We have evaluated an extension of the 3D 3C rapid-expansion method for time-domain electromagnetic modeling with pseudospectral evaluation of spatial derivatives that includes anisotropic conductivity and the earth-air interface. We found that transverse isotropic anisotropy can be included in the modeling with the manipulation of the conductivity tensor. We model the response of the earth-air interface by using the upward continuation of the time derivative of the magnetic induction. All three electric field components are collocated with the electric conductivities and are modeled independently and simultaneously with spectral accuracy in space and time. Numerical tests against the analytical solution for a half-space and spectral methods for 1D anisotropic layered earth models demonstrate the excellent accuracy of this approach.