Self-learning regression interpolation based on Ricker kernel function for seismic data

Abstract

Seismic data interpolation techniques are extremely economical for removing negative effects resulting from insufficient spatial sampling. In recent years, self-learning mechanism-based methods (relatively intelligent methods), such as machine learning (ML) and deep learning, have increasingly attracted the attention of many scholars. Support vector regression machine (SVR), a kind of ML method, can obtain good reconstructed performance for seismic data interpolation. However, the performance is influenced directly by the kernel function, which controls the map from the input space to the feature space. In other words, a good and suitable kernel function can contribute to the extraction of good features and improve the self-learning ability. In this paper, Ricker kernel function suitable for seismic data, rather than the traditional Gaussian kernel function, will be introduced and applied in the new SVR-based interpolation method. In detail, the Ricker wavelet is widely used to simulate seismic data. And the Ricker kernel function can be used specially for the seismic data process. Under the guarantee of the special kernel function, the input time-space vector series are trained as a better model for future prediction of missing seismic data. Numerical experiments on synthetic and real field data show better reconstruction ability than that of SVR based on the traditional kernel function. Furthermore, we discuss the difference between the relatively shallow ML method (SVR) and the deep learning neural networks method. Except for the computer hardware, deep neural learning methods will impose stringent requirements on the training data, not only with respect to quantity but also including data quality. From this perspective, SVR shows more flexibility in the self-learning process.