As Rothman (1985) points out, the selection of the cooling function is very important and can greatly speed convergence. In my method, I treat the sample interval function as a cooling function. To find a good cooling function, I first created a linear cooling function and plotted how the energy decreased as a function of sample interval. This is shown in Figure 12. In this particular example, there appear to be three sample intervals associated with large drops in energy: 185, 130, and 70. I decided to create a cooling schedule that treats the sized 70 sample interval as the critical temperature. This is shown in Figure 13. The critical temperature is where convergence is most significant.

Figure 12

Figure 13

Notice that in Figure 13, the energy drops off much quicker than in Figure 12 and therefore requires fewer iterations.

Figure 14 shows the result of applying the cooling schedule in Figure 13. It has converged to the desired event. Figure 15 shows the application of the calculated displacements to the left side of the fault. Its results are about the same quality as Figure 16, which shows the results of applying the actual known displacement to the left side of the fault.

Figure 14

makefinalmod
Applied result, the ``model'' in the center shows the result of applying the calculated displacement to the left side of the fault.
Figure 15 |

makefinalideal
Ideal applied result, the ``ideal'' in the center shows the result of applying the known displacement to the left side of the fault.
Figure 16 |

6/8/2002