Cooling schedule

As () 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 . 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 . The critical temperature is where convergence is most significant.

 

trialschedule
Figure 12 Trial cooling schdule. Top: input cooling schedule drops linearly with iterations. Middle: energy(617#617) drops in steps with iterations. Bottom: energy(617#617) drops in step with sample interval. This is used to determine the more efficient cooling schedule in Figure .

 

coolingschedule
Figure 13 Cooling schedule. Top: input cooling schedule based on trial cooling schedule designed to spend more iterations near the critical tempurature. Middle: energy(617#617) drops in steps with iterations. Bottom: energy(617#617) drops in step with sample interval.

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

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

 

anneal_final
Figure 14 Cross-correlagram with overlay of final solution and known displacement.

 

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

 

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