Least-squares Kirchhoff migration with non-smooth regularisation strategy for subsurface imaging
Jie Hou 1 2 3 Yanfei Wang 1 2 3 4
+ Author Affiliations
- Author Affiliations
1 Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China.
2 University of Chinese Academy of Sciences, Beijing 100049, China.
3 Institutions of Earth Science, Chinese Academy of Sciences, Beijing 100029, China.
4 Corresponding author. Email: yfwang@mail.iggcas.ac.cn
Exploration Geophysics 49(6) 793-802 https://doi.org/10.1071/EG16132
Submitted: 3 November 2016 Accepted: 22 October 2017 Published: 21 December 2017
Abstract
During the past several decades, many types of wave-equation migration methods arise for subsurface structure imaging. The classical Kirchhoff migration, however, is still widely adopted in the petroleum industry owing to its flexibility and computational efficiency. In constant density isotropic acoustic media, a basic assumption of the Kirchhoff migration is that every point of the subsurface model is supposed to be a diffractor which scatters wavefield energy to every direction, and hence collecting the scattered energy of all directions is the basic requirement for focusing the diffractor. Factors influencing the final image quality include incomplete data acquisition, multipathing from the surface to the imaging point, and insufficient illumination under complex overburden. All these factors can be theoretically taken into account in the migration weighting coefficient. However, computation of the weighting coefficient is hard work. In view of this difficulty, a fast regularising least-squares Kirchhoff migration algorithm is presented in this paper. It not only accounts for the irregular and incomplete data sampling (e.g. limited recording aperture, coarse sampling and acquisition gaps), but also compensates for the anomalous ray coverage and multipathing problem except for the shadow zone in the media. For the purpose of attenuating migration artefacts and providing a clear and accurate image of subsurface reflectivity, regularisation strategies are applied. The classical regularisation strategy may easily lead to over-regularisation or insufficient regularisation; we try to balance these two effects in this paper. The method is called the hybrid regularisation which incorporates smoothing and non-smoothing scale operators. The algorithm is implemented using a fast gradient decent solution method based on the Rayleigh quotient being used. Numerical experiments show that this hybrid regularisation method is powerful in handling the sparsity and smoothness of the model parameters.
Key words: fast gradient algorithm, least-squares migration, non-smooth regularisation.
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