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Seminar | Mathematics and Computer Science Division

Algorithms for Signal Processing and Imaging with Vibration Data

LANS Seminar

Abstract: Subsurface imaging is a large-scale inverse problem governed by the wave equation. Over the past decade geophysicists have increasingly relied on long-term recordings of the Earth’s ambient seismic noise field (low-amplitude vibrations caused by natural sources and human activities) as a source of energy for imaging the subsurface. Using the ambient seismic noise field has enabled lower-cost data acquisition, but we encounter a major bottleneck in the process of preparing data into a form that can be used for this inverse problem. Algorithms to process this ambient noise traditionally require time-lagged comparisons between every pair of sensors in an array (an all-to-all style communication), and these comparisons must be repeatedly done over many time windows. This scalability issue has become increasingly problematic as new sensor technologies are enabling continuous data acquisition with 100s-1000s of times more sensors, and requiring little added cost or labor. This bottleneck will be illustrated in high-density sensor networks used to study infrastructure on permafrost in Alaska, in studying earthquake hazard analysis in California, and in studying urban hydrology and geohazards in Pennsylvania.

In this talk I will show several new algorithms to significantly reduce the complexity of analyzing these data. The strategies behind these new algorithms fall into two categories: (1) revisiting the math behind some required data products to devise new embarrassingly parallel algorithms, and (2) operating directly on lossy-compressed data without decompressing it. While these methods were developed in the context of ambient seismic noise, the algorithms in category (1) can be applied to other diffuse noise field imaging problems, and the algorithms in category (2) may be applied to efficiently discover correlations or repetitive patterns in many other time-series sensor networks.