@article{HastermannReinhardtKleinetal.2021, author = {Hastermann, Gottfried and Reinhardt, Maria and Klein, Rupert and Reich, Sebastian}, title = {Balanced data assimilation for highly oscillatory mechanical systems}, series = {Communications in applied mathematics and computational science : CAMCoS}, volume = {16}, journal = {Communications in applied mathematics and computational science : CAMCoS}, number = {1}, publisher = {Mathematical Sciences Publishers}, address = {Berkeley}, issn = {1559-3940}, doi = {10.2140/camcos.2021.16.119}, pages = {119 -- 154}, year = {2021}, abstract = {Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, this filter also has limitations due to its inherent assumptions of Gaussianity and linearity, which can manifest themselves in the form of dynamically inconsistent state estimates. This issue is investigated here for balanced, slowly evolving solutions to highly oscillatory Hamiltonian systems which are prototypical for applications in numerical weather prediction. It is demonstrated that the standard ensemble Kalman filter can lead to state estimates that do not satisfy the pertinent balance relations and ultimately lead to filter divergence. Two remedies are proposed, one in terms of blended asymptotically consistent time-stepping schemes, and one in terms of minimization-based postprocessing methods. The effects of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for balanced motions of two prototypical Hamiltonian reference systems.}, language = {en} } @article{CreightonParsekianAngelopoulosetal.2018, author = {Creighton, Andrea L. and Parsekian, Andrew D. and Angelopoulos, Michael and Jones, Benjamin M. and Bondurant, A. and Engram, M. and Lenz, Josefine and Overduin, Pier Paul and Grosse, Guido and Babcock, E. and Arp, Christopher D.}, title = {Transient Electromagnetic Surveys for the Determination of Talik Depth and Geometry Beneath Thermokarst Lakes}, series = {Journal of geophysical research : Solid earth}, volume = {123}, journal = {Journal of geophysical research : Solid earth}, number = {11}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2018JB016121}, pages = {9310 -- 9323}, year = {2018}, abstract = {Thermokarst lakes are prevalent in Arctic coastal lowland regions and sublake permafrost degradation and talik development contributes to greenhouse gas emissions by tapping the large permafrost carbon pool. Whereas lateral thermokarst lake expansion is readily apparent through remote sensing and shoreline measurements, sublake thawed sediment conditions and talik growth are difficult to measure. Here we combine transient electromagnetic surveys with thermal modeling, backed up by measured permafrost properties and radiocarbon ages, to reveal closed-talik geometry associated with a thermokarst lake in continuous permafrost. To improve access to talik geometry data, we conducted surveys along three transient electromagnetic transects perpendicular to lakeshores with different decadal-scale expansion rates of 0.16, 0.38, and 0.58m/year. We modeled thermal development of the talik using boundary conditions based on field data from the lake, surrounding permafrost and a borehole, independent of the transient electromagnetics. A talik depth of 91m was determined from analysis of the transient electromagnetic surveys. Using a lake initiation age of 1400years before present and available subsurface properties the results from thermal modeling of the lake center arrived at a best estimate talk depth of 80m, which is on the same order of magnitude as the results from the transient electromagnetic survey. Our approach has provided a noninvasive estimate of talik geometry suitable for comparable settings throughout circum-Arctic coastal lowland regions.}, language = {en} } @article{TronickeTrauth2018, author = {Tronicke, Jens and Trauth, Martin H.}, title = {Classroom-sized geophysical experiments}, series = {European Journal of Physics}, volume = {39}, journal = {European Journal of Physics}, number = {3}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0143-0807}, doi = {10.1088/1361-6404/aaad5b}, pages = {15}, year = {2018}, abstract = {Modern mobile devices (i.e. smartphones and tablet computers) are widespread, everyday tools, which are equipped with a variety of sensors including three-axis magnetometers. Here, we investigate the feasibility and the potential of using such mobile devices to mimic geophysical experiments in the classroom in a table-top setup. We focus on magnetic surveying and present a basic setup of a table-top experiment for collecting three-component magnetic data across well-defined source bodies and structures. Our results demonstrate that the quality of the recorded data is sufficient to address a number of important basic concepts in the magnetic method. The shown examples cover the analysis of magnetic data recorded across different kinds of dipole sources, thus illustrating the complexity of magnetic anomalies. In addition, we analyze the horizontal resolution capabilities using a pair of dipole sources placed at different horizontal distances to each other. Furthermore, we demonstrate that magnetic data recorded with a mobile device can even be used to introduce filtering, transformation, and inversion approaches as they are typically used when processing magnetic data sets recorded for real-world field applications. Thus, we conclude that such table-top experiments represent an easy-to-implement experimental procedure (as student exercise or classroom demonstration) and can provide first hands-on experience in the basic principles of magnetic surveying including the fundamentals of data acquisition, analysis and processing, as well as data evaluation and interpretation.}, language = {en} }