Automatic picking is usually accomplished through optimization. It involves two steps: defining an objective function and optimization picking. Two types of objective functions commonly used are error measures (Martinson et al., 1982; Zhang and Claerbout, 1990) and coherence measures (Leaney and Ulrych, 1987; Biondi, 1990). Optimal picking either minimizes an error measure or maximizes a coherence measure. A variety of algorithms have been employed to extremize objective functions. Among them, iterative methods and search methods are the most popular ones. Iterative methods are computationally efficient, but have two drawbacks: they require an initial solution, and, for non-linear optimization problems, they may not find the globally optimal solution. Search methods do not have these two problems, however, they are often computationally expensive, and sometimes even impossible to implement. The accuracy of a serach method depends on the increment at which the solution space is sampled.
In this paper, I generalize the concept of error measure from two channels to multichannel, and define picking as a process of estimating parameters through constrained optimization. I show that if an L2 norm is used, minimizing an error measure is equivalent to maximizing a coherence measure. I use a fast search algorithm to get an initial solution to the non-linear optimization problem, and then refine the solution by estimating the residuals through linear optimization. I apply this method to several picking problems in data processing and obtain satisfactory results.
The first section of this paper describes different objective functions and their relations. The following sections explain how to solve the constrained non-linear optimization problem to obtain an initial pick and how to estimate residual corrections to improve the results. The fourth section shows the application of the method to specific problems, such as dip-picking, event-picking, well-log interpolation and velocity picking. Finally, I will discuss possible improvements and extensions of the method.