2D joint inversion of MT, gravity, magnetic and seismic first-arrival wave traveltime with cross-gradient constraints
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摘要:
为了准确的探测和描绘地下复杂的地质结构，同时克服地球物理单一方法反演的多解性和单一参数反演模型的不一致性等问题，近年来基于交叉梯度联合反演的综合地球物理解释已经得到了广泛的关注和应用.本文首先研究了两种地球物理方法的交叉梯度联合反演算法，在此基础上，推导并实现了多种地球物理方法（大地电磁，重力，磁法，地震初至波走时）的多交叉梯度约束的二维联合反演算法；其次，我们设计了结构不一致模型和复杂模型，针对多物性联合反演算法的准确性和有效性进行了模拟试算，并对复杂模型的单独反演结果和联合反演结果进行了交叉梯度值和物性交会图的对比；最后，本文将成熟的卫星资料多光谱综合分析技术应用到联合反演中，将多物性参数反演模型结果图通过RGB（红-绿-蓝）模式进行合成，得到融合的RGB合成图.结果表明：通过对结构不一致模型和复杂模型的联合反演结果和单独反演结果的对比分析，可以得出联合反演得到的结果更接近真实模型，并从得到的交叉梯度值进一步证明了联合反演模型相似度高，也从物性交会图中得到联合反演的物性相关性更好的结论，反向证明了算法的正确性.最终从得到的RGB合成图像，我们可以更直观的分析反演结果，更有利于准确划分地下模型结构.
Abstract:To accurately detect complex geological structures in the subsurface and solve the problems in geophysical inversion such as multiple solutions and inconsistency of the single parameter inversion model, the comprehensive geophysical interpretation based on the cross-gradient joint inversion has been widely concerned and applied in recent years. In this paper, we first study the cross-gradient joint inversion algorithm of two geophysical methods. Then, we derive and implement the 2D joint inversion algorithm of multiple cross-gradients constraints of various geophysical methods (magnetotellurics (MT), gravity, magnetic, and seismic first-arrival traveltime). Next, we design models with inconsistent structure and a complex structure, respectively, and carry out simulation calculations focusing on the accuracy and effectiveness of the multiple joint inversion algorithm. Meanwhile, the results of separate inversion and joint inversion of complex model are compared with the cross-gradient value and cross-plots of pairs of different physical properties. Finally, this work applies the mature satellite data multi-spectral comprehensive analysis technology to the joint inversion, and synthesizes the multiple parameter inversion model results through RGB (red-green-blue) mode to obtain the fused RGB composite image. The results show that whether in the physical value or in the spatial geometry, the result of the joint inversion is closer to the real model. Furthermore, we also prove that this joint inversion model has a higher structure similarity and physical correlation by comparing the cross-gradient value and crossplots of pairs of different physical properties. From the obtained RGB composite images, we can analyze the inversion results more intuitively, which permits to accurately classify models of underground models.
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图 2
在结构不一致模型中单独反演(A)和联合反演(B)的电阻率(a1, b1)、密度(a2, b2)、磁化率(a3, b3)和速度模型(a4, b4)模型
Figure 2.
Resistivity (a1, b1), density (a2, b2), magnetization (a3, b3) and velocity (a4, b4) models obtained from separate inversion (A) and joint inversion (B) in structural inconsistency model
图 3
在结构不一致模型中单独反演(a)和联合反演(b)的拟合差迭代曲线
Figure 3.
The iterative curve of the RMS misfit of the separate inversion (a) and the joint inversion (b) in structural inconsistency model
图 5
MT正演响应视电阻率和视相位拟断面图
Figure 5.
Pseudo-sections illustrating forward modeling responses of apparent resistivity and apparent phase obtained by MT
图 6
重力、磁法和地震走时正演响应
Figure 6.
Forward modeling responses of gravity, magnetic and seismic traveltime methods
图 7
在复杂模型中单独反演(A)和联合反演(B)的电阻率(a1, b1)、密度(a2, b2)、磁化率(a3, b3)和速度模型(a4, b4)模型
Figure 7.
Resistivity (a1, b1), density (a2, b2), magnetization (a3, b3) and velocity (a4, b4) models obtained from separate inversion (A) and joint inversion (B) in complex model
图 8
在复杂模型中单独反演(a)和联合反演(b)的拟合差迭代曲线
Figure 8.
The iterative curve of the RMS misfit of the separate inversion (a) and the joint inversion (b) in complex model
图 10
联合反演交叉梯度RMS值的迭代曲线
Figure 10.
Iterative curves of cross-gradient RMS value of joint inversion
图 11
不同物性参数之间的单独反演(a)和联合反演(b)交会图
Figure 11.
Crossplots of pairs of different physical properties for models from separation inversion (a) and joint inversion (b)
图 12
单独反演(a)和联合反演(b)的RGB合成图
Figure 12.
RGB images composed from the separate inversion (a) and joint inversion (b)
表 1
单独反演和联合反演的交叉梯度RMS值
Table 1.
Cross-gradients RMS values for separate and joint inversion
∇mMT ∇mGrv ∇mMag ∇mSeis ∇mMT 0 (8.38×10-9) (1.79×10-9) (2.10×10-9) ∇mGrv 2.33×10-7 0 (1.51×10-9) (1.81×10-9) ∇mMag 3.36×10-8 1.15×10-8 0 (3.51×10-10) ∇mSeis 1.15×10-8 1.97×10-8 2.15×10-9 0 注：括号内的数值表示联合反演中每对物性参数之间的交叉梯度RMS值. 
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