Seismic data antialiasing interpolation using sparse Radon transform and dynamic mask function

Abstract

Interpolation of regularly sampled data with aliasing is important for seismic data processing. However, conventional antialiasing interpolation methods based on a low-frequency constraint may generate inaccurate interpolation results for high-frequency data with severe wrap around. We have developed a sparse Radon transform-based projection onto convex sets interpolation method with a 2D dynamic mask function. The new mask function exploits the frequency and dip information in a 2D domain and can better guide the interpolation of high frequencies with severe wrap around. The implementation of the proposed method includes four steps: (1) perform a forward f-k transform on the input data, extract the unaliased low-frequency low-wavenumber information from it, and perform the inverse f-k transform to obtain the unaliased part of the input data; (2) perform a sparse Radon transform on the unaliased data obtained in step one and apply an exponential threshold to obtain a mask function; (3) perform a sparse Radon transform on the input data, apply the mask function in step two to it, and perform the inverse Radon transform; and (4) reinsert the original traces in the input data. The four steps are repeated until an acceptable result is reached. Numerical examples of synthetic and field data demonstrate that the proposed method is an effective and robust method for aliased seismic data interpolation. The results of the proposed method have higher precision than that of the conventional antialiasing interpolation methods. Data with 80% regularly missing traces are still well interpolated using the proposed method.