基于有限差分法正演的大地电磁测深带地形三维反演研究
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摘要
研发了一套基于有限差分(FD)方法的大地电磁测深数据带地形三维反演算法及代码。其中，在大地电磁场正演数值模拟方面，开发了起伏地形条件下基于交错网格剖分、有限差分方法的大地电磁测深三维正演代码；在满足平面波场假设的前提下，使用长方体网格剖分模拟三维起伏地形，实现了带地形三维正演计算。设计了理论模型，将计算结果分别与前人的解析解响应与有限元法的计算结果进行对比，验证了所研发的带地形三维正演代码的正确性与可靠性。
在反演方面，本研究基于非线性共轭梯度方法编写了大地电磁测深带地形三维反演代码，试验了不同的共轭梯度搜索因子β，避免了目标函数对海森矩阵(参数二次导数矩阵)的显式计算和存储，初步实现了大地电磁资料的带地形三维反演。为了检验所研发的带地形三维反演计算的可靠性和稳定性，我们首先对一系列理论模型进行正演计算，利用其生成的合成数据模拟实测数据进行反演，验证了三维大地电磁带地形反演方法的可靠性。其次分别利用了面积性阵列和二维剖面的实测大地电磁数据进行反演试算，并与现有的不带地形大地电磁测深三维反演方法的结果进行比较，证明了所研发的大地电磁三维带地形反演方法在实际应用中的适应性和稳定性。
为满足实际工作中带地形反演的可视化需求，本研究开发了基于matlab的大地电磁三维正反演可视化套件来辅助进行正反演工作。该套件实现了大地电磁标准数据格式的导入与正则化，模型网格自动剖分，数字高程模型数据的导入，地形/海洋模型的人工编辑，反演模型三维交互式显示以及等功能。此外，为研究三维地形对大地电磁测深方法的影响，本研究利用所开发的带地形正反演方法和可视化建模套件，建立了一系列典型的地形和异常体组合模型，进行了大量的正反演运算，得到了具有代表性的正反演结果，对于地形起伏较大地区的三维以至二维大地电磁解释与反演工作具有较强的指导意义。
An inversion algorithm of three-dimensional (3D) magnetotelluric(MT) inversionwith topography based on finite difference (FD) method is presented. Astaggered-mesh, finite-difference method is utilized for the3D magnetotelluricnumerical simulation with surface topography. Rectangular mesh grid is used fordiscretization to meet the plane wave assumptions in magnetotelluric forwardcalculations with topography. Magnetotelluric responses are generated with atopographic model of a hemisphere pit to compare with the analytic response,verifying the correctness and reliability of the forward code. Another topographymodel of square frustum hill is tested to compare with a previous result from finiteelement method, adding
In the inversion part, a3D MT inversion scheme with topography is developed basingon nonlinear conjugate gradient method. Different conjugate gradient search directionupdater β are tested to improve the global convergence. Explicit calculations andstorage of the Hessian matrix are avoided to save both memory storage andcomputing time. A series of forward models with surface topography is established togenerate synthetic data, which is inverted by the3D inversion method withtopography. The results are hence compared with the results from3D MT inversionwith no topography implications. Field dataset from a geothermal investigation isused to further test the reliability and stability of the inversion scheme.
A Matlab based visualization package is designed and developed to support the3Dmodeling and inversion procedure and to visualize the inversion results. Thevisualization package consists of a series of data and model editing functionsincluding the import and regulation of MT data, auto meshing of the model grids, theimport of digital elevation data, as well as the edit of topography/bathymetry in themodel. To better understand the topography effects in3D, a series of complexsynthetic models with topography are designed and generated with the numericalmodeling and inversion scheme, as well as the visualization package presented here.Synthetic models with typical topography and anomaly combinations are tested withthe modeling and inversion scheme presented to provide a common guide to theinterpretation of3D and2D magnetotelluric data in cases with rugged terrain.
在反演方面，本研究基于非线性共轭梯度方法编写了大地电磁测深带地形三维反演代码，试验了不同的共轭梯度搜索因子β，避免了目标函数对海森矩阵(参数二次导数矩阵)的显式计算和存储，初步实现了大地电磁资料的带地形三维反演。为了检验所研发的带地形三维反演计算的可靠性和稳定性，我们首先对一系列理论模型进行正演计算，利用其生成的合成数据模拟实测数据进行反演，验证了三维大地电磁带地形反演方法的可靠性。其次分别利用了面积性阵列和二维剖面的实测大地电磁数据进行反演试算，并与现有的不带地形大地电磁测深三维反演方法的结果进行比较，证明了所研发的大地电磁三维带地形反演方法在实际应用中的适应性和稳定性。
为满足实际工作中带地形反演的可视化需求，本研究开发了基于matlab的大地电磁三维正反演可视化套件来辅助进行正反演工作。该套件实现了大地电磁标准数据格式的导入与正则化，模型网格自动剖分，数字高程模型数据的导入，地形/海洋模型的人工编辑，反演模型三维交互式显示以及等功能。此外，为研究三维地形对大地电磁测深方法的影响，本研究利用所开发的带地形正反演方法和可视化建模套件，建立了一系列典型的地形和异常体组合模型，进行了大量的正反演运算，得到了具有代表性的正反演结果，对于地形起伏较大地区的三维以至二维大地电磁解释与反演工作具有较强的指导意义。
An inversion algorithm of three-dimensional (3D) magnetotelluric(MT) inversionwith topography based on finite difference (FD) method is presented. Astaggered-mesh, finite-difference method is utilized for the3D magnetotelluricnumerical simulation with surface topography. Rectangular mesh grid is used fordiscretization to meet the plane wave assumptions in magnetotelluric forwardcalculations with topography. Magnetotelluric responses are generated with atopographic model of a hemisphere pit to compare with the analytic response,verifying the correctness and reliability of the forward code. Another topographymodel of square frustum hill is tested to compare with a previous result from finiteelement method, adding
In the inversion part, a3D MT inversion scheme with topography is developed basingon nonlinear conjugate gradient method. Different conjugate gradient search directionupdater β are tested to improve the global convergence. Explicit calculations andstorage of the Hessian matrix are avoided to save both memory storage andcomputing time. A series of forward models with surface topography is established togenerate synthetic data, which is inverted by the3D inversion method withtopography. The results are hence compared with the results from3D MT inversionwith no topography implications. Field dataset from a geothermal investigation isused to further test the reliability and stability of the inversion scheme.
A Matlab based visualization package is designed and developed to support the3Dmodeling and inversion procedure and to visualize the inversion results. Thevisualization package consists of a series of data and model editing functionsincluding the import and regulation of MT data, auto meshing of the model grids, theimport of digital elevation data, as well as the edit of topography/bathymetry in themodel. To better understand the topography effects in3D, a series of complexsynthetic models with topography are designed and generated with the numericalmodeling and inversion scheme, as well as the visualization package presented here.Synthetic models with typical topography and anomaly combinations are tested withthe modeling and inversion scheme presented to provide a common guide to theinterpretation of3D and2D magnetotelluric data in cases with rugged terrain.
引文
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