Waveform data from a borehole network of broadband seismographic stations have been used to study microearthquakes along the Parkfield segment of the San Andreas fault (SAF). Analysis of almost 10 years of such data demonstrates that much of the seismicity in this region consists of repeating sequences, quasiperiodic sequences of earthquakes that are essentially identical in terms of waveform, size, and location. Scalar seismic moments have been estimated for 53 of these repeating sequences and combined with equivalent estimates from 8 similar but larger event sequences from the Stone Canyon section of the fault and the main Parkfield sequence. These estimates show that seismic moment is being released as a function of time in a very regular manner. Measurements of the moment release rate, combined with an assumed tectonic loading rate, lead to estimates of the seismic parameters source area, slip, and recurrence interval. Such parameters exhibit a systematic dependence upon source size over a range of 1010 in seismic moment that can be described by three simple scaling relationships. Several implications of these scaling relationships are explored, including the repeat time of earthquakes, average stress drop, strength of the fault, and heat generated by earthquakes. What emerges from this analysis of moment release rates is a quantitative description of an earthquake process that is controlled by small strong asperities that occupy less than 1% of the fault area. This means that the fault is highly heterogeneous with respect to stress, strength, and heat generation. Such heterogeneity helps to explain many of the apparent contradictions that are encountered in the study of earthquakes, such as why faults appear weak, why significant heat flow is not observed, how significant high frequencies can be generated by large earthquakes, and how various geologic features such as pseudotachylytes might form.