Pre-stack Complex Seismic Wavefield Interpolation Reconstitution And De-noising Technique

In the seismic exploration，due to the complex surface condition and technicallimitations，the collected seismic data often exists missing traces and noise. Therefore,it has practical significance to develop the quick and efficient interpolation anddenoising techniques for prestack complex seismic wavefield. General interpolationand denoising methods for the complex seismic wavefield always show lowcalculation accuracy and efficiency. Seismic interpolation and denoising can betreated as mathematical inverse problems. Most existed methods are based on thel2-norm optimization problems, the obtained solution is local smooth. Local smooth areoften not what we need, so one has to use new constraint conditions. Compressivesensing (CS) comes from the field of image acquisition, which mainly comprisessparse representation of signal and design of measuring matrix. A link between dataspace and model space is established through sparse transform in this theory, whichprovides an effective solution for solving wavefield interpolation and denoising.When compressive sensing is employed to solve the problems of interpolation anddenoising, optimized characterization of seismic wavefield and efficient and accuratecalculations of iterative algorithm are critical to the theory, however, the commonlyused inversion methods for compressive sensing can not be well suited for complexseismic wavefield data. Therefore, the dissertation use CS theory in the paper topropose VD-seislet and OC-seislet as sparse transforms for characterization ofcomplex wavefield, at the same time, the research also establishes the interpolationand denoising method for complex wavefield under the framework of Bregmaniterative algorithm. The dissertation analyzes typical complex wavefield containing scattering wavesand strong noise, the key issues for complex wavefield interpolation and denoising areproposed based on compressed sensing according to its characteristics: selection offorward operator L and iterative algorithm. Bregman iterative algorithm in TotalVariation Denoising areas is introduced and modified to suit the compressive sensing,in which with sparse characterization is the core, it can compress incomplete or noisyseismic data with optimally transform basis function. The problem of seismicwavefield interpolation and denoising as treated as constrained optimization problems，which is solved by the mixedl1-l2norm inverse problem by using improvedBregman iterative algorithm. Meanwhile, H-curve standard is employed to adaptivelyselect the most suitable threshold parameters. After combining with soft thresholding,compressive sensing theory can be used for iterative inversion process in transformdomain, then, the results are transformed back to the data domain; finally, de-noisingand removing aliasing can be achieved as well as restoring valid information. Theproposed methods can accomplish quick and accurate interpolation and denoising forcomplex prestack complex seismic wavefield.After the iterative framework is determined, this dissertation discusses sparsetransforms, which are used to characterize seismic wave field under the theory ofcompressed sensing. Seislet transform is based on wavelet lifting scheme and seismicpattern. Different patterns will produce different types of seislet transform. Thisdissertation chooses VD-seislet and OC-seislet transforms to sparsely representdifferent types of complex seismic wavefield.VD-seislet transform is a new analysis method for prestack reflections in CMPdomain, which can compress the reflection wave away from strong random noise. Inthis method, VD (velocity dependent) dip is taken as identifying patterns of seismicdata, where the local dip of prestack data is obtained from the time-distancerelationship in velocity analysis, because the velocity scanning is not sensitive to thestrong random noise. Therefore, as a bridge between local dip and scanned velocity, the time-distance equation keeps strong random noise away from the reflection events.In the dissertation, I provide the application of VD-seislet transform for separation ofsignal and noise and the interpolation of missing data. Synthetic models and field dataare used to test the denoising capability for strong random noise and the interpolationfor missing data by using VD-seislet transform in complex wave field.OC (offset continuation) operator is an alternative integration continuous operatorto predict seismic data between different offsets. The detailed derivation process ofOC operator is described in the dissertation, and then I propose OC-seislet transformby taking the OC operator as patterns of seismic data in seislet transform. OC-seislettransform is a sparse transform, which represent seismic data based on the dynamicrelationship. It can better characterize complex seismic wavefield with the existenceof scattered waves and strong random noise; it also provides an essential basis ofmathematical transform for compressive sensing theory, what is able to solveinterpolation and denoising problems for complex seismic wavefield. In thisdissertation, OC-seislet transform is combined with the improved Bregman iterativealgorithm to solve the interpolation problems of incomplete seismic data includingscattered wave. After applying synthetic models and field data and comparing with thePOCS iteration method applied in industry, the results show efficiency and validity ofthe proposed method. Moreover, OC-seislet transform can also be used to removestrong noise from complex wave field, by using swell noise as an example, theadvantages of this transform on attenuation of strong random noise is proven inpractice.