Figure 4. Cumulative rate for all characteristic rupture sources in the calculation sequence is shown as heavy solid line. The mean rate for each characteristic rupture source was used without sampling. The distribution of magnitudes obtained at the branch tips of the calculation sequence (heavy dashed line) shows the smoothing effect of sampling over parametric distributions in the calculation. A Gutenberg-Richter (G-R) model (light broken line) fit by least-squares over the range 6.5<=M<=7.7 to the cumulative rates obtained at the branch tips has b-value of 0.91±0.02 (one standard deviation) and a=4.56±0.15. Two relations for the cumulative rate of "background" earthquakes (shown by light solid lines) are derived from the two G-R models: a (incremental)=3.129, b=0.8624; and a (incremental)=2.989, b=0.8320.