Automatic dip-picking by non-linear optimization

Lin Zhang and Jon Claerbout

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ABSTRACT

We have developed a new automatic dip-picking method that is superior to the dip-scan method in several aspects. In our method, we estimate the dip of an event through the relative time-shift between neighboring traces. The optimal time-shift is defined to be the minimizer of a non-quadratic objective function that measures the discrepancies between the neighboring traces after these traces are shifted relative to one another. To eliminate aliasing effects, data-dependent weighting functions are included in the objective function. This non-linear optimization problem is solved by searching. Once a preliminary solution is obtained, the objective function is approximately reduced to a quadratic form and the residual time-shift is then estimated by solving a linear equation. In the end, the time-shift is converted into the dip.

Examples with synthetic and field data show that the combination of the linear and non-linear optimizations enables our algorithm to have the properties of antialiasing, high resolution and high accuracy. The applications of the algorithm include event-picking, moveout corrections, local dip-filtering and missing data interpolation.