Downward Continuation Of Airborne Gravity Anomaly With Machine Learning

Downward continuation of gravity is a classical problem in physical geodesy.It is also one of the keen procedures in the processing of airborne gravity for further applications.Downward continuation of gravity is inherently unstable,during which the noise in airborne gravity would amplify.Classical downward continuation methods are based on inverse Poisson integral,including iteration,regularization,FFT,least square collocation,semi-parameter estimation and so on.This thesis focuses on the application of machine learning in the downward continuation.I thoroughly investigate the theories and methods of downward continuation of gravity anomaly and improve the methods using vertical gradients of gravity.I propose the algorithms of computations of vertical gradient of gravity and direct downward continuation based on machine learning methods respectively.Simulated numerical experiments and the process of airborne gravity observations justify the proposed methods.The main research and results in this thesis include:1.Thoroughly investigating the theories and methods of downward continuation using vertical gradients.Based on Lagrange mean-value theorem,I derive the strict formula for downward continuation.Furthermore,I present the approximations and extrapolations tactics for vertical gradients.The improved method is more theoretically strict and applicable as well;2.Taking Taiwan area for example,thoroughly analyzing the features of EGM2008 model-derived gravity vertical gradients radial distributions.I select 100points randomly in Taiwan area and simulate the vertical gradients every 100 meters upward with EGM2008 model.The Pearson coefficients between heights and corresponding vertical gradients and the differences between gradients on different layers demonstrate that the vertical gradients are almost linear in radial direction and vary relatively slowly.3.Taking simulated experiments in Taiwan area,which justify the proposed improved methods using vertical gradients.Based on EGM2008 model,I simulate the gravity anomaly at 5156m and corresponding gravity gradients.The area is22~°～25~°,120~°～122~°,and the spatial resolution is 2‘.Moreover,the white noise of 2m Gal is added to the simulated data.This is the data for the simulated experiments in the whole thesis.The improved downward continuation methods using gradients downward continue the simulated airborne gravity to 3360 land gravity points and the accuracy is 2.34m Gal.4.Proposing the machine learning algorithms for vertical gradients and presenting the strict procedures and numerical methods.The method regards the computation of vertical gradients using discrete gravity anomaly as a mapping.Taking advantage of numerical constraints,we estimate the integral templates with massive training samples.It avoids the“singularity”in the traditional integration methods.The accuracy of newly proposed method in the simulated experiment of the previous simulated data is 3.88m Gal;meanwhile,the traditional method is 14.94m Gal.5.Proposing the machine learning algorithms for direct downward continuation of gravity anomaly.The simulated experiments justify the new method,which regards the downward continuation of discrete gravity anomaly as a mapping.I put forward the concepts of“approximated inverse Poisson integral”and“approximated discrete inverse Poisson integral templates”.This method takes the airborne gravity as feature vector input and the corresponding land gravity as target vector output.We estimate the integral templates with massive training samples and apply them to the target area.This method is based on the physical interpretations of downward continuation and avoids the“illness”in the traditional methods.The accuracy of this method in the simulated experiments reaches 2.50m Gal.6.Using the three methods(improved method using vertical gradients,computation of vertical gradients with machine learning and direct downward continuation with machine learning)proposed in this thesis to downward observed gravity anomaly in Taiwan area.The downward continuation area is22~°～25~°,120~°～122~°.The airborne gravity is at 5156 meters high.The 3360land gravity points cover the whole area of Taiwan Island.The accruacy of the improved gradient method reaches 9.04m Gal,and the direct learning downward continuation algorithm is 8.33m Gal.