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Speed and precision of dip moveout

Patrick Blondel

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The oil industry's need for high-quality images of the Earth's interior has become more and more pressing in last ten years. In practice, the quality of seismic imaging increases with the amount of data acquired. Therefore, seismic surveys often include three-dimensional and high-coverage acquisitions that result in a huge quantity of data to process. For timely results each step of the processing sequence must be as fast as possible. A time-consuming step in a standard seismic imaging flow is dip moveout correction. Therefore, enhancing the speed of this step without sacrificing precision is essential to improve the state of seismic imaging.

The rapid processing of a huge amount of data requires us to simplify complex algorithms. Under the constant velocity assumption, the formulation of the dip moveout correction reduces to the equation for an ellipse. Because its expression remains simple in three dimensions, the process is computationally efficient. However, in the case of an irregular data acquisition geometry, the chaotic spatial spreading forbids a trace-parallel implementation. This problem is solved by a time-parallel implementation that allows a fast processing for any azimuthal distribution in the data.

There are two ways to improve precision in amplitude balancing and focusing of the seismic images with the dip moveout process. The first is to apply a proper weight along the operator, which is achieved at almost no extra computational cost. The second way is to consider depth-variable velocity. The dip moveout correction then becomes computationally expensive. However, an approximation valid for gently dipping reflectors allows the variable-velocity process to be almost as fast as the constant-velocity process while improving the focusing of seismic events. This method is easily applicable in three dimensions as a first-order approximation of the theoretic ``saddle'' operator.

The oil industry has become more reliant on seismic data interpretation than in the past. Two decades ago, only basic processing was required to find a potential oil trap. Gradually, the processing sequence has been refined to detect and outline new traps that were previously considered not interesting or not even considered at all. However, seismic acquisition and processing can be improved to more accurately reflect the Earth's structure. Currently, we enhance the acquisition by densifying the shot and geophone distribution or shooting three-dimensional surveys and we refine the imaging tools by taking into account variable velocity and amplitude effects. Consequently, the processing industry needs to develop fast and accurate three-dimensional processing tools.

Nowadays, a standard industrial seismic processing sequence almost always involves the dip moveout correction. When a constant-velocity Earth model is considered, the speed of this process makes it very attractive, even for three-dimensional data. However, the imaging quality may be poor in the case of three-dimensional data, when the amplitude and aliasing effects are not accurately considered. On the other hand, the dip moveout process can gain in precision by considering variable velocity, but it then loses rapidity.

In this paper, I address the problems of speed and precision of the dip moveout process in a three-dimensional Earth model. Part I reports on research in which I make the limiting assumption of a constant velocity model in order to design a simple, fast dip moveout process. After an analysis of the amplitude and phase of the dip moveout operator, I present a parallel implementation of the process. In the work described in Part II, I make the assumption of a depth-variable velocity model in order to increase the precision of that process. This part compares the results of two different methods of v(z) dip moveout in two dimensions (, ) after post-stack migration. Finally, it includes a formulation for an accurate three-dimensional dip moveout process in a depth-variable velocity medium that Craig Artley, Alexander Popovici, Matthias Schwab, and I derived in a previous paper ().

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