Examples for the trial-and-error method gravity modeling http://www.searchanddiscovery.com/documents/2008/08189blaich/images/fig04.htm

Waveform modeling Sidao Ni et al. Science 296, 1850 (2002)

Chen et al. 2007

SA exmaple Error function F(x,y) has its global maximum value of 1.0 at x = 0, y = 0. However, it also has several secondary maxima Error function global maximum at (0, 0)

Effect of T on pdf distribution The effect of this temperature T is to exaggerate or accentuate the differences between different values of the error function.

Figure 4.5. For a model with 8 model parameters (each having 8 possible values) heat bath algorithm starts with a randomly chosen model shown by shaded boxes in (a). Each model parameter is then scanned in turn keeping all others fixed. (b) shows scanning through the model parameter m 2. Thus m26 is replaced with m23 and we have a new model described by shaded boxes in (c). This process is repeated for each model parameter.

Figure 4.6. Model generation probabilities (left) and their corresponding cumulative probabilities (right) at different temperatures. At high temperature, the distribution is nearly flat and every model parameter value is equally likely. At intermediate temperature, peaks start to appear and at low temperature, the probability of occurrence of the best solution becomes very high. A random number is drawn from a uniform distribution and is mapped to the cumulative distribution (fight) to pick a model.

Application of heat bath SA seismic waveform inversion 100 iterations Tk = T0(0.99)k (k: number of iteration)

Real data inversion: SA

11 models that gave a correlation value of 0.74 or greater

Neighborhood Algorithm (Sambridge, 1999, GJI)