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The equivalent source is a simple and effective method to level and manipulate magnetic data. However, large misfits between the predicted and synthetic data for different components of the magnetic field are observed when a single layer equivalent source is used. Therefore, a dual-layer equivalent sources method, based on a shallow-layer and an additional deep-layer is proposed. This technique successfully overcomes the inherent problem of inversion that equivalent property concentrates in the shallow layer, by changing the dimensions of deep equivalent cells, and by using a preconditioned matrix based on a weighted function, which enhances the effects of the deep layer. The results indicate that, by adding a deep equivalent-source layer, this new method significantly improves the accuracy in the prediction of the three components of the magnetic field, especially for the long-wavelength fields.

Plain Language Summary The total-field magnetic anomaly (commonly expressed as Delta B) and the three components (B-x, B-y, B-z) of the magnetic field are sensitive to the magnetized bodies, which are present in the Earth's crust. Usually, only Delta B is measured in field experiments. The scalar Delta B cannot fully express the characteristics and the information embedded in the vector field. An effective way to solve this problem is to transform Delta B into the three components of the magnetic field, i.e., the vector field. Here, a dual-layer equivalent source algorithm, which can be adapted to the measured magnetic anomaly (Delta B) and which is independent from their distribution and terrain relief, is proposed. The dual-layer consists in a shallow equivalent-source layer, which is located near the observation surface to recover the short-wavelength field, and a deep equivalent-source layer, which is located deep in the Earth's crust to retrieve long-wavelength signals. Furthermore, an inversion algorithm with a preconditioned matrix is used to avoid physical-properties concentrating at the shallow layer. The application of such technique on synthetic and real data shows that the proposed algorithm is stable, accurate, and presents fewer boundary effects when compared to previous methods in literature.