Automatic Picking in the Semblance Domain

Abstract

The specific goal of this work was to develop a method for automatic velocity picking based on the semblance function as a nonlinear optimization problem. We define the steps of conventional velocity analysis (CVA) for each CMP in the following way: first, stacking velocities are estimated by means of semblance sum along hyperbolic time trajectories producing a map of S(vrms, t0); second, manual picking is performed on this semblance map for several stacking time t0; third, interval velocities, vint, are calculated based on the picked stacking velocities, vrms, to construct an earth velocity time model, that do not require a reference earth model. The present work is multi-task as: 1. to eliminate the picking step by considering that stacking velocities are based on an interval velocity model; 2. to search for an interval velocity model that best explains the estimated stacking velocities; and 3. the search is automatic, but subject to physical constraints. Introduction Many velocity functions can be defined to represent the underground aiming the geological knowledge. Among them, the relationship between interval velocity and stacking velocity plays an important role in CVA. A primary goal in seismic data processing is the determination of both these velocities, and in CVA interval velocities are calculated from the picked stacking velocities on a semblance map using a mathematical model as, for example, the Durbaum-Dix type (Hubral and Krey, 1980). The classical drawback of the semblance peak-picking is that a visual interpretation of the map is necessary, and it is based on the amplitude and a velocity window of the semblance map, theorectically for all the CMP. The present study proposes the elimitation of the complete manual peak-picking step by seting up a model driven strategy. Therefore, methods of CVA without manual picking stand as an interesting approach. The restrictions of the present development can be stated as: (1st) limited to 1-D models; (2nd) use of the DurbaumDix model for the relation between vint and vrms; (3rd) it does not taken into account lateral variations; and (4th) the structural dips are not taken into account (Koren and Ravve, 2002). Method The CVA is performed by manual picking of points to construct a curve of velocity versus time in the semblance map for each individual common mid-point (CMP) section. But, this task carries a strong subjective decision, and it is present in the free and professional software systems. The result of this operation is a time-distance map of seismic velocity based on CMP families, and this map can be used directely for NMO correction and stack, and for time migration (Vieira, 2011). This work describes the solution and implementation of the velocity analysis as a non-linear optmization problem under a priori information and constraints, as a possibility for diminishing the direct subjective participation of the semblance map interpretation. The result of the optimization is the root-mean square velocity, vrms. This technique was originally described by (Toldi, 1989), that we denominate automatic velocity analysis (AVA), and the basic reference for the implementation was based on Press et al., (2002), and the process steps are shown in Figure 1. The optimization realized in the semblance domain was based on two methods: 1. Global Search using the Simplex method; 2. Local Search based on the Conjugate Gradient method. Enter control parameters: CMP, iterations Choose the interval velocity model Calculate the complex semblance function Apply the Simplex method to locate a Global minimum Apply the Conjugate gradient method Generate the semblance map for each CMP Present the composite result of the optimization Figure 1: Flowchart of the optimization process.