Mismatches between data and physics for geophysical applications

我的研究致力于为通过地震技术获得的数据的数值处理和反演创造实用的方法。在我们的领域，我们获得了大量的数据，其中包含有关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。推动我们科学发展的大量地震数据在某些方面是高度冗余的，但同时在其他方面是稀疏的，几乎不够用。利用数据的冗余来分离信号和噪声。只有在这一初始步骤之后，才会从信号中提取采样不太好的信息，并进行反演以估计地球模型。这种分而治之的方法存在两个问题。首先，初始信号提取和随后的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局限性，信号在分离过程中会丢失。我的研究计划的目标是用一种结合了信号提取和估计步骤的综合方法取代上面的两步方法。这将通过嵌入反馈回路的处理步骤来完成，反馈回路的作用是连贯的，并行的，而不是串行的。实现这一目标的研究计划将需要实际的和发现型的元素，第一个是仔细的编程和数据分析，第二个是在处理算子及其联系中实现波物理的新方面。这个发现基金提案涵盖了第二个要素。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，以揭示细微和微妙的数据变异性。这些领域的进展将对3D地震技术产生革命性的影响，使其成为盖层完整性评估等领域的核心技术，这对油砂蒸汽注入（SAGD）和二氧化碳处理至关重要。通过提高地震数据处理的效率和对低采样的鲁棒性，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.