Simulated annealing for pattern detection and seismic analysis

Simulated annealing (SA) is adopted to detect the parameters of line, circle, ellipse, and hyperbola. The equation of pattern is defined under translation and rotation. The distance from all points to all patterns is defined as the system error. Also we use the minimum error to determine the number of patterns. The parameters of the pattern are learned with probability in SA. The proposed SA parameter detection system can search a set of parameter vectors for the global minimal error. In the seismic experiments, the system can well detect line of direct wave and hyperbola of reflection wave in the real seismic data. In the seismic data processing, the reflection curves on common depth reflection point (CDP) gathers are hyperbolic patterns. So using SA, the parameters of each hyperbolic pattern can be detected. The parameters are used to calculate the root-mean-squared velocity V_rms. The V_rms is used to the normal-moveout (NMO) correction and stacking to reconstruct the image of the subsurface. Using the result of SA hyperbolic parameter detection, it is a novel method in the seismic velocity analysis.