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

该提案描述了一个系统的五年研究项目，将现代计算和应用谐波分析中的最新技术应用于地震成像，反演和处理中的问题。这些新技术的应用需要从传统的算子设计转向多尺度框架分解的构建。 这些分解必须由多维原型波形或原子组成，这些波形或原子模仿地震和地下反射体的定向和局部化的多个长度尺度特征。 通过DNOISE项目，我们寻求资金来补充和扩大在成像和建模地震实验室（SLIM）中运行的当前工业研究项目。 其中一个主要挑战将是恢复技术的发展，不仅是不完整的和嘈杂的数据稳定-他们还必须保持成像过程中的频率内容。 我们计划利用最近提出的统一不确定性原则，在信息论领域的地震成像问题，以解决这一挑战。 不确定性原理提供了通过非线性优化技术来预测信号恢复精度的机制，该技术促进了信号稀疏性。我们希望回答这个基本问题：``给定某些采集几何形状，可以达到什么样的精度？为了回答这个问题和其他问题，我们建议扩展当前的理论，并开发（i）适应地震成像背景的方向框架，可以处理在不规则网格上采样的图像;（ii）适用于框架的统一不确定性原则，包括那些由地震成像算子产生的原则;（iii）适用于非常大的地震数据集的专门的非线性优化算法。通过用基于促进稀疏帧扩展的更精确的非线性模型的反演技术取代基于线性最小二乘的反演技术，DNOISE的结果将是地震图像的质量和分辨率的大幅提高。

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.