Unstructured duple mesh based dual-parameters simultaneous inversion for 2D Radio-magnetotelluric data
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摘要:
Radio-magnetotelluric（RMT）是以无线电发射机为信号源的一种地球物理勘探方法，近年来被广泛应用于数米至数十米内的近地表工程和环境地球物理勘探.目前，各类电磁资料的反演均是以寻求满足目标拟合差的地下介质电阻率分布为目的.然而，对于勘探频率为10~300 kHz的RMT数据，由介电常数所引起的波动场在总场中的比例可达20%以上，在这种情况下，忽略介电常数，仅通过电阻率参数的反演来进行数据拟合势必降低反演资料解释的准确性.为解决这一问题，本文研究了基于电阻率-介电常数的双参数同步反演算法.构建了一个全新的双参数目标函数，并推导了双参数反演迭代方程组；通过灵敏度分析，研究了电阻率和介电常数对正演响应的影响，并据此提出相对电导率的概念，统一了反演参数的灵敏度；通过理论模型分析了参考频率、双参数正则化因子对反演结果的影响，并给出了一般性的参数优选方案.此外，为了能够灵活处理复杂地形，本文采用非结构的正反演双网格进行模型离散，并通过局部加密技术保证反演的速度和精度.最后，对一带地形的理论模型分别进行了单参数和双参数反演，结果表明单参数反演无法正确反映出地电信息，而双参数反演能够准确得到异常的分布，验证了本文所开发的双参数反演程序的有效性.
Abstract:The radio-magnetotelluric (RMT) method is an electromagnetic method that employs the signals from remote radio transmitters. As a kind of near-surface geophysical prospecting method, RMT is widely used for engineering and environmental exploration in recent years. At present, most geophysical inversion for electromagnetic data is aimed at the reconstruction of the resistivity and make the forward responses fit the observed data. However, the percentage of wave field which caused by permittivity in the total field can be up to 20% for the RMT data which collected at the frequency ranges from 10~300 kHz. Inversion for reconstructing a resistivity model but neglecting the effect of permittivity may lead to a false interpretation. To solve this problem, this paper presents an algorithm for the simultaneous inversion of the dielectric permittivity and the electrical resistivity dual-parameters. We developed a new dual-parameters based objective function and derived the dual-parameters inverse equations. With sensitivity analysis, we evaluated the effect of the resistivity and permittivity on the forward responses, proposed the concept of the relative electrical conductivity and unified the scale of the sensitivity of the two parameters. We studied the effect of reference frequency and the two regularization factors on the inversion results, put forward an optimum parameter selection scheme in the general cases. Based on unstructured triangle meshes, our code can model arbitrary surface topography. The local refinement technology was used for mesh discretization, which improved the speed and accuracy of inversion procedure. At last, the reliability and effectiveness of our dual-parameters inversion program are demonstrated by synthetic examples. Data with topography are inversed by both ordinary and our new schemes. The ordinary resistivity inversion cannot reflect the anomalous body correctly, while our dual-parameters inversion can provide better results.
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Key words:
- Permittivity /
- Displacement currents /
- Simultaneous inversion /
- RMT /
- Unstructured mesh
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图 2
理论模型及正演网格剖分示意图
Figure 2.
A synthetic model and the unstructured mesh for forward calculation
图 4
不同参考频率的选取对反演系数矩阵的影响
Figure 4.
The effect of reference frequency on the inverse coefficient matrix
图 5
反演网格剖分示意图，其中黑线为反演网格，灰线为正演网格
Figure 5.
An illustration of mesh for inversion calculation. The inversion mesh is shown in black line and the forward mesh is shown in gray line
图 6
不同参考频率下σr和εr同步反演结果
Figure 6.
The σr and εr simultaneous inversion with different reference frequencies
图 7
基于GN算法的双参数同步反演流程图
Figure 7.
The flow chart of dual-parameters simultaneous inversion based on GN algorithm
图 8
对数电阻率和相对介电常数同步反演结果
Figure 8.
The result of simultaneous inversion for logarithmic resistivity and relative permittivity parameters
图 9
log10ρ和εr同步反演时的系数矩阵
Figure 9.
The coefficient matrix of simultaneous inversion for log10ρ and εr parameters
图 10
只考虑介电常数模型约束的反演结果
Figure 10.
The simultaneous inversion result which calculated without consideration of permittivity model constraint The subplots
图 12
λ=0.5, γ=0.1时εr和σr同时反演结果
Figure 12.
The simultaneous inversion for εr and σr parameters with regularization factors of λ=0.5, γ=0.1
图 13
λ=0.5, γ=0.01时εr和σr同时反演结果
Figure 13.
The simultaneous inversion for εr and σr parameters with regularization factors of λ=0.5, γ=0.01
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