples on the primary velocity picking.The effects of different q1 and q2 values on sparsity and resolution were investigated,and a set of optimal values were selected.The model data and the actual data show that the proposed method can obtain higher resolution velocity spectrum than the conventional similar velocity analysis method,and the picking velocity is more accurate,which is conducive to the practical application of velocity modeling.The methods proposed in this paper are all based on nonlinear Radon transform(parabolic Radon transform,hyperbolic Radon transform),take multiple data as the premise,carry out high-resolution processing methods,and obtain data with higher sparsity through sparse constraints to effectively suppress multiples,protect primaries and build high-resolution velocity spectrum.Moreover,the high-resolution Radon domain data can be obtained by combining machine learning to remove the transform domain illusion and achieve the purpose of suppressing multiples efficiently.The stability of the inversion method has been improved,and it has a certain application prospect in practical production.