Journal of Computational Mathematics (JCM) is an international scientific computing journal founded by Professor Feng Kang in 1983, which is the first Chinese computational mathematics journal published in English. JCM covers all branches of modern computational mathematics such as numerical linear algebra, numerical optimization, computational geometry, numerical PDEs, and inverse problems. JCM has been sponsored by the Institute of Computational Mathematics of the Chinese Academy of Sciences.

We study a Filon-type method for the computation of multivariate highly oscillatory integrals over a general simplex. A new kind of multivariate Hermite interpolation is proposed. The existence of the multivariate Hermite interpolation leads towards the construction of an extended Filon-type methods. Such methods attain good accuracy for all values of the oscillatory parameter when increasing, as required, the interpolation order. Numerical experiments are provided to illustrate the effectiveness of our approach.

Ocean Bottom Node (OBN) acquisition is a technique for marine seismic survey that has gained increased attention in recent years. The removal of shear wave noise from the vertical component of receivers plays a crucial role in the subsequent processing and interpretation of OBN data. Previous solutions suffer from noise residue or signal impairment for complex noise and signal overlap scenarios. In this work, we present and explore a self-supervised deep learning approach to attenuate shear wave noise in OBN data. It applies a deep neural network (DNN) to perform adaptive subtraction and comprises two steps to remove the noise associated with the two horizontal components of receivers, respectively. The two horizontal components are considered as noise reference and are sequentially fed into the DNN, and the DNN predicts the actual leaked noise from the contaminated vertical components data. The self-supervised method achieves improvements in the signal-to-noise ratio (SNR) on a set of synthetic data. The implementation of our method on field data demonstrates that it effectively attenuates the shear wave noise and preserves the valid signal.

We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example is integrals of products of Legendre functions.