We derive magnetization vector tomography imaging equations and compare them with the magnetization scalar tomography imaging equation. The derived equations are applicable to 3‐D and 2‐D magnetization vector inversion problems, vertical component magnetic field data and total intensity of magnetic field data. In the inversion process, an improved Gauss‐Sadel iterative method with a weight coefficient determined by magnetic prism's buried depth is introduced. 2‐D model forward and inversed studies show that when the model consists of two layers, each has 51 prisms, the inversed vertical and horizontal magnetization components with the zero magnetization initial model are consistent well with the model parameters, except the edge effect near the boundary. When the model consists of five layers, and each has 51 prisms, the inversed vertical and horizontal magnetization components can be obtained with a homogeneous initial magnetization model instead of zero initial magnetization one, and the boundary effect also exists. Up to now, we cannot get much more details of fine magnetization structures from the inversion results. This aim will be reached by further work in the future.

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Simulated annealing (SA) is used to invert 1D controlled source audio-frequency magnetotelluric (CSAMT) data. In the annealing process, the system energy is taken as the root-mean-square fitting error between model responses and real data. The model parameters are the natural logarithms of the resistivity and the thickness in each layer of the earth. The annealing temperature decreases exponentially, while the model is refreshed randomly according to the temperature and is accepted according to a Boltzmann probability. We first tested the SA on synthetic data and developed a cooling schedule of model updates specifically for CSAMT data inversion. The redesigned cooling schedule reduces the magnitude of the model updating, and makes the solution converge rapidly and stably. For a three-layer model whose resistivity increases with depth, SA has difficulty in obtaining the global solution for the middle layer. However, the solution for such a layer can be significantly improved by using the mean value of the estimates. The inversion of field data from a northern suburb of Beijing, China, demonstrates that starting from a 1D smooth inversion to determine the range of SA parameters permits the SA to obtain very good results from the CSAMT survey data.