Affiliation:
1. Harbin Institute of Technology, Department of Mathematics and Center of Geophysics, Harbin, China. (corresponding author)
2. Peking University, School of Earth and Space Sciences, Beijing, China.
Abstract
Seismic samples are generally designed to be placed on perfect Cartesian coordinates, that is, on-the-grid. However, sampling geometry is disturbed by obstacles in field applications. Large obstacles result in missing samples. For small obstacles, geophones or sources are placed at an available off-the-grid location nearest to the designed grid. To achieve simultaneous off-the-grid regularization and missing data reconstruction for 3D seismic data, we develop a new mathematical model based on a new combined sampling operator, a 3D curvelet transform, and a fast projection onto convex sets (FPOCS) algorithm. The sampling operator is combined with a binary mask for on-the-grid samples reconstruction and a barycentric Lagrangian (BL) operator for off-the-grid samples regularization. A 2D BL operator is obtained using the tensor product of two 1D BL operators. The inversion problem is efficiently solved based on FPOCS. This method is tested on synthetic and field data sets. The reconstruction results outperform the methods based on the binary mask in terms of signal-to-noise ratio and visual effect.
Funder
National Key Research and Development Program of China
Fundamental Research Funds for the Central Universities
National Natural Science Foundation of China
Publisher
Society of Exploration Geophysicists
Subject
Geochemistry and Petrology,Geophysics