Optical Flow Method For Calculation Angle Gathers In Reverse-time Migration Imaging

Angle gathers are an important output part of reverse-time migration imaging.Therefore,the set of angle gathers generated by reverse time migration is particularly important.In the previous methods,it is often necessary to face the problem of instability.In those areas with large amplitudes,there may be cases where the angle is not solved,the direction is unstable,the solution angle is inaccurate,and instability results.This dissertation focuses on the above problems of angular gathers and uses the optical flow method to calculate the angular gathers in the reverse time migration.Through data tests,it is concluded that using the optical flow method to calculate angle gathers can solve the above unstable conditions.Therefore,this study uses the optical flow method to calculate the angular gathers.Applying the optical flow in the wave field can directly calculate the propagation direction of the source wave field and the propagation direction of the wave point of the detection point.The direction vector is stable and the precision is higher.The result is more accurate.The system derives the overall formula for calculating angular gathers using the optical flow method,and derives the formula for calculating the reflection angle,formation dip,and azimuth angle by combining the structure tensor,wave front vector,and instantaneous wave field vector.The optical flow method is no longer the result of directly obtaining the propagation direction information,but it adopts an iterative solution to set the threshold in advance,and calculates the difference between the horizontal and vertical components of the two optical flows obtained before and after two consecutive moments.When the absolute value is less than the preset threshold,the iteration stops.The result obtained at this time is the final optical flow solution of the imaging point,that is,the propagation direction of the incident and the reflection that the imaging point needs to calculate.The iterative process is also a process of constantly modifying both directions of calculations,eventually leading to the most accurate results.In addition,a predetermined weighting factor is added to the expression of the optical flow so that the molecular term and the denominator can be more effectively and reasonably combined,and the stability of the expression and denominator terms can be effectively controlled.Effectively avoid the situation where the optical flow is zero.The main advantage of the optical flow method for computing angular gathers is that it is not simply composed of the product of the spatial derivative and the temporal derivative.The poynting vector is compared with the optical flow method,not only the advantages of the optical flow method are obtained from the two expressions,but also the data are tested and compared.The results all indicate that the optical flow vector is superior to the poynting vector.The following is a comparison of the two expressions.When the initial value of the optical flow vector in the optical flow vector expression is zero,the result at this time is a special solution of the optical flow vector.In addition,there is a regularization term in the denominator term,which ensures the stability of the propagation direction calculated by the algorithm.Even when the derivative of the displacement versus time is zero,the optical flow vector values at these points are not necessarily zero.It also depends on whether the partial derivative of displacement to space is zero.In the poynting vector,when the derivative of the displacement to time is zero,the calculated poynting vector is zero regardless of whether the derivative of the displacement to space is zero.When the derivative of the displacement vs.time is zero in the optical flow vector,only when the derivative of the displacement vs.space is zero,the result of the calculated optical flow vector is zero.Large sampled data can be processed in time and space,and it is less sensitive to wavefield energy and noise levels than other methods.