The process of adiabatic acceleration of relativistic cosmic rays between two converging shocks, through the first-order Fermi mechanism, to which the unusual ground level event (GLE) of August 4, 1972, was attributed earlier is examined quantitatively, the nature of interplanetary shock waves and their propagation being taken into account. In the formal computational model the net evolution of the particle flux is determined by the balance between the acceleration of particles reflected from the moving shock waves and the loss of those particles which pass through the shocks. Comparison of the results of the theoretical calculations with the measurements has revealed that the observed abnormalities are a natural consequence of the proposed process. In particular, the computed times of maximum and the ratio of the enhancement at the mountain altitude South Pole station to that at the sea level polar neutron monitors are in good agreement, as is the rapid decay of the particle flux after the maximum. The initial growth of the nucleonic intensity appears to be delayed with respect to the prediction, but this discrepancy can be ascribed to the complexities in attempting to uniquely disentangle the GLE from the behavior of the total cosmic ray flux and to the late development of the particle reflection coefficient of the interplanetary shock fronts. An intensive search has revealed that the requisite conditions for observing GLE representing acceleration between converging shocks has occurred only twice over a period of two solar cycles, and on both occasions an abnormal GLE was in fact observed.