Seismic VD-seislet Transform And Its Key Technology For Applications

Seismic exploration is one of the most important methods in geophysical exploration.In the case of ensuring accuracy and resolution,exploration depth can reach Moho surface.Now,seismic exploration is the main method to determine the oil,gas and other fossil resources.As the national key research and development program“deeply resources prospecting and exploration”carrying out,seismic method has also become an important method in deep mineral resources exploration.The quality of seismic data is the key to obtain high precision subsurface images.Using the special geometry,seismic waves propagate in complex underground media based on wave dynamics and kinematics theory and produce seismic data with special time-space distribution.This data structure is different from conventional image.How to describe the special wave characterize properties is the main task in seismic data processing.Because of the complexity of exploration,many problems in seismic data processing,such as the signal-to-noise ratio,data fidelity,are not well solved,which can be treated as characterization of data pattern.Therefore,it is important to study pattern analysis and sparse representation of seismic data.This study is one of the leading edges in seismic data processing.Compressive sensing?CS?is a theory proposed for signal processing,which is based on compressibility signal in sparse transform domain.Sparse transforms,such as Fourier transform,wavelet transform,have played important roles in seismic data processing.Theoretical basis of many processing techniques is compressive sensing.However,most sparse transforms are not specially designed for seismic data and show inadaptability.These methods cannot provide the best sparse representation for seismic data.This also leads to limitations when applying compressed sensing to solve seismic data processing problems.Wavelet-like transforms,such as curvelet,shearlet,seislet,use the directional characteristics of the data and create a new direction in the study of wavelet transform.Seislet transform is a kind of wavelet-like transform that is specially designed according to seismic data attributes,which shows its superiority in some processing tasks.The earlier seislet transforms use some attributes of seismic data,such as local slopes,but they are easily affected by random noise.Therefore,it is important to develop a new seislet transform that can accurately represent seismic wave field under strong random noise environment.Seismic data pattern analysis is the core content to solve the problem of seismic data representation.In this thesis,I study local slope attribute of seismic events in common-middle-point?CMP?dataset.Based on the theory of seismic wave kinematics,one can use the time-distance equation of reflections to establish the relationship between velocities and local slopes of near-offset data.Then,one can get the velocity-dependent expression of the local slope in the range of near-offset according to the classical hyperbolic equation.However,due to the anisotropy of media and complex reflection interface,the reflections do not meet the standard hyperbolic form at far offset,therefore,I need a new time-distance equation to describe different offset distance.According to time-shift NMO equation,the thesis proposes a relationship between local slopes and two parameters?velocity and anisotropy coefficient?for large offset.The new local slope property provides a geophysical support for image processing tools.By matching seismic data pattern analysis to image processing methods,we propose a sparse wavelet-like transform--VD-seislet transform,which can represent seismic data well.Since total energy of plane wave propagation in different seismic traces remains unchanged,one can use time-domain all-pass filter to solve the partial plane-wave differential equation and obtain the relationship between prediction operator and temporal-spatial varying slope.The thesis combines the prediction with lifting scheme to establish the theory framework of generalized VD-seislet transform.The thesis also proposes several applications based on VD-seislet transform and study the corresponding key technologies in seismic data processing.This thesis converts signal and noise separation in VD-seislet transform domain to adaptive parameter analysis and studies the principle of selecting the best threshold value.Signal and noise separation can be treated as variation problem,which is solved by shrinkage threshold algorithm based on VD-seislet transform.A cross plot between data error and sparse transform coefficients in the variation problem is used to analyse the optimal penalty parameter,which is converted to the adaptive threshold in the wavelet-like shrinkage algorithm.Finally,the thesis implements the key technique of non-iterative signal and noise separation.The thesis proposes a seislet-TV regulation method to set up a new model for signal and noise separation.This model takes advantage of VD-seislet transform and TV algorithm;it can reach to a balance between local smoothing of seismic data and protection of geological structure.The split Bregman algorithm is used to solve the new model.Finally,the thesis implements the key technique of iterative signal and noise separation.The thesis treats seismic data interpolation problem as a linear inverse problem.Because seismic data show sparsity in VD-seislet transform domain,compressive sensing is able to solve the corresponding constrained optimization problem.Seismic data interpolation can be converted into ₀L norm constrained optimization problem,which can be further converted to unconstrained optimization problem with ₁L-₂L norm by using basis pursuit method.Based on the VD-seislet transform,the thesis proposes a Bregman shaping iteration to solve the corresponding inverse problem.Meanwhile,an iterative control criterion is proposed to match the iteration,which can reduce computation costs and guarantee the accuracy of data reconstruction.Finally,the thesis implements the key technique of the missing trace reconstruction.In summary,the thesis studies velocity-dependent slope pattern for seismic data,which is combined with discrete wavelet transform framework to propose an effective seismic data representation method—VD-seislet transform.The new transform comes from the guidance of interdisciplinary theory?seismic data pattern analysis and image processing?.Based on VD-seislet transform,the thesis studies the mathematics foundation of several data processing problems in seismic exploration,carries out the research on key technologies for application,solves the problem about signal and noise separation and missing data interpolation.This study not only improves the development of exploration seismology but also provides an enlightenment for the integration of other interdisciplinary interdisciplines.