A Study Of Estimation Of Primaries By Sparse Inversion In Combination With Sparse Transformation

Feedback iteration method based on the wave equation in the filed of multipleattenuation, the SRME(Surface-related multiple elimination) has developed into theindustry is relatively mature efficient and effective approach to reduce the surfacemultiples in the recent20years, EPSI (estimation of primaries by sparse inversion)was developed following the SRME method based on a large scale inversion anddirectly to a wavelet estimation method in recent years, which not only avoids theSRME method prediction and subtraction the process but further improve thecalculation precision of primaries. Original EPSI method is the gradient of primariesimpulse response of the update, it is based on the sparse inversion problem of L0norm constraint, using the conventional steepest descent algorithm, each timeprimaries impulse response gradient for update with time window and set ofconstraints on the inversion parameters. When making gradient update process, thewindow contains primary information and cannot contain multiple imformation withinversion parameters should be debug many times. So the original EPSI haverestrictions in a variety of conditions and stability problems.In order to avoid the original EPSI method of sparse inversion based on L0normconstraint in the process of solving the problem. In the condition of sparse enough, L0norm optimization problem can be converted into the L1norm constrained convexoptimization problem, we adopt a algorithm that called SPGL1(Spectrum ProjectedGradient L1) is used, because it is a kind of robust optimization inversion method,even there is not local minimum solution can converge to global solutions, in theprocess of inversion primaries impulse response since the prestack data, so the3Dcurvelet transform is introduced as a sparse constraint conditions, primaries impulse response in the curvelet domain performance more sparse, the inversion of primariesimpulse response result with the source wavelet convolution. So the original EPSIimprovement, not only primary inversion raised the calculation precision ofestimation, but avoids restrictions the variety of conditions in the inversion process.Sparse inversion based on L1norm constraint primary estimation method can not onlyimprove the accuracy of primary estimation but also improved the relative calculationefficiency. Through the numerical simulation data and real data test showed theeffectiveness of the proposed method and stability.Original EPSI through a large scale inversion process to implement primaryestimation, so calculation time consuming, equivalent to more than100times theSRME method of computation. At the same time as a result of the inversion is to getprimary impulse response, for deep reflection information, whether it’s original EPSIor improved L1norm constraint sparse constraint inversion of primary estimationmethod, primary impulse response of the inversion results are not ideal, a lot ofeffective information is not complete, deep for subsequent migration imaging andbrought certain influence seismic interpretation, in order to respond in primaryimpulse response inversion, multiples attenuation effect and get a better compromisebetween computational complexity, we can use SRME and combining curvelettransform EPSI method based on L1norm constraint joint multiple attenuation,through the theoretical data of the experiment, the ideal result is obtained through, notonly primary estimation precision is improved, the deep reflection have beenimproved largely, and the computation is greatly reduced, the ideal expectations.Combined with sparse transformation based on L1norm constraint on the sparseconstraint inversion method is not only suitable for sea of conventional towingacquisition technology, in view of the ocean bottom cable (OBC) data acquisitionmethods, we improve the inversion formula, the conventional towing data informationand submarine cable data information application in it at the same time, also can usethis method to primary sparse constraint inversion of submarine cable data estimation,in order to increase the speed of sparse transform, and applied to two-dimensional curvelet transform and one dimensional wavelet transform in combination withmathematical sparse transform method, adopted double convex optimization method,the inversion of primary impulse response in the process of using the objectivefunction is a collection of convex function and application of the constraint is also aconvex function, in order to improve the speed and reduce memory footprint sparsetransformation, using the two-dimensional curvelet transform combined with wavelettransform, the method of impulse response of primary using SPGL1, at the same timeintroduced the pareto curve as a convergence criterion, improves the convergencespeed, using the least-squares QR decomposition algorithm for wavelet estimation,through alternating optimization iteration process, and finally achieve a more accurateinversion primary impluse response, and then get primary information, at the sametime to get the source wavelet, in OBC data of the application of an improved sparseinversion primary is estimated at a time. This method is suitable for the OBC eachcomponent in the data. We adopted in the simulation example hydrophone data,namely pressure component for another primary of estimates. It have been the goodeffect verified by theoretical data.For passive source seismic data, using conventional seismic interference theory ofcross-correlation algorithm of virtual shot records contain of surface multiples. Yet bya passive source data estimation by primaries sparse inversion, contains only primary,can be obtained without surface multiples of the virtual shot record. Due to timewindow selection and inversion parameters of the passive source data set moredifficult, we improved the original passive data sparse inversion solution of primaryof estimates,it will be based on primary impulse response source of passive sparseinversion estimation to solve the problem is transformed into the L1norm constraintoptimization inversion problem, avoided the traditional sparse inversion of primaryestimation process with time window to prevent trapped in local optimum in inversion.In the passive source data of the impulse source type uses the solution of theoptimization process, and combined with two-dimensional curvelet transform and onedimensional wavelet transform method, the SPGL1algorithm based on L1norm constraint and energy of the L2norm constraint inversion with least-squares QRdecomposition algorithm respectively, the passive data in the sparse transform domaininversion, so that we can be obtained results can directly obtain primary reflectioninformation, the effect is more superior, imaging quality has been further improved.For the combination of sparse transformation based on L1norm constraintestimation of primaries by sparse inversion based on the data matrix formula isderived and improvement of the application to the Marine towing data of conventionalocean bottom cable (OBC), and passive seismic data, through the model and realdata,it have reached a certain application effect. From the earliest SRME method isput forward, and then to traditional EPSI method, finally, we further improve EPSImethod, not only avoid the SRME method of prediction and subtraction, the processof inversion condition was optimized at the same time, improve the inversion speed,multiple removing areas and EPSI method for the future of the large-scale industrialapplication provides reference.