Seismic data interpolation beyond aliasing using regularized nonstationary autoregression |

In the second step, a similar problem is solved, except that the filter is known, and the missing traces are unknown. In the decimated-trace interpolation problem, we squeeze (by throwing away alternate zeroed rows and columns) the filter in equation 3 to its original size and then formulate the least-squares problem,

subject to

where represents the interpolated output, and and use the original shift as the interval; i.e., the shift interval equals 1.

We carry out the minimization in equations 4, 13, and 14 by the conjugate gradient method (Hestenes and Stiefel, 1952). The constraint condition (equation 15) is used as the initial model and constrains the output by using the known traces for each iteration in the conjugate-gradient scheme. The computational cost is proportional to , where is the number of iterations, is the filter size, and is the data size. In our tests, and were approximately equal to 100. Increasing the smoothing radius in shaping regularization decreases in the filter estimation step.

Seismic data interpolation beyond aliasing using regularized nonstationary autoregression |

2013-07-26