Application Of Basis Pursuit Algorithm Based On Compressed Sensing Theory In Impedance Inversion

Seismic impedance inversion is a core technology in the field of seismic exploration and plays an important role in reservoir prediction and oil and gas reservoir description.It integrates seismic and logging data,contains a wealth of lithology and physical information,can more truly reflect the underground geological structure and reservoir lithology characteristics,greatly improving the success rate of drilling,exploration and development is important in accordance with.With the deepening of exploration and development,exploration and development gradually to the complex hidden and deep unconventional oil and gas reservoir direction,so the accuracy of seismic inversion and resolution requirements are getting higher and higher.Most of the wave impedance inversion methods are based on the hypothesis of sparse reflection coefficient,and the reflection coefficient is directly solved when the 2-norm constraint is very small,and the wave impedance inversion result is obtained by recursive inversion.Sparse Spike Inversion method is one of the most typical methods,although it has the advantages of less dependence on the model and suitable for areas without wells or wells.However,due to the sparseness of the solution of the 2-norm constrained optimization problem,the reflection coefficient series obtained by this method is dense,and the longitudinal resolution of the wave impedance is low and it is difficult to identify the thinner formation boundary.In order to obtain the optimal sparse solution,Tao et al.Developed the 0-norm and 1-norm optimization problem based on the theory of compression sensing.Based on this paper,we discuss the matching pursuit method based on 0-norm and the base pursuit method based on 1-norm respectively.Matching pursuit method specially fit signal sparse decomposition,widely used in the field of seismic data reconstruction and signal denoising.The base pursuit method is suitable for solving the sparse solution accurately and thus can be applied with seismic inversion.Basis pursuit inversion is a new inversion methodology developed in recent years.It constructs an over-complete wavelet dictionary in advance,then searches the solution space to get a sparse solution.However,since the conventional basis pursuit inversion method depends on the seismic data only,the inversion resolution is still insufficient and may cause the inversion results being not consistent with the actual geological situation.In this paper,an improved base pursuit inversion method and matching inversion process are developed.Before the inversion,the seismic data are reconstructed by matching pursuit method,and the signal-to-noise ratio of the data is further improved.And then build the complete wavelet library based on the calibration wavelet.At last,introducing geological model constraint in the basis pursuit inversion and creating new objective function constrained via prior model,then converting to a constrained optimization problem and solving it by the Primal-Dual log-Barrier Programming algorithm,the issue of insufficient resolution in the conventional basis pursuit inversion can be effectively addressed.Two-dimensional model tests indicate that the inversion result obtained by the improved basis pursuit inversion has better resolution than that of the conventional basis pursuit inversion method.Furthermore,better inversion result in the application of practical data is achieved.