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With the rapid development of the transient electromagnetic method (TEM), the numerical simulations of three-dimensional anisotropic media have garnered attention. This study used the rational Krylov method to realise the three-dimensional modelling of the ground magnetic-source airborne transient electromagnetic data for arbitrary anisotropic media. First, based on Maxwell's equations, a time-domain electromagnetic equation was derived for anisotropic media. The finite difference method was employed to discretise the equation, and the electromagnetic field was then expressed as the product of an exponential matrix and a vector related to the source. Subsequently, the rational Arnoldi algorithm was adopted to construct the rational Krylov subspace orthogonal basis vectors, and the electromagnetic fields at different times were obtained based on a model reduction strategy. The accuracy of the proposed algorithm was verified through the comparisons of its results with those of other software packages. We calculated the response for different anisotropic parameters of the typical three-dimensional anisotropic models, and analysed the influence of the anisotropic media on the ground magnetic-source airborne transient electromagnetic data. The proposed three-dimensional forward TEM algorithm provides important technical support for identifying the anisotropic geological bodies and lays the foundation for further inversion research. [ABSTRACT FROM AUTHOR]