Seismic Data Interpolation Using 5D-FCN: A Preliminary Study

Convolutional neural networks (CNNs) have emerged as a primary method for seismic data interpolation. These networks are trained on a large dataset, and interpolation can be accomplished by inputting incomplete data into the learned network without the need for parameter selection, as in the traditional method. However, most studies have focused on 2-D/3-D interpolation cases, leaving 5-D situations not properly handled. To address this issue, we propose a novel 5-D convolutional block designed to capture features in seismic records in 5-D, leading to the construction of a simple and effective 5-D fully convolution network (5D-FCN). Specifically, leveraging the linearity of convolution, we represent a 5-D convolution operator with the aid of a number of 3-D convolution operators. This allows for efficient implementation of 5-D convolution using 3-D convolution on popular deep-learning platforms such as Pytorch and TensorFlow. We conduct experiments on both synthetic and field examples. Compared with the 3-D-CNN-based 3-D network (3D-Unet) method, which interpolates 5-D data by spliting it into a combination of 3-D blocks, and the damped rank-reduction (DRR) method, the 5D-FCN demonstrates superior interpolation performance. In the synthetic example, the signal-to-noise ratio (SNR) values for data recovered by DRR, 3D-Unet, and 5D-FCN are 13.54, 12.08, and 15.00 dB, respectively. In the field example, our method exhibits superior spatial coherence in the reconstruction results.