A theoretical description of para-hydrogen-induced polarization (PHIP) is developed, applicable to coupled multi-spin systems that are polarized at an arbitrary magnetic field. Scalar spin-spin interaction is considered to be the leading factor governing PHIP formation and transfer. At low magnetic fields, these interactions make the spins strongly coupled and cause efficient, coherent re-distribution of spin polarization. We describe the effects of strong coupling and field cycling for a three-spin system and compare calculated spectra with the experimental examples available. By using a fast field-cycling device, which shuttles the whole NMR probe, and thereby makes high-resolution NMR detection at high field possible, we studied PHIP patterns for a set of different fields between 0.1 mT and 7 T. PHIP spectra were measured for ethylbenzene as the product of a catalytic reaction between para-hydrogen and styrene. Additionally, the polarizations of ethylbenzene bound to the catalyst, and of the starting styrene molecule were analyzed. This is the first time that the full field dependence of PHIP has been determined experimentally. The spectra obtained are in perfect agreement with the simulations for the CH(2) and CH(3) protons of ethylbenzene and even for its weakly-polarized aromatic protons. Analysis of styrene polarization shows that the time profile of the field variation has pronounced effects on the PHIP pattern. Our study gives evidence that scalar spin-spin interactions determine the PHIP patterns. Possible applications of the theory are discussed.