摘要
为了降低重力与磁法单独反演中的非唯一性问题,本文实现了一种基于Gramian约束的重磁三维联合反演算法.使用基于模型参数或其空间梯度的Gramian算子,将其添加到目标函数中,约束剩余密度与剩余磁化率模型参数或其梯度更具相关性.采用高斯-牛顿法对目标函数进行最优化求解,对求解方程进行了简化,节省内存并提高了计算效率.反演过程中使用对数法约束模型参数的上下界,使反演结果更符合真实地质情况.提出了新的模型更新步长计算策略,同时考虑了数据拟合与联合约束的影响,使联合反演更加稳定.通过三个数值模型验证了算法的可靠性,并进一步将该算法应用于加拿大McFaulds湖实测航空重磁数据.对比了反演结果切片并展示了交会图,联合反演得到的剩余密度与剩余磁化率的物性、梯度分布都比单独反演的相关性更强.联合反演提供了一个既能拟合数据又在一定程度上满足耦合条件的反演解.验证了所开发的联合反演算法在实际数据上的有效性与适用性.
This paper proposes an approach for the joint inversion of gravity and magnetic data using Gramian constraints to address the non-uniqueness of the inverse problem.The Gramian constraints can be constructed either directly from the model or from the spatial gradient of the model.By utilizing the Gramian operator,the correlation between the anomalous density and magnetic susceptibility can be enhanced.The Gauss-Newton method is employed to minimize the objective functional,and the equation for model update is simplified to reduce computational costs.To ensure the inversion results align well with geological models,we restrict the boundary of the model parameters using the logarithmic method.Additionally,we introduce a novel step-length calculation strategy specifically tailored for the joint inversion approach.To validate our algorithm,we conducted experiments using three synthetic models.Furthermore,we applied the method to airborne gravity and magnetic surveys in the McFaulds Lake area,Ontario,Canada.The inversion results and cross-plots demonstrate a stronger relationship between the physical property parameters or gradient distributions of anomalous density and susceptibility obtained through joint inversion compared to those obtained through separate inversions.The joint inversion algorithm effectively produces inversion results that accurately fit the data and satisfy the coupling assumption.Consequently,we successfully validate the effectiveness and applicability of the developed joint inversion algorithm using practical data.
作者
孔瑞金
胡祥云
蔡红柱
KONG RuiJin;HU XiangYun;CAI HongZhu(School of Geophysics and Geomatics,China University of Geosciences,Wuhan 430074,China;State Key Laboratory of Geological Processes and Mineral Resources,Wuhan 430074,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2023年第8期3493-3513,共21页
Chinese Journal of Geophysics
基金
国家自然科学基金项目(42274085)资助。
关键词
重磁勘探
联合反演
Gramian约束
高斯-牛顿法
Gravity and magnetic methods
Joint inversion
Gramian constraints
Gauss-Newton method
