By constructing more than 30 numerical models of spontaneous earthquake rupeture on heterogeneous faults, the complexity of the far-field pulse shapes (the source time function), that is, the pulse consisting of several distinct subpulses, is investigated. The influence of multiple strength barriers and/or dry friction on the far-field waveforms has been studied using the simple model of a square fault with uniformly spaced square barriers. A central asperity is allowed to break to initiate the dynamic process. It is found that the pulse duration is shorter the greater the density of barriers (ratio of barrier size to barrier spacing). The presence of friction has been found to have three different consequences. First, the slipping area is reduced giving rise to a shorter pulse duration. Second, the rate of slip propagation is reduced which increases the pulse duration. Third, the frictional stress drop, if present, increases the amplitude of the pulse. The interaction of these effects together with the effect of the barriers results in different pulses depending on the relative role of these effects. Breaking of multiple asperities with relatively short time delay between their fracturing produced a single pulse with ripples in its rising portion, the pulse duration depending on the total time required for the asperities to break. Breaking of, say, two asperities with sufficient time delay between them produced a double pulse which is in accord with the asperity model of complex earthquakes. In one case of a fault with barriers and friction, an additional peak was observed in some directions from the source, the peak form and amplitude being essentially the same as those of the peaks due to breaking of asperities. One may conclude that each subpulse observed on a complex far-field pulse is not necessarily interpretable as being due to the failure of an asperity on the fault. Furthermore, for the subpulses which can be related to asperity fracture, the duration is not determined by the size of the corresponding asperity but rather by the physical conditions on the fault surrounding the asperity. ¿ American Geophysical Union 1988