基于贝叶斯误差学习的地震勘探全波形反演理论及其应用

Exploration of tight oil & gas is a challenging research field in exploration geophysics, which is important for the explorations of oil & gas resources in our country. In this project, we focus on the problems that the acoustic or elastic wave equations cannot fully reflect the laws of wave propagations in the accumulate areas of tight oil & gas when we use the method of full waveform inversion. Novel machine learning algorithms will be designed to learn errors brought by forward modelling. Based on the learning algorithms, Bayesian inverse theory with non-Gaussian prior measure and non-Gaussian modelling error measure will be established. In addition, new regularization model will be derived by employing the Bayesian inverse theory. Then, an error learning based full waveform inversion theory will be constructed, which brought new ideas for explorations of tight oil & gas from mathematical theory perspective. This project focus on studies about mathematical theories driven by real word applications. It integrates the theory of forward equations, the Bayesian inverse theory and machine learning algorithms, which is meaningful both for studying of mathematical theories and explorations of tight oil & gas.

致密油气勘探是地震勘探领域中具有挑战性的研究课题，其对我国油气资源的开发有着重要的意义。本项目拟对全波形反演理论中，声波或弹性波方程无法准确刻画致密油气等非常规油气富集区域波的传播规律这一难题，发展新的机器学习理论与算法进行正演模型误差学习，并基于学习理论建立含有非高斯先验、非高斯模型误差测度的贝叶斯反演理论。进一步，根据贝叶斯反演理论推导出新的正则化模型，构建出基于学习算法的全波形反演方法，从而在数学理论上为致密油气勘探提出新的思路。本项目是应用问题驱动的数学理论与方法研究，集正演方程理论、贝叶斯反演理论、学习算法于一体，无论是对数学研究本身还是对油气勘探问题，都具有重要的意义。

致密油气的勘探是地震勘探领域中具有挑战性的研究难题，全波形反演方法是进行致密油气探测的重要技术手段。本项目针对全波形反演理论中声波或弹性波方程难以精准刻画波在复杂介质中传播的难题，将这一难题进行合适的数学抽象，分离出这一难题中的数学理论难点，即：模型误差的精准刻画与自动学习估计。针对模型误差的建模预估计，本课题发展了基于混合概率测度的模型误差无限维贝叶斯方法，提出了带有模型误差学习的逐次线性化方法；针对模型误差的自适应迭代学习，发展了无限维平均场变分推断理论，从而实现了误差分布超参数的自适应学习；针对后验计算复杂度高的问题，通过分析概率、物理模型，构建了新的模型数据双驱动深度学习反演方法。本项目是问题驱动的应用数学研究，其研究成果不仅丰富了现有的无限维贝叶斯与机器学习理论，同时也为地震勘探反问题的求解提供了新的思路。