Mismatches between data and physics for geophysical applications

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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.