基于广义模型约束的时间域航空电磁反演研究

Inversions of time-domain airborne EM based on generalized model constraints

由于航空电磁具有海量数据,因此快速有效的成像和反演手段至关重要.本文针对层状介质模型推导与实现了广义模型约束条件下时间域航空电磁一维反演.从正则化反演的目标函数出发,通过改变模型约束项构造Lp范数反演和聚焦反演,进而通过改变模型求解域构造出基于小波变换的稀疏约束反演.针对不同反演方法目标函数的构建方式,本文进一步从数学原理上分析不同反演方法的预期效果,并通过理论模型和实测数据进行验证.结果表明L0.8范数反演、聚焦反演和基于小波变换的稀疏约束反演可以得到更符合地下层状介质陡变界面的反演结果.

Since Airborne Electromagnetic (AEM) survey produces massive data, an effective imaging and inversion tool is very important. In this work, we take a layered earth model as an example to derive the one-dimensional (1D) time-domain AEM inversion under generalized model constraints. Starting from the objective functional for the regularized inversion, we establish the Lp-norm inversion and focusing inversion by changing the model constraints, and the sparse constraint inversion based on wavelet transform by changing the model solution domain. Further we mathematically analyze the effectiveness of different inversion methods taking into account the structures of their objective functions and verify our conclusions via both a synthetic model and survey data. Results show that for a layered earth model with distinct layer interfaces, the L0.8 -norm inversion, focusing inversion, and sparse constraint inversion based on wavelet transform can obtain the subsurface structures such as steep interfaces that are more close to real ones.