Research On 3D L_p-norm Inversion Of Gravity And Magnetic Data

Gravity and magnetic surveys,widely used in mineral and oil explorations and in engineering and environmental problems,are important methods for understanding subsurface density and susceptibility distributions.Three-dimensional inversion is an effective means for quantitative interpretation of gravity and magnetic data.However,due to the non-uniqueness of gravity and magnetic inversion and the complexity of real geological conditions,the classical L₂-norm inversion has several weaknesses.First,gravity data generally contain positive and negative anomalies simultaneously,which means that we cannot incorporate positivity constraints into gravity inversion to reduce superfluous structures of solutions.In this case,we can only estimate locations to center and rough distributions of causative sources from results of 3D L₂-norm inversion.Second,petrophysical measurements are sometimes taken on outcrop and borehole rocks,and provide valuable information for constraining gravity and magnetic inversions.The classical L₂-norm inversion fails to effectively take advantage of the known petrophysical information and produces results characterized by low depth resolution.Third,magnetic amplitude inversion can reduce remanence effects in the presence of strong remanent magnetization.However,in magnetic amplitude inversion,problems such as lack of phase information and incorrect total magnetization directions will further lower the depth resolution of inversion results.Faced with the above three problems,we perform a comprehensive study on applying L_p-norm?0?p?2?optimization to inversion of gravity and magnetic data.To deal with the first problem,we develop an L_p-norm?1?p?2?algorithm for 3D smooth inversion of gravity data.This algorithm can correctly recover dips,depths to top,and depths to bottom of causative sources by using gravity data only.To overcome the second problem,we propose an L_p-norm?0?p?1?algorithm for 3D sparse inversion of gravity and magnetic data.This algorithm can make full use of the known petrophysical information and produce results characterized by sharp boundaries and high depth resolution.Moreover,we also analyze and reveal the equivalence between the proposed algorithm and binary or ternary inversion.To address the last problem,we extend the 3DL_p-norm?0?p?1?sparse inversion algorithm to the magnetic amplitude case.The resultant sparse magnetic amplitude inversion algorithm can simultaneously reduce remanence effects and improve the depth resolution of solutions.Furthermore,we also demonstrate the equivalence of this algorithm and binary inversion.All the proposed algorithms are tested by synthetic and real-data examples and produce favorable results.Our L_p-norm?0?p?2?inversion algorithms are applicable for inverting the data which are either linearly or nonlinearly related to model parameters,which means our algorithms are general in gravity and magnetic inversion.