Three-dimensional magnetotelluric inversion using conjugate gradients
Three-dimensional magnetotelluric inversion using conjugate gradients
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DOI：
10.1111/j.1365-246x.1993.tb05600.x
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发表时间：
1993-10
影响因子：
2.8
通讯作者：
R. Mackie;T. Madden
中科院分区：
文献类型：
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作者：
R. Mackie;T. Madden
我们已经开发了一种使用共轭梯度松弛方法的反演程序。虽然人们可以将该方法推广到所有反问题，但我们演示了它在三维地球模型反演大地电磁数据中的应用。这个过程允许我们绕过灵敏度矩阵A的实际计算或ATA项的反演。实际上，使用松弛方法，只需要计算灵敏度矩阵或其转置乘以任意向量的效果。我们表明，这些都需要一个具有分布式源集的前向问题，这些源集要么在体积中（对于a乘以向量），要么在表面上（对于AT乘以向量）。这大大减少了进行三维反演所需的计算量。在本文中，我们通过假设模型在水平方向上重复来简化边界条件，但这并不是该方法的必要约束。该算法将无噪声合成三维大地电磁数据的数据误差降低到2%的水平。
SUMMARY We have developed an inversion procedure that uses conjugate gradient relaxation methods. Although one can generalize the method to all inverse problems, we demonstrate its use to invert magnetotelluric data for 3-D earth models. This procedure allows us to bypass the actual computation of the sensitivity matrix A or the inversion of the ATA term. In fact, with the relaxation approach, one only needs to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector. We show that each of these requires one forward problem with a distributed set of sources either in the volume (for A multiplying a vector) or on the surface (for AT multiplying a vector). This significantly reduces the computational requirements needed to do a 3-D inversion. For this paper, we have simplified the boundary conditions by assuming the model is repeated in the horizontal directions, but this is not a necessary constraint of the method. The algorithm reduces data errors to the 2 per cent level for noise-free synthetic 3-D magnetotelluric data.