Gravity Field Downward Continuation Forecast-Correction Method

With the research and development of gravity magnetic field exploration methods,the methods of earth gravity field measurement have become various.In order to meet the various needs of the inversion gravity field,it is usually necessary to unify various data to the same interface for calculation.The analytical extension problem of gravity and magnetic anomalies is formed.Gravity field upward extension has a strict theoretical model,which is a stable and convergent process,which is easier to implement in practice.Downward extension is an unstable and divergent process,which is theoretically an ill-posed problem.Methods for dealing with this problem include the traditional downward continuation spatial domain difference method,the conventional downward FFT method,the integral iteration method,and the like.However,the results of the conventional downward FFT method are unstable,and the depth of the delay is shallow.The depth of the extended FFT method cannot exceed 3 to 5 times.The integral iteration method can better solve the instability of the downward continuation and increase the point distance of the downward extension(10~50 dot distance);however,it requires multiple iterations due to the calculation,which will generate more noise.Sub-iterations are accumulated,resulting in reduced computational efficiency and accuracy.In view of the insufficiency of the process of downward extension,computational complexity,small downward extension depth,and inaccurate results.This paper proposes a multi-step method based on ordinary differential equations for downward continuation,using Adams forecast-Correction formula,introducing a vertical firstorder derivative that extends upward to different heights,and proposes a downward continuation forecast-correction method for the gravity field in the spatial domain.In order to test the effect of this method,it is compared with the FFT down method,the integral iterative method,Milne downward continuation,and the third-order Adams down method.The three models of different depths of the down-expansion experiment are carried out.The data show that compared with the traditional FFT method and iterative delay method,the predictioncorrection method of this paper has stable delay process,large delay depth,strong anti-noise ability,small boundary loss,small relative error and accurate results.Compared with the thirdorder Adams down-expansion method,when the depth of the delay is gradually increased,the relative error of the method is smaller,and the local and shallow anomalies can be highlighted.The measured data of Xxx shows that the gravity field downward extension forecast-correction method is stable and accurate,which can identify the detail anomaly and restore the true anomaly distribution.The theoretical model and the actual field data test show that the method has good stability for downward extension and high extension accuracy.