The spiral structure of the interplanetary magnetic field (IMF) is known to induce intramagnetospheric azimuthal magnetic field B , which strongly correlates with the IMF B . We reconstruct this effect for the first time in 3-D, using a large set of data taken in the near/inner magnetosphere and a flexible magnetic field model based on expansions in radial basis functions (RBF). The RBF model serves here as a magnifying glass with tunable resolution, focused on the specific region of interest. In this study, we used it to explore the IMF-induced B both on a global scale (i.e., for the entire range of local times) and in the night sector only, to better visualize details in the region with the strongest "penetration" magnitude. The induced B was found to maximize on the nightside at distances R ∼10-12 R E , where it concentrates around the solar-magnetic equator and bifurcates into a pair of peaks located in predawn and postdusk sectors. The B "penetration" is associated with the IMF-induced asymmetry of field-aligned currents at the plasma sheet boundary. Even on a statistical level, the peak values of the induced B can substantially exceed the external IMF B . The effect is significantly stronger under southward IMF B z conditions and grows with increasing geodipole tilt angle. Key Points: • Global/local 3-D distributions of IMF-induced B are derived in closed field line domain using a new technique and large multiyear database • The induced B maximizes near SM equator at Xsm ∼ −10 R E where it splits into a pair of duskside/dawnside peaks and can significantly exceed IMF B • The effect is associated with asymmetry of Birkeland currents and increases under southward IMF