Automatic velocity picking by simulated annealing

Representation of the velocity model

Although we are picking $\rho$ instead of picking actual velocities, discussing the representation of the velocity model is still helpful to better understand the shape and size of model parameters. Kirkpatrick et al. (1983) report that the run time of simulated annealing is related almost linearly to the number of parameters being estimated. Thus, a proper presentation of velocity model which requires fewer parameters will greatly decrease the computational cost of SA. Generally, two widely used classes of velocity models are blocky and smooth velocity models. Blocky models represent the geologically stratified sedimentary rocks, while smooth models have many numerical advantages. Both have been utilized for velocity optimizations using global methods (Docherty et al., 1997; Jervis et al., 1996; Mansanné, 2000).

Here, we are optimizing the residual migration parameter $\rho$ rather than velocity itself. Regarding the initial velocity model, $\rho$ values at different location might be independent with each other, suggesting it is better for us to use a grid to represent the $\rho$ model. At this stage, we optimize the $\rho$ model point by point using grid samplings.

When perturbing the system, we select one sample in the velocity model randomly, and change the velocity at that point to a random velocity value within a reasonable range. The main obstacle for a practical application of such a global optimization method is the computational cost. The larger the parameter space that must be searched and the greater the number of parameters, the more expensive the method tends to be. Thus, the prior knowledge could be both useful for speed and convergence. There are two slots where the prior knowledge can be inserted into the algorithm: initialization and constrains. However, experiments show that incorporating the prior knowledge into initialization is more efficient than into constrains. Thus, we initialize the system by the semblance peaks and randomly perturbing the system by changing the value to any possible $\rho$ value defined by residual migration. Weights for the two objective functions are chosen arbitrarily. The results are presented in the next section.

Automatic velocity picking by simulated annealing