A matrix method dealing with electromagnetic induction in a spherically symmetric multi-layered medium is presented. The induction effects have been formulated as,
X=U⋅(∏
Dk)⋅
Q and
CJ=GJ⋅(∏
Dk)⋅
Q, where, the vector
Q and
C represent the electromagnetic fields outside and inside the conducting sphere, and
X the current system of the source. The matrix
U, Dk and
GJ represent induction effects in the spherical layers. By this method the shielding effect due to a medium with spherical symmetry of electrical conductivity distribution can be precisely approximated and the fields within each layer of the sphere and the current system of the source can be conveniently evaluated from observation of the geomagnetic field at the earth's surface. An application is made to investigating the shielding effects of the conducting earth upon the source field of long-term geomagnetic variation for a 25-layered mantle model. The results show that for variations with period less than 720 years the mantle makes noted contribution to shielding effect and in order to estimate the effect of a fine-structured mantle a multi-layered model has to be considered.
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