Dynamic non-linear optimization for imaging in seismic exploration (DNOISE)

这项建议描述了一个系统的五年研究项目，将现代计算中的最新技术应用到地震成像、反演和处理中的问题上，并应用调和分析。这些新技术的应用需要地震转移，从传统的操作员设计转向构建多尺度帧分解。这些分解必须由多维原型波形或原子组成，模仿地震和地下反射器的方向性和局部化多个长度尺度特征。通过DNOISE项目，我们寻求资金来补充和扩大目前在地震成像和建模实验室(SLIM)运行的工业研究项目。因此，主要挑战之一将是恢复技术的发展，这些技术不仅对不完整和有噪音的数据是稳定的，而且在成像过程中必须保持频率内容。我们计划通过利用最近在信息论领域提出的统一不确定性原则来解决地震成像问题来解决这一挑战。这些不确定性原则提供了通过促进信号稀疏性的非线性优化技术来预测信号恢复准确性的机制。我们希望回答这样一个基本问题：“在给定某些采集几何形状的情况下，可以达到什么精度？”为了回答这个问题和其他问题，我们提议扩展目前的理论，并开发(1)适应地震成像环境的定向框架，可以处理在不规则网格上采样的图像；(2)适用于框架的统一不确定性原则，包括由地震成像算子引起的原则；(3)适用于非常大的地震数据集的专门的非线性优化算法。通过将基于线性最小二乘的反演技术替换为基于促进稀疏框架展开的更精确的非线性模型的反演技术，DNOISE的结果将是地震图像质量和分辨率的实质性改善。

This proposal describes a systematic five-year research project to apply recent techniques in modern computational and applied harmonic analysis to problems in seismic imaging, inversion, and processing. The application of these new techniques requires a seismic shift that moves away from traditional operator design towards the construction of multi-scale frame decompositions.  These decompositions must consist of multi-dimensional prototype waveforms or atoms that mimick the directional and localized multiple lengthscale character of seismic and subsurface reflectors.  With the project DNOISE, we seek funding to complement and expand current industrial research projects operating in the Seismic Laboratory for Imaging and Modeling (SLIM).    One of the main challenges will be the development of recovery techniques that are not only stable for incomplete and noisy data - they must also preserve frequency content during imaging.  We plan to address this challenge by leveraging the recently proposed uniform uncertainty principles in the field of information theory to the seismic-imaging problem.  Uncertainty principles provide machinery to predict the accuracy of signal recovery by techniques in nonlinear optimization that promote signal sparsity. We hope to answer the basic question: ``What accuracy is attainable given certain acquisition geometries?'' To answer this and other questions, we propose to extend the current theory, and to develop (i) directional frames adapted to the seismic-imaging context that can deal with images sampled on irregular grids; (ii) uniform uncertainty principles that apply to frames, including those that arise from seismic-imaging operators; (iii) specialized nonlinear optimization algorithms suitable for very large seismic data sets. By replacing inversion techniques based on linear least-squares with those based on a more accurate nonlinear model that promote sparse frame expansions, the outcome of DNOISE will be a substantial improvement in the quality and resolution of seismic images.