  Context. Solar Energetic Particles (SEPs) with energy in the GeV range can
propagate to Earth from their acceleration region near the Sun and produce
Ground Level Enhancements (GLEs). The traditional approach to interpreting and
modelling GLE observations assumes particle propagation only parallel to the
magnetic field lines of interplanetary space, i.e. it is spatially 1D. Recent
measurements by PAMELA have characterised SEP properties at 1 AU for the ~100
MeV-1 GeV range at high spectral resolution. Aims. We model the transport of
GLE-energy solar protons through the Interplanetary Magnetic Field (IMF) using
a 3D approach, to assess the effect of the Heliospheric Current Sheet (HCS) and
drifts associated to the gradient and curvature of the Parker spiral. The
latter are influenced by the IMF polarity. We derive 1 AU observables and
compare the simulation results with data from PAMELA. Methods. We use a 3D test
particle model including a HCS. Monoenergetic populations are studied first to
obtain a qualitative picture of propagation patterns and numbers of crossings
of the 1 AU sphere. Simulations for power law injection are used to derive
intensity profiles and fluence spectra at 1 AU. A simulation for a specific
event, GLE 71, is used to compare with PAMELA data. Results. Spatial patterns
of 1 AU crossings and the average number of crossings are strongly influenced
by 3D effects, with significant differences between periods of A+ and A-
polarities. The decay time constant of 1 AU intensity profiles varies depending
on the polarity and position of the observer, and it is not a simple function
of the mean free path as in 1D models. Energy dependent leakage from the
injection flux tube is particularly important for GLE energy particles, in many
cases resulting in a roll-over in the fluence spectrum.
