Least-squares Reverse Time Migration Based On First-order Velocity-stress Wave Equation In VTI Media

A large number of production examples show that most of the actual sedimentary seismic strata show seismic anisotropy,at least weak anisotropy.Ignoring this feature will result in inaccurate velocity estimation,thus lowering the imaging resolution of target region.Due to the influence of acquisition aperture,complex underground structures and limited wave field bandwidth,conventional migration methods can only provide blurred imaging of underground structures,and usually can only provide more accurate information of underground structures,which can not meet the needs of exploration and development of lithologic reservoirs.LeastSquare Migration(LSM)uses the idea of model matching data to treat imaging as an inversion problem in the sense of least squares.The conjugate gradient method(or steepest descent method,Gauss-Newton method,etc.)iterates to minimize the error function,and obtains the imaging results with higher resolution and better amplitude fidelity,which has a good application prospect.Firstly,the propagation of seismic wave in anisotropic VTI media is studied,and the corresponding reverse time migration algorithm is implemented.Aiming at the low frequency noise problem of reverse time migration,the cross-correlation imaging condition based on wavefield separation is obtained which used Poynting vector,and an reverse time migration algorithm for VTI media based on directional wave separation is developed.This algorithm is simple and easy to implement,and can effectively suppress low-frequency noise.The validity and superiority of the algorithm are verified by numerical experiments.Secondly,conventional least-squares reverse time migration(LSRTM)algorithm based on the second-order equation ignores the influence of anisotropy and density causes mismatch of the simulated seismic data and the true observation data,and that affects convergent rate as well as imaging quality.In this paper,we introduce the LSRTM algorithm to the first-order velocity-stress equation in VTI media and also provide the framework of the first-order LSRTM.We then build up the first-order velocity-stress equation in VTI media and then derive the corresponding perturbation equations and adjoint equations.The gradient is calculated by using adjoint-state method.Finally,the framework and implementation process of LSRTM method based on first-order velocity-stress equations are formed.In addition,we demonstrate the validity of our algorithm by numerical tests.Amount of the sensitivity tests indicate that velocity and Thomsen parameters have obvious influence on the imaging results and the velocity sensitivity is highest.Finally,we optimized the problems of large computational complexity and poor robustness for the conventional least squares reverse time migration algorithm.Firstly,we introduced the plane-wave coding strategy to compress seismic data,which greatly improves the computational efficiency on the basis of ensuring the imaging accuracy.Secondly,considering that the conventional LSRTM algorithm based on L2-norm is very sensitive to seismic noise,here we developed a least squares reverse time migration algorithm based on Student's t distribution to improve the robustness of the algorithm,and demonstrated the validity and superiority of the algorithm by numerical experiments.Sensitivity analysis of migration velocity error shows that the algorithm needs relatively accurate migration velocity.