Automatic velocity picking by simulated annealing

Introduction

Measuring errors in velocity is one of the key steps in the processing of seismic data. An accurate velocity model produces accurate depth migration and optimal stack response and can be used directly as the lithology indicator. Residual migration has been shown to be a powerful tool for performing velocity error analysis because of its low computational cost (Rothman et al., 1985; Sava, 2003). After residual migration, we have a cube of residual migration images as a function of $\rho$, the ratio of true velocity to current velocity. Semblance panels corresponding to each value of $\rho$ are computed to evaluate the focusing of the residual migration. However, manual velocity picking is required to obtain the updated velocity model.

An ideal velocity model is both geologically significant and geophysically smooth. It is easy to pick the peaks (maximum values) of the semblance panels for each CMP at each depth. The peak $\rho$ values correspond to the optimal focusing update of the velocity model; however, those values often have large variations both horizontally and vertically. To solve the nonlinear velocity inversion problem, Singh et al. (2008) proposed a customized, multiobjective evolutionary algorithm. The simulated annealing algorithm is also a global optimization method and is capable of coping with the nonlinear relationship between the seismic data and the velocity model.

The simulated annealing algorithm is a Monte Carlo approach for minimizing multivariate functions. The term ``simulated annealing'' derives from the roughly analogous physical process of heating and then slowly cooling a substance to obtain a strong crystalline structure. In the simulation, a minimum of the cost function corresponds to this ground state of the substance. The simulated annealing process gradually lowers the temperature in stages until the system freezes and no further changes occur.

In this paper, we customize the simulated annealing algorithm to automatically pick the semblance panels and give an optimized velocity model which is both semblance focused and smooth. The algorithm is briefly explained and its objective functions are introduced. We perform experiments on different sets of initialization and constraint parameters, the results and the convergence of which are compared. To test the accuracy of the velocity models, we apply them to the residual migration cube.

Automatic velocity picking by simulated annealing