Research On Three-dimensional Focusing Inversion To Gravity And Magnetic Data Based On Inequality Constraints

Gravity and magnetic 3D inversion is one of the most important method in geophysics,which can obtain subsurface density and susceptibility distributions.Due to the existence of non-uniqueness and instability in gravity and magnetic inversion.Constraint inversion has been widely concerned,which adds constraint conditions such as model function term constraints and parameter constraints to the inversion solution process.Meanwhile,traditional gravity and magnetic inversion is usually based on the tikhonov regularization inversion with smoothest standard,and it always obtains smooth solutions,which cannot accurately reflect the boundary of the subsurface anomalies.In order to improve the deficiency of traditional inversion,this paper adopts focusing inversion to 3D gravity and magnetic inversion based on the minimum support function to highlight the anomaly boundary and make inversion model more focused.In addition,superfluous structures of gravity and magnetic inversion make solutions in a low resolution.Inequality constraints are introduced to restrict inversion parameters within upper and lower bounds to achieve parameter constraint,which can limit solutions to a meaningful range and improve the resolution of the inversion results.This study applies focusing inversion method based on inequality constraints,and adopts the range of physical properties as inequality constraints into the gravity and magnetic 3D inversion process by logarithmic transformation function.The objective function of gravity and magnetic focusing inversion based on inequality constraint is constructed by integrating the two ideas of focusing inversion method based on minimum support functional and inequality constraints.Finally,combined with conjugate gradient algorithm to interation calculate.In order to verify the feasibility of the method,three representative model tests,including single block anomaly body model test,inclined plate anomaly body model test,and two block anomaly body combination model test,are carried out by taking 3D gravity inversion as an example.Theoretical model tests show that the focusing inversion can accurately recover the shape and range of anomalies,and can relatively clearly reflect the boundary of the anomalies.However,there are still some defects,such as the existence of false anomalies in the depth.Meanwhile,focusing inversion with inequality constraints can suppress the false anomalies effectively and further improve the multi-solution problem.In addition,the constraint of the partition inequality can also improve the flexibility of the application of priori physical property information,and obtain a solution that is closer to the real model.Therefore,the results highlight the advantages and disadvantages of 3D focusing inversion method based on inequality constraints,and verify that the method is feasible in theory.At last,the method is applied to inversion of the measured gravity and magnetic data in Xiangshan area to make the processing results more reasonable within the constraint range of the practical geological data.The feasibility of the method in practical application is discussed by comparing with euler deconvolution inversion method.The results show that the inversion method proposed in this paper is effective in determining the horizontal position and depth of the subsurface anomalies under certain prior conditions.