The Study On Seismic Data Reconstruction Method Based On Curvelet Transform

The seismic data sampled from field are often incomplete because of the continuous expansion of seismic exploration field,the complex and varing geological environment in the exploration area,the elimination of the waste traces,as well as various human factors.The incomplete data may lead to false frequency in imaging profile and false prediction of multiple wave,which will bring some difficulty to seismic data processing and interpretation work.Therefore,the reconstruction of missing seismic data is a necessary step in seismic data processing.There are many shortcomings in the conventional method of seismic data reconstruction.Curvelet transform has some characteristics,such as compact structure,anisotropy and direction selectivity.These characteristics enable it to have good sparsity and then express curve's characteristics well.Due to the seismic data contains many curve elements,Curvelet transform can express seismic singal very sparsely.This thesis studies the method of missing seismic data reconstruction based on Curvelet transform.Main work of this thesis is as follows:1.A method for reconstruction of missed seismic data is proposed,which is based on Curvelet tranform and semi-iterative projection onto convex sets.A mathematical model for seismic data reconstruction is established firstly,which can be described as a convex optimization problem by adding a sparsity constraint;then in solving the model,the semi-iterative method is introduced to predict the direction of the next gradient to speed up the data research,so as to improve the convergence speed of the algorithm;finally,the proposed method is applied to the reconstruction of both synthetic and real seismic data.2.For the problem that seismic data contains various noises,a method for seismic data reconstruction is proposed,which is based on Curvelet transform and improved linear Bregman algorithm.Bregman algorithm can effectively solve the basis pursuit problem by minimizing the Bregman distance between two points,and also has better anti-noise ability.This thesis introduces the Bregman algorithm into the seismic data reconstruction,and then solving the model of seismic data reconstruction can be described as a basis pursuit problem.For the iteration stagnant phenomenon in the conventional Bregman algorithm,which influences the iterative convergence rate,this thesis counteracts the iterative stagnant process by weighting each updated data with the last data to improve the iterative convergence rate.The experiment results show that both of the above algorithms can provide good reconstruction results for noise-free synthetic seismic data,and the semi-iterative projection onto convex sets algorithm converges faster than the improved linear Bregman algorithm does.For the field seismic data with various noises,compared with projection onto convex sets menthod,the improved linear Bregman algorithm can provide a better reconstruction result,and the reconstructed data has a higher Singal to Noise Ratio.