@phdthesis{Mauerberger2022,
  author    = {Mauerberger, Stefan},
  title     = {Correlation based Bayesian modeling},
  doi       = {10.25932/publishup-53782},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-537827},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 128},
  year      = {2022},
  abstract  = {The motivation for this work was the question of reliability and robustness of seismic tomography. The problem is that many earth models exist which can describe the underlying ground motion records equally well. Most algorithms for reconstructing earth models provide a solution, but rarely quantify their variability. If there is no way to verify the imaged structures, an interpretation is hardly reliable. The initial idea was to explore the space of equivalent earth models using Bayesian inference. However, it quickly became apparent that the rigorous quantification of tomographic uncertainties could not be accomplished within the scope of a dissertation. In order to maintain the fundamental concept of statistical inference, less complex problems from the geosciences are treated instead. This dissertation aims to anchor Bayesian inference more deeply in the geosciences and to transfer knowledge from applied mathematics. The underlying idea is to use well-known methods and techniques from statistics to quantify the uncertainties of inverse problems in the geosciences. This work is divided into three parts: Part I introduces the necessary mathematics and should be understood as a kind of toolbox. With a physical application in mind, this section provides a compact summary of all methods and techniques used. The introduction of Bayesian inference makes the beginning. Then, as a special case, the focus is on regression with Gaussian processes under linear transformations. The chapters on the derivation of covariance functions and the approximation of non-linearities are discussed in more detail. Part II presents two proof of concept studies in the field of seismology. The aim is to present the conceptual application of the introduced methods and techniques with moderate complexity. The example about traveltime tomography applies the approximation of non-linear relationships. The derivation of a covariance function using the wave equation is shown in the example of a damped vibrating string. With these two synthetic applications, a consistent concept for the quantification of modeling uncertainties has been developed. Part III presents the reconstruction of the Earth's archeomagnetic field. This application uses the whole toolbox presented in Part I and is correspondingly complex. The modeling of the past 1000 years is based on real data and reliably quantifies the spatial modeling uncertainties. The statistical model presented is widely used and is under active development. The three applications mentioned are intentionally kept flexible to allow transferability to similar problems. The entire work focuses on the non-uniqueness of inverse problems in the geosciences. It is intended to be of relevance to those interested in the concepts of Bayesian inference.},
  language  = {en}
}
@phdthesis{Chen2016,
  author    = {Chen, Kejie},
  title     = {Real-time GNSS for fast seismic source inversion and tsunami early warning},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-93174},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xii, 81},
  year      = {2016},
  abstract  = {Over the past decades, rapid and constant advances have motivated GNSS technology to approach the ability to monitor transient ground motions with mm to cm accuracy in real-time. As a result, the potential of using real-time GNSS for natural hazards prediction and early warning has been exploited intensively in recent years, e.g., landslides and volcanic eruptions monitoring. Of particular note, compared with traditional seismic instruments, GNSS does not saturate or tilt in terms of co-seismic displacement retrieving, which makes it especially valuable for earthquake and earthquake induced tsunami early warning. In this thesis, we focus on the application of real-time GNSS to fast seismic source inversion and tsunami early warning. Firstly, we present a new approach to get precise co-seismic displacements using cost effective single-frequency receivers. As is well known, with regard to high precision positioning, the main obstacle for single-frequency GPS receiver is ionospheric delay. Considering that over a few minutes, the change of ionospheric delay is almost linear, we constructed a linear model for each satellite to predict ionospheric delay. The effectiveness of this method has been validated by an out-door experiment and 2011 Tohoku event, which confirms feasibility of using dense GPS networks for geo-hazard early warning at an affordable cost. Secondly, we extended temporal point positioning from GPS-only to GPS/GLONASS and assessed the potential benefits of multi-GNSS for co-seismic displacement determination. Out-door experiments reveal that when observations are conducted in an adversary environment, adding a couple of GLONASS satellites could provide more reliable results. The case study of 2015 Illapel Mw 8.3 earthquake shows that the biases between co-seismic displacements derived from GPS-only and GPS/GLONASS vary from station to station, and could be up to 2 cm in horizontal direction and almost 3 cm in vertical direction. Furthermore, slips inverted from GPS/GLONASS co-seismic displacements using a layered crust structure on a curved plane are shallower and larger for the Illapel event. Thirdly, we tested different inversion tools and discussed the uncertainties of using real-time GNSS for tsunami early warning. To be exact, centroid moment tensor inversion, uniform slip inversion using a single Okada fault and distributed slip inversion in layered crust on a curved plane were conducted using co-seismic displacements recorded during 2014 Pisagua earthquake. While the inversion results give similar magnitude and the rupture center, there are significant differences in depth, strike, dip and rake angles, which lead to different tsunami propagation scenarios. Even though, resulting tsunami forecasting along the Chilean coast is close to each other for all three models. Finally, based on the fact that the positioning performance of BDS is now equivalent to GPS in Asia-Pacific area and Manila subduction zone has been identified as a zone of potential tsunami hazard, we suggested a conceptual BDS/GPS network for tsunami early warning in South China Sea. Numerical simulations with two earthquakes (Mw 8.0 and Mw 7.5) and induced tsunamis demonstrate the viability of this network. In addition, the advantage of BDS/GPS over a single GNSS system by source inversion grows with decreasing earthquake magnitudes.},
  language  = {en}
}