Research And Application Of Damped Least Squares Wave Impedance Inversion Method

Many of the oil and gas reservoirs have entered the stage of fine exploration and development,which requires geophysical workers to make more accurate feedback and imaging of changes in the physical parameters of the underground medium.The essence of geophysical exploration is actually a geophysical inverse problem solving process.In this solution process,the inversion method used has a great influence on the inversion results.Seismic wave impedance inversion technique is one of the most representative inverse problems.According to the type of seismic data used in the inversion process,it can be divided into pre-stack wave impedance inversion and post-stack wave impedance inversion.Nowadays,there are many kinds of post-stack wave impedance inversion methods,and the technology is mature.It is not only practical to study the advantages and disadvantages of different inversion methods,applicability,various factors affecting the inversion effect and the selection of control parameters in inversion.The application provides guidance and avoids the blindness of the application.The application history of optimization theory in solving geophysical inverse problems can be traced back to the 1980 s.It is usually by setting the objective function and searching in the global or local range to find the minimum or maximum point of the objective function,so that reaching the purpose of finding the solution.Since the equations to be solved in geophysics are often nonlinear and highly ill-conditioned,and the solution has serious multi-solutions,there are usually two schemes for solving such equations.One is to solve the problem of geophysical nonlinearity.It is transformed into a linear problem,and the linearization method is used to solve the nonlinear problem.Another idea is to solve it by a completely nonlinear method.Compared with linear inversion theory,nonlinear inversion is much more difficult in theory and implementation than linear inversion,and linear inversion is more mature in terms of method principle and operability.Based on the constrained sparse spike inversion method,the damping coefficient given method under the trust region method is studied,and the wave impedance inversion objective function under the least squares meaning is established,which reduces the Jacobian matrix in the traditional least squares method.The cost is calculated,and the non-definite and singular problems of the Jacobian matrix are solved.The iterative method of damping coefficient is optimized,which makes the algorithm have better stability and global convergence.The theoretical models of different wavelets,different noises and different initial wave impedances are tested respectively.Combined with the two-dimensional Marmousi model,good inversion results are obtained by inversion.The actual data is used for inversion,and the inversion results are good,which proves the feasibility and effectiveness of the proposed method.