Mismatches between data and physics for geophysical applications

我的研究致力于创造实用的方法，对通过地震技术获得的数据进行数值处理和反演。在我们的领域中，我们获得了大量的数据，其中包含关于地下地质的编码信息，问题是如何在丰富的波传播和信号分析理论的背景下解码这些信息。这种大数据解码过程通常以连续方式应用，它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可信的模型。推动我们科学的大量地震数据在某些方面是高度冗余的，但在另一些方面却是稀疏的，几乎不够。利用数据的冗余性将信号与噪声分离。只有在这第一步之后，才能从信号中提取采样较少的信息，并将其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逼近的局限性，信号在分离过程中丢失。我的研究计划的目标是用一种结合信号提取和估计步骤的综合方法来取代上面的两步方法。这将通过嵌入反馈循环中的处理步骤来完成，反馈循环以连贯和并行的方式动作，而不是串联的。实现这一目标的研究计划将需要实用和发现型元素，第一是仔细编程和数据分析，第二是在处理运算符及其联系中实现波物理的新方面。这份探索奖助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，以揭示微妙和微妙的数据变异性。这些领域的进展将对三维地震技术产生革命性的影响，将其集中在盖层完整性评估、油砂注汽(SAGD)和二氧化碳处置等领域。通过提高地震数据处理的效率和对不良采样的健壮性，我们可以从总体上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.