Large-scale stochastic inverse and data assimilation problems with applications to subsurface imaging

传感技术和实验测量的改进导致了许多领域的数据爆炸。例如，在成像和逆问题中就是这种情况。虽然许多数值算法可用于处理这些数据，但直到最近，处理数据的计算成本才是主要问题。例如，在对地球陆地表面以下的空间成像的领域中，应用于地下水和石油勘探、CO2封存、污染物定位等，研究人员过去只能进行有限数量的测量，只能粗略地重建地下。如今，可以在不同的位置和时间收集数十万个测量数据。因此，要处理的数据量以及可能的预测的分辨率都大大增加，使得许多现有的方法不切实际。为了探索与测量一致的解决方案的范围，流行的方法是基于地下属性的随机或概率描述，称为随机反演。这项研究将采用新的数值算法来解决随机反演在这种情况下的计算挑战。近年来，人们对地下（地下）重新产生了兴趣，例如在CO2储存的背景下。在这个例子中，从热电厂的排放物中提取CO2，然后将其注入地下不透CO2的地质层下。这是一种有效的技术，可以减少二氧化碳排放到大气中，并允许继续使用化石燃料工厂，如煤电厂，而不会释放大量的温室气体。然而，这项技术也有缺点;特别是它需要监测地下的二氧化碳羽流，以确保没有泄漏到地面。例如，在注射部位上方的表面区域有人居住的情况下，这对于向公众提供保证是重要的。虽然泄漏极为罕见，不会引起严重关注（二氧化碳只有在高浓度时才会有毒），但为了完全可靠，需要进行这种监测。除其他目标外，该项目将开发新的计算机算法，以便根据例如在井场进行的测量结果重建CO2羽流的位置。

Improvements in sensing technology and experimental measurements have led to an explosion of data in many fields. This is the case for example in imaging and inverse problems. Although many numerical algorithms are available to process this data, until recently the computational cost of processing the data was not the main issue. For example in the field of imaging the space below the land surface of the earth, with application in groundwater and oil exploration, CO2 sequestration, contaminant location, etc., researchers used to have only a limited number of measurements and only coarse reconstruction of the underground was possible. Nowadays it is possible to have hundreds of thousands of measurement data collected at different locations and times. As a result the volume of data to process as well as the resolution of the predictions that are possible have increased tremendously, making many existing methods impractical. To explore the range of solutions consistent with measurements, the prevalent approach is based on a stochastic or probabilistic description of the subsurface properties and is called stochastic inversing. This research will apply novel numerical algorithms to address computational challenges for stochastic inversing in this context.In recent years, there has been a renewed interest in the subsurface (underground) for example in the context of CO2 storage. In this example, CO2 is extracted from emissions in thermal power plants and then injected underground under a geologic layer that is impermeable to CO2. This is an effective technology to reduce CO2 emissions to the atmosphere and allows the continued use of fossil fuel plants such as coal plants without releasing large amounts of greenhouse gases. This technology however has drawbacks; in particular it requires monitoring of the CO2 plume underground to make sure that there is no leak to the surface. This is important for example to provide guarantees to the public, in cases where the surface area above the injection site is populated. Although leakage is extremely rare and would not be a serious cause of concern (CO2 does not become toxic until high levels of concentration), such monitoring is required for complete confidence. Among other objectives, this project will develop novel computer algorithms to allow reconstructing the location of CO2 plumes from measurements taken for example at well sites.