Mismatches between data and physics for geophysical applications

我的研究致力于创造实用的方法，用于通过地震技术获得的数据的数值处理和反演。在我们的领域，我们获得了大量的数据，其中包含了地下地质的编码信息，问题是在波传播和信号分析的丰富理论的背景下解码这些信息。这种大数据解码过程通常以串行方式应用，首先尝试将信号从随机和相干噪声中分离出来，然后估计产生该信号的最合理的模型。驱动我们科学的大量地震数据在某些方面是高度冗余的，但同时在其他方面又是稀疏的，几乎不够用。利用数据的冗余性将信号从噪声中分离出来。只有在这一初始步骤之后，才从信号中提取采样较少的信息，并进行反演以估计地球模型。这种分而治之的方法有两个问题。首先，初始信号提取和后续反演之间的脱节是人为的，而不是自然的。其次，由于我们的信号估计技术和数值近似的限制，在分离过程中信号丢失。 我的研究计划的目标是用一种综合方法取代上述两步方法，该方法结合了信号提取和估计步骤。 这将通过嵌入反馈回路中的处理步骤来完成，这些反馈回路连贯且并行地而不是串行地起作用。实现这一目标的研究计划将需要实用和发现型元素，首先是仔细的编程和数据分析，第二是在处理算子及其连接中实现波物理学的新方面。这项发现补助金提案涵盖了这些要素中的第二个。 该研究计划的一个关键成果将是提高地球物理信息的分辨率，以揭示微妙和微妙的数据变化。这些领域的进展将对三维地震技术产生变革性影响，将其集中在盖层完整性评估等领域，这对油砂蒸汽注入（SAGD）和二氧化碳处理至关重要。通过使地震数据处理更加高效和稳健，我们可以对地震采集和生产的环境足迹产生积极影响。

My research is dedicated to the creation of practical methods for numerical processing and inversion of data acquired through seismic techniques. In our field, we acquire enormous volumes of data, which contain encoded information about geology in the subsurface, and the problem is to decode that information in the context of rich theories of both wave propagation and signal analysis. This big-data decoding process is usually applied in a serial fashion, which attempts first to separate the signal from random and coherent noise, and then to estimate the most plausible models that produce that signal. The large volumes of seismic data driving our science are highly redundant in some respects, but at the same time sparse and barely sufficient in others. The redundancy of the data is utilized to separate the signal from noise. Only after this initial step is the less well-sampled information extracted from the signal and inverted to estimate an Earth model. There are two problems with this divide and conquer approach. First, the disconnect between the initial signal extraction and the subsequent inversion is artificial, not natural. Second, signal is lost during the separation process because of limitations in our signal estimation techniques and the numerical approximations made. The goal of my research program is to replace the two-step approach above with an integrated approach, which combines the signal extraction and estimation steps. This will be done with processing steps embedded in feedback loops which act coherently and in parallel, not serially. A research program achieving this goal will require both practical and discovery-type elements, the first being careful programming and data analysis, the second being the realization of new aspects of wave physics in processing operators and their connections. This Discovery Grant proposal covers the second of these elements. A key outcome of the research program will be to improve the resolving power of geophysical information to expose subtle and delicate data variability. Progress in these areas will be transformative for 3D seismic technology, placing it centrally in areas like caprock integrity assessments, essential for steam injection in oil sands (SAGD), and CO2 disposal. By making the seismic data processing more efficient and robust to poor sampling, we can positively impact the environmental footprint of seismic acquisition and production in general.