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Ergodic sampling: efficient and economical geophysical data acquisition design
Zhang, Mengli
Zhang, Mengli
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2022
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2024-04-22
Abstract
I develop a new sampling method and practical procedure for efficient and economical acquisition of spatial geophysical data and general survey planning. The research addresses the critical component of data collection in mineral exploration and many other geoscience problems that rely on geophysical data. The fundamental basis of the research in this thesis is the compressive sensing method, and I improve upon the sampling strategy component by re-examining the many properties embedded in the Nyquist sampling and generalize these properties to irregularly spaced sampling patterns. I form a new sampling method termed ergodic sampling. For the scenarios examined, the method has been numerically demonstrated that an optimized subset of the samples required by Nyquist sampling method can collect nearly the same information and, when coupled with compressive sensing reconstruction, the underlying signal can be reconstructed. The ergodic sampling framework I developed includes ergodic equations, ergodic properties, ergodic optimization, ergodic patterns, and ergodic templates to build the whole system. Based on this method, I develop both point-based ergodic pattern and line-based ergodic pattern applying to different types of geophysical sensors and stations. To achieve different goals of geophysical data acquisition design, I also develop two ergodic design strategies of saving cost and increasing information. I seek to use my ergodic sampling strategy to achieve the goal of collecting as much information as possible with the smallest number of measurements, in the shortest time, and at the lowest cost. Such specially designed, optimized geometries can use as few as only 10% to 50% of stations in traditional acquisitions but can acquire the similar information to image subsurface and identify interested targets. As a result, my economical acquisition can save 50% to 90% of station deployment and related labor and time. The significant reduction in the acquisition cost, and the ability to collect much more information by using the same number of stations in an optimized irregular pattern, brought about by the ergodic sampling, can enable more exploration projects or other geoscience problems with limited budgets.
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