Next: NON-LINEAR OPTIMIZATION Up: Zhang and Claerbout: Automatic Previous: Zhang and Claerbout: Automatic

# Introduction

Picking is a process of identifying the events or estimating the parameters of the events on seismic sections. This process can be done manually, or automatically by computers. Because human eyes have strong capability of recognizing seismic events on a noisy background, manual picking are often more robust than any computer algorithms. But manual picking has the disadvantage of being inaccurate in estimating the parameters of events. Also, manual picking is inefficient and expensive. When a seismic section contains a great many of events, automatic picking becomes more than necessary.

A commonly used algorithm for automatic dip-picking is dip-scan. The basic principle of the algorithm is that the optimal estimate of the dip of an event corresponds to the maximum value of the local slant-stack. This method does not work when data is insufficiently sampled. Moreover, the accuracy of the estimation is limited by the dip-sampling interval of the dip-scan and its spatial resolution is limited by the spatial extent of the dip-scan.

Claerbout (1990) proposed an automatic dip-picking method that is based on a plane-wave destructor operator. Because the plane-wave destructor is a 2-D filter that can be represented by a differencing star, this algorithm is computationally efficient and inexpensive. It has its spatial resolution equal to the spatial-sampling interval of data. The disadvantage of the method is that the finite difference operator is susceptible to spatial aliasing as well as distortions at spatial frequencies that are high but not yet aliased. Using a high-order finite differencing operator would reduce the distortions, but it will also reduce the spatial resolution.

While studying the missing data interpolation, Nichols (1990) used the plane-wave destructor operator to estimate the dips of events. He solved the aliasing problem by using the smoothed version of data to obtain the initial estimates, and then refining them after the missing traces are interpolated. The application of this method is limited to data that has low frequency and low wavenumber components.

In this paper, we describe a new algorithm that does automatic dip-picking. We assume that the events on a seismic section do not intersect. In other words, at each point on the seismic section, there is a unique value that defines the dip of the event at that point. We also assume that data is adequately sampled along the time axis, but we do not make any assumptions on the spatial-sampling rate. In our method, the relative time-shift between neighboring traces is estimated by minimizing a non-quadratic objective function. Data-dependent weighting functions are included in the objective function to remove the effects of aliasing on picking. After a preliminary estimate of the relative time-shift is resolved, the objective function is approximately reduced to a quadratic form and the residual time-shift is obtained by solving a linear equations. Finally the time-shift is converted into the dip.

The paper is organized in four parts: first, we will formulate the non-linear optimization problem and explain why the effects of aliasing on dip-picking disappear; then we show that the residual time-shift can be estimated efficiently and accurately by solving a linear optimization problem; third, we will use examples with synthetic and field data to confirm the results predicted by theory and illustrate the applications of the algorithm. Finally, in conclusion, we will discuss the possible improvements and extensions of the algorithm.

Next: NON-LINEAR OPTIMIZATION Up: Zhang and Claerbout: Automatic Previous: Zhang and Claerbout: Automatic
Stanford Exploration Project
1/13/1998