An Equivalent Source Optimization Strategy For Gravity Anomaly Profile Transformations

Equivalent source technique makes use of the uniqueness of the solutions of the first kind of boundary value problem of Laplace equation.The results of various potential field transformations can be obtained at one time.However,because the measured data are always finite,discrete and contain errors,the equivalent source cannot be strictly equivalent to the field source of the measured gravity anomaly.Based on this,we discussed the reliability of the equivalent source gravity anomaly transformation firstly.The model test shows that: when the gravity anomaly contains obvious regional field components,the conventional equivalent source setting method will lead to: 1)the number of equivalent sources is too large,and the way of the point-to-point setting has certain blindness;2)results of the transformations is very sensitive to the setting depth of equivalent source,and too deep or too shallow will lead to unfitting;3)the transformations are easy to oscillate in the boundary part,especially the shear difference between the calculated value of the vertical first derivative and the calculated value of the upward continuation and the theoretical value.In this paper we discussed,based on model test,the reliability of gravity anomaly profile transformations through equivalent sources,and we proposed a set of optimization measures for the setting of equivalent sources to overcome the defects found: first,the source layer is divided laterally into segments which use the abscissas of the extreme points of the residual field as nodes,and a same number of line masses are put on each one of the segmentations;second,the source and data are extended along both sides of the profile;finally,the transformations is realized through the line masses solved by Tikhonov regularization.Model tests verify that: 1)Source segmentation could reduce the number of line masses in the premise of data transformation reliability;2)Extending the equivalent sources alone could eliminate oscillation of the derivatives,and extending the source layer and the data simultaneously could further depress the scissors differentials between calculated and theoretical values of the first vertical derivative and upward continuation.At last,we applied these optimization measures to an actual gravity profile collected above a mining tunnel,and obtained more reliable transformation results similar to those of the model tests.