C-RESPONSE OF GEOMAGNETIC DEPTH SOUNDING ON A 1D THIN SHELL MODEL |
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| Authors: | LI Shi-wen WENG Ai-hua TANG Yu ZHANG Yan-hui LI Jian-ping YANG Yue |
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| Institution: | College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China |
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| Abstract: | This paper tries to formulate the C-response of geomagnetic depth sounding(GDS)on an Earth model with finite electrical conductivity. The computation is performed in a spherical coordinate system. The Earth is divided into a series of thin spherical shells. The source is approximated by a single spherical harmonic P10 due to the spatial structure of electrical currents in the magnetosphere. The whole solution space is separated into inner and external parts by the Earth surface. Omitting displacement current, the magnetic field in the external space obeys Laplacian equation, while in the inner part, due to the finite conductivity, the electromagnetic fields obey Helmholtz equation. To connect the magnetic fields in the inner and external space, the continuity condition of magnetic fields is used on the Earth surface. The external magnetic fields are expressed by the inner and external source coefficients, from which a new parameter called C-response is computed from the inner coefficient divided by the external coefficient, thus normalizing the actual source strength. The inner magnetic fields in each layer can be recursively derived by the continuity boundary condition of both normal and tangential components of the magnetic field from the initial boundary condition at core-mantle-boundary. The consistency of our C-responses with that from a typical 1-D global model validates the accuracy of the proposed algorithm. Numerical results also show that the C-response estimated from the geomagnetic transfer function method will deviate exceeding 5%from the actual response at longer periods than about 106s, which means that ignoring the curvature of the Earth at extreme long periods will make inversion result unreliable. Therefore, an accurate C-response should be computed in order to lay a solid foundation for reliable inversion. |
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| Keywords: | geomagnetic depth sounding C-response electrical conductivity spherical coordinate system 1-D model |
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