Gravity Gradient Tensor Abnormal Inversion Method Using Logarithm Boundary Method And The Vertical Weighting

Airborne gravity gradient measurement in addition to is fast,economical,flexible,and has other characteristics outside.Compared to the airborne gravity surveying,it not only can measure gravity first-order derivative and its component,but also can measure the second order derivative of gravity,namely each component of gravity gradient tensor.Because the high-order derivative of gravity has higher resolution and special detection function to small geological body.The comprehensive utilization of the gradient tensor component information can improve the accuracy of the geological interpretation.So in the recent decades,airborne gravity gradient measurement is developing very rapidly.Some developed countries have already had a mature airborne gravity gradient measurement technology.They have made great progress in airborne gravity gradient measurement systems and inverse interpretation methods.And in domestic,airborne gravity gradient measurement field is still blank.But the good news is,at present our country has carried out the airborne gravity gradiometer research and development.Furthermore,we have advance on studying the inverse method and the inversion software aim at the tensor anomalies of the airline gravity gradient measurement.Under the common constraints of the observation data fitting and other conditions,we construct the optimal 3D density distribution solution which takes the minimum model target function.First we put the smooth factor into the model function to make the inverse modeling smooth.This thesis aims at low vertical resolution in the problems of airborne gravity gradient inversion.We solve this problem through imposing the depth weight function in the inversion process.In addition,we use Lagrange method to join logarithm boundary constraint conditions to meet the requirements that the inversed density distribution value is positive.The boundary constraint conditions are easy to achieve,and usually can obtain the good effect.The most important thing is to realize the program of three-dimensional gravity gradient inversion.Through lots of experiments,I get the best choice of all parameters value,and they are consistent with the research results of Li(1994),verify the correctness of the parameter selection.Under the premise of program correctness,I test different models of the accurate data and error data with the smooth factor,the depth weight function,and the constraints condition put into the minimization process.Then solve the inversion problem with the first order Newton method.Comparing and analyzing the results,we can see that the three-dimensional density distribution constructed by this method can basically reflects the three dimensional spatial position of the geologic body.Especially,the depth resolution is improved obviously.At last,I achieved the joint inversion model experiment with the component Uxz,Uyz and Uzz.It came out that the joint inversion is better than the single component inversion for determining the boundary or inversing the density parameters on the condition of existing data error.