能源勘探领域长期面临非均一地震数据插值的难题。由于检波器无法精确放置在理论网格点,现有均一插值技术常导致结果存在偏差和细节失真。

为解决此问题,提出一种基于扩散概率模型的非均一插值新方法。扩散概率模型是一种新兴的生成式深度学习模型，分为扩散和生成两个过程。在扩散过程中，对完整地震数据迭代施加噪声，训练神经网络的去噪能力。在生成过程中，使用神经网络对噪声数据迭代去噪，得到重构数据。本文利用插值算子计算迭代数据与采集数据的偏差，作为神经网络的额外输入，提高扩散概率模型的非均一插值能力。在数值实验部分，使用二维合成数据集与实际数据集对非均一采样进行了测试，并使用均一插值模型与本文所提模型进行比较。

结果表明该方法显著提升了扩散概率模型对非均一采样的处理能力，在合成数据与实际数据测试中，信噪比大约提高了7 dB，有效提高了深度学习方法对非均一插值的精度，为非均一地震数据插值算法提供了新的思路。

The non-uniform interpolation of seismic data is identified as a prolonged challenge in energy exploration. Since geophones cannot be precisely placed at positions corresponding to theoretical grid points, current uniform interpolation techniques frequently suffer deviations and detail distortion.

This study proposed a novel non-uniform interpolation method based on a diffusion probabilistic model, which is an emerging generative model in deep learning that involves the diffusion and generation processes. In the diffusion process, noise is added to the complete seismic data iteratively to train the denoising capability of the neural network. In the generation process, the neural network is employed for iterative denoising of data containing noise to obtain the reconstructed data. In this study, interpolation operators were employed to calculate the deviations between iterative and sampled data. These deviations were then used as the additional inputs of the neural network to improve the non-uniform interpolation capability of the diffusion probabilistic model. In the numerical experiments, the non-uniform sampling was tested using 2D synthetic and actual datasets, and the uniform interpolation model was compared with the model in this proposed study.

The results indicate that the proposed method significantly enhanced the processing capability of the diffusion probabilistic model for non-uniform sampling. The tests of synthetic and actual data revealed an increase of approximately 7 dB in the signal-to-noise ratio. Therefore, the proposed method can effectively improve the precision of deep learning for non-uniform interpolation, providing a new approach for non-uniform interpolation algorithms of seismic data.