@phdthesis{Metz2023,
  author    = {Metz, Malte},
  title     = {Finite fault earthquake source inversions},
  doi       = {10.25932/publishup-61974},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-619745},
  school      = {Universit{\"a}t Potsdam},
  pages     = {143},
  year      = {2023},
  abstract  = {Earthquake modeling is the key to a profound understanding of a rupture. Its kinematics or dynamics are derived from advanced rupture models that allow, for example, to reconstruct the direction and velocity of the rupture front or the evolving slip distribution behind the rupture front. Such models are often parameterized by a lattice of interacting sub-faults with many degrees of freedom, where, for example, the time history of the slip and rake on each sub-fault are inverted. To avoid overfitting or other numerical instabilities during a finite-fault estimation, most models are stabilized by geometric rather than physical constraints such as smoothing. As a basis for the inversion approach of this study, we build on a new pseudo-dynamic rupture model (PDR) with only a few free parameters and a simple geometry as a physics-based solution of an earthquake rupture. The PDR derives the instantaneous slip from a given stress drop on the fault plane, with boundary conditions on the developing crack surface guaranteed at all times via a boundary element approach. As a side product, the source time function on each point on the rupture plane is not constraint and develops by itself without additional parametrization. The code was made publicly available as part of the Pyrocko and Grond Python packages. The approach was compared with conventional modeling for different earthquakes. For example, for the Mw 7.1 2016 Kumamoto, Japan, earthquake, the effects of geometric changes in the rupture surface on the slip and slip rate distributions could be reproduced by simply projecting stress vectors. For the Mw 7.5 2018 Palu, Indonesia, strike-slip earthquake, we also modelled rupture propagation using the 2D Eikonal equation and assuming a linear relationship between rupture and shear wave velocity. This allowed us to give a deeper and faster propagating rupture front and the resulting upward refraction as a new possible explanation for the apparent supershear observed at the Earth's surface. The thesis investigates three aspects of earthquake inversion using PDR: (1) to test whether implementing a simplified rupture model with few parameters into a probabilistic Bayesian scheme without constraining geometric parameters is feasible, and whether this leads to fast and robust results that can be used for subsequent fast information systems (e.g., ground motion predictions). (2) To investigate whether combining broadband and strong-motion seismic records together with near-field ground deformation data improves the reliability of estimated rupture models in a Bayesian inversion. (3) To investigate whether a complex rupture can be represented by the inversion of multiple PDR sources and for what type of earthquakes this is recommended. I developed the PDR inversion approach and applied the joint data inversions to two seismic sequences in different tectonic settings. Using multiple frequency bands and a multiple source inversion approach, I captured the multi-modal behaviour of the Mw 8.2 2021 South Sandwich subduction earthquake with a large, curved and slow rupturing shallow earthquake bounded by two faster and deeper smaller events. I could cross-validate the results with other methods, i.e., P-wave energy back-projection, a clustering analysis of aftershocks and a simple tsunami forward model. The joint analysis of ground deformation and seismic data within a multiple source inversion also shed light on an earthquake triplet, which occurred in July 2022 in SE Iran. From the inversion and aftershock relocalization, I found indications for a vertical separation between the shallower mainshocks within the sedimentary cover and deeper aftershocks at the sediment-basement interface. The vertical offset could be caused by the ductile response of the evident salt layer to stress perturbations from the mainshocks. The applications highlight the versatility of the simple PDR in probabilistic seismic source inversion capturing features of rather different, complex earthquakes. Limitations, as the evident focus on the major slip patches of the rupture are discussed as well as differences to other finite fault modeling methods.},
  language  = {en}
}
@phdthesis{Samaras2016,
  author    = {Samaras, Stefanos},
  title     = {Microphysical retrieval of non-spherical aerosol particles using regularized inversion of multi-wavelength lidar data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-396528},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 190},
  year      = {2016},
  abstract  = {Numerous reports of relatively rapid climate changes over the past century make a clear case of the impact of aerosols and clouds, identified as sources of largest uncertainty in climate projections. Earth's radiation balance is altered by aerosols depending on their size, morphology and chemical composition. Competing effects in the atmosphere can be further studied by investigating the evolution of aerosol microphysical properties, which are the focus of the present work. The aerosol size distribution, the refractive index, and the single scattering albedo are commonly used such properties linked to aerosol type, and radiative forcing. Highly advanced lidars (light detection and ranging) have reduced aerosol monitoring and optical profiling into a routine process. Lidar data have been widely used to retrieve the size distribution through the inversion of the so-called Lorenz-Mie model (LMM). This model offers a reasonable treatment for spherically approximated particles, it no longer provides, though, a viable description for other naturally occurring arbitrarily shaped particles, such as dust particles. On the other hand, non-spherical geometries as simple as spheroids reproduce certain optical properties with enhanced accuracy. Motivated by this, we adapt the LMM to accommodate the spheroid-particle approximation introducing the notion of a two-dimensional (2D) shape-size distribution. Inverting only a few optical data points to retrieve the shape-size distribution is classified as a non-linear ill-posed problem. A brief mathematical analysis is presented which reveals the inherent tendency towards highly oscillatory solutions, explores the available options for a generalized solution through regularization methods and quantifies the ill-posedness. The latter will improve our understanding on the main cause fomenting instability in the produced solution spaces. The new approach facilitates the exploitation of additional lidar data points from depolarization measurements, associated with particle non-sphericity. However, the generalization of LMM vastly increases the complexity of the problem. The underlying theory for the calculation of the involved optical cross sections (T-matrix theory) is computationally so costly, that would limit a retrieval analysis to an unpractical point. Moreover the discretization of the model equation by a 2D collocation method, proposed in this work, involves double integrations which are further time consuming. We overcome these difficulties by using precalculated databases and a sophisticated retrieval software (SphInX: Spheroidal Inversion eXperiments) especially developed for our purposes, capable of performing multiple-dataset inversions and producing a wide range of microphysical retrieval outputs. Hybrid regularization in conjunction with minimization processes is used as a basis for our algorithms. Synthetic data retrievals are performed simulating various atmospheric scenarios in order to test the efficiency of different regularization methods. The gap in contemporary literature in providing full sets of uncertainties in a wide variety of numerical instances is of major concern here. For this, the most appropriate methods are identified through a thorough analysis on an overall-behavior basis regarding accuracy and stability. The general trend of the initial size distributions is captured in our numerical experiments and the reconstruction quality depends on data error level. Moreover, the need for more or less depolarization points is explored for the first time from the point of view of the microphysical retrieval. Finally, our approach is tested in various measurement cases giving further insight for future algorithm improvements.},
  language  = {en}
}
@phdthesis{Lontsi2016,
  author    = {Lontsi, Agostiny Marrios},
  title     = {1D shallow sedimentary subsurface imaging using ambient noise and active seismic data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103807},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xix, 119},
  year      = {2016},
  abstract  = {The Earth's shallow subsurface with sedimentary cover acts as a waveguide to any incoming wavefield. Within the framework of my thesis, I focused on the characterization of this shallow subsurface within tens to few hundreds of meters of sediment cover. I imaged the seismic 1D shear wave velocity (and possibly the 1D compressional wave velocity). This information is not only required for any seismic risk assessment, geotechnical engineering or microzonation activities, but also for exploration and global seismology where site effects are often neglected in seismic waveform modeling. First, the conventional frequency-wavenumber (f - k) technique is used to derive the dispersion characteristic of the propagating surface waves recorded using distinct arrays of seismometers in 1D and 2D configurations. Further, the cross-correlation technique is applied to seismic array data to estimate the Green's function between receivers pairs combination assuming one is the source and the other the receiver. With the consideration of a 1D media, the estimated cross-correlation Green's functions are sorted with interstation distance in a virtual 1D active seismic experiment. The f - k technique is then used to estimate the dispersion curves. This integrated analysis is important for the interpretation of a large bandwidth of the phase velocity dispersion curves and therefore improving the resolution of the estimated 1D Vs profile. Second, the new theoretical approach based on the Diffuse Field Assumption (DFA) is used for the interpretation of the observed microtremors H/V spectral ratio. The theory is further extended in this research work to include not only the interpretation of the H/V measured at the surface, but also the H/V measured at depths and in marine environments. A modeling and inversion of synthetic H/V spectral ratio curves on simple predefined geological structures shows an almost perfect recovery of the model parameters (mainly Vs and to a lesser extent Vp). These results are obtained after information from a receiver at depth has been considered in the inversion. Finally, the Rayleigh wave phase velocity information, estimated from array data, and the H/V(z, f) spectral ratio, estimated from a single station data, are combined and inverted for the velocity profile information. Obtained results indicate an improved depth resolution in comparison to estimations using the phase velocity dispersion curves only. The overall estimated sediment thickness is comparable to estimations obtained by inverting the full micortremor H/V spectral ratio.},
  language  = {en}
}
@phdthesis{Niederleithinger2010,
  author    = {Niederleithinger, Ernst},
  title     = {Optimierung und Erweiterung der Parallel-Seismik-Methode zur Bestimmung der L{\"a}nge von Fundamentpf{\"a}hlen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49191},
  school      = {Universit{\"a}t Potsdam},
  year      = {2010},
  abstract  = {Das Parallel-Seismik-Verfahren dient vor allem der nachtr{\"a}glichen L{\"a}ngenmessung von Fundamentpf{\"a}hlen oder {\"a}hnlichen Elementen zur Gr{\"u}ndung von Bauwerken. Eine solche Messung wird beispielsweise notwendig, wenn ein Geb{\"a}ude verst{\"a}rkt, erh{\"o}ht oder anders als bisher genutzt werden soll, aber keine Unterlagen mehr {\"u}ber die Fundamente vorhanden sind. Das Messprinzip des schon seit einigen Jahrzehnten bekannten Verfahrens ist relativ einfach: Auf dem Pfahlkopf wird meist durch Hammerschlag eine Stoßwelle erzeugt, die durch den Pfahl nach unten l{\"a}uft. Dabei wird Energie in den Boden abgegeben. Die abgestrahlten Wellen werden von Sensoren in einem parallel zum Pfahl hergestellten Bohrloch registriert. Aus den Laufzeiten lassen sich die materialspezifischen Wellengeschwindigkeiten im Pfahl und im Boden sowie die Pfahll{\"a}nge ermitteln. Bisher wurde meist ein sehr einfaches Verfahren zur Datenauswertung verwendet, das die L{\"a}nge der Pf{\"a}hle systematisch {\"u}bersch{\"a}tzt. In der vorliegenden Dissertation wurden die mathematisch-physikalischen Grundlagen beleuchtet und durch Computersimulation die Wellenausbreitung in Pfahl und Boden genau untersucht. Weitere Simulationen kl{\"a}rten den Einfluss verschiedener Mess- und Strukturparameter, beispielsweise den Einfluss von Bodenschichtung oder Fehlstellen im Pfahl. So konnte gekl{\"a}rt werden, in welchen F{\"a}llen mit dem Parallel-Seismik-Verfahren gute Ergebnisse erzielt werden k{\"o}nnen (z. B. bei Fundamenten in Sand oder Ton) und wo es an seine Grenzen st{\"o}ßt (z. B. bei Gr{\"u}ndung im Fels). Auf Basis dieser Ergebnisse entstand ein neuer mathematischer Formalismus zur Auswertung der Laufzeiten. In Verbindung mit einem Verfahren zur Dateninversion, d. h. der automatischen Anpassung der Unbekannten in den Gleichungen an die Messergebnisse, lassen sich sehr viel genauere Werte f{\"u}r die Pfahll{\"a}nge ermitteln als mit allen bisher publizierten Verfahren. Zudem kann man nun auch mit relativ großen Abst{\"a}nden zwischen Bohrloch und Pfahl (2 - 3 m) arbeiten. Die Methode wurde an simulierten Daten ausf{\"u}hrlich getestet. Die Messmethode und das neue Auswerteverfahren wurden in einer Reihe praktischer Anwendungen getestet - und dies fast immer erfolgreich. Nur in einem Fall komplizierter Fundamentgeometrie bei gleichzeitig sehr hoher Anforderung an die Genauigkeit war schon nach Simulationen klar, dass hier ein Einsatz nicht sinnvoll ist. Daf{\"u}r zeigte es sich, dass auch die L{\"a}nge von Pfahlw{\"a}nden und Spundw{\"a}nden ermittelt werden kann. Die Parallel-Seismik-Methode funktioniert als einziges verf{\"u}gbares Verfahren zur Fundamentl{\"a}ngenermittlung zugleich in den meisten Bodenarten sowie an metallischen und nichtmetallischen Fundamenten und kommt ohne Kalibrierung aus. Sie ist nun sehr viel breiter einsetzbar und liefert sehr viel genauere Ergebnisse. Die Simulationen zeigten noch Potential f{\"u}r Erweiterungen, zum Beispiel durch den Einsatz spezieller Sensoren, die zus{\"a}tzliche Wellentypen empfangen und unterscheiden k{\"o}nnen.},
  language  = {de}
}