@article{EsfahaniGholamiOhrnberger2020, author = {Esfahani, Reza Dokht Dolatabadi and Gholami, Ali and Ohrnberger, Matthias}, title = {An inexact augmented Lagrangian method for nonlinear dispersion-curve inversion using Dix-type global linear approximation}, series = {Geophysics : a journal of general and applied geophysics}, volume = {85}, journal = {Geophysics : a journal of general and applied geophysics}, number = {3}, publisher = {GeoScienceWorld}, address = {Tulsa, Okla.}, issn = {0016-8033}, doi = {10.1190/geo2019-0717.1}, pages = {EN77 -- EN85}, year = {2020}, abstract = {Dispersion-curve inversion of Rayleigh waves to infer subsurface shear-wave velocity is a long-standing problem in seismology. Due to nonlinearity and ill-posedness, sophisticated regularization techniques are required to solve the problem for a stable velocity model. We have formulated the problem as a minimization problem with nonlinear operator constraint and then solve it by using an inexact augmented Lagrangian method, taking advantage of the Haney-Tsai Dix-type relation (a global linear approximation of the nonlinear forward operator). This replaces the original regularized nonlinear problem with iterative minimization of a more tractable regularized linear problem followed by a nonlinear update of the phase velocity (data) in which the update can be performed accurately with any forward modeling engine, for example, the finite-element method. The algorithm allows discretizing the medium with thin layers (for the finite-element method) and thus omitting the layer thicknesses from the unknowns and also allows incorporating arbitrary regularizations to shape the desired velocity model. In this research, we use total variation regularization to retrieve the shear-wave velocity model. We use two synthetic and two real data examples to illustrate the performance of the inversion algorithm with total variation regularization. We find that the method is fast and stable, and it converges to the solution of the original nonlinear problem.}, language = {en} } @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} } @article{MarschallSkorovZakharovetal.2020, author = {Marschall, Raphael and Skorov, Yuri and Zakharov, Vladimir and Rezac, Ladislav and Gerig, Selina-Barbara and Christou, Chariton and Dadzie, S. Kokou and Migliorini, Alessandra and Rinaldi, Giovanna and Agarwal, Jessica and Vincent, Jean-Baptiste and Kappel, David}, title = {Cometary comae-surface links the physics of gas and dust from the surface to a spacecraft}, series = {Space science reviews}, volume = {216}, journal = {Space science reviews}, number = {8}, publisher = {Springer}, address = {Dordrecht}, issn = {0038-6308}, doi = {10.1007/s11214-020-00744-0}, pages = {53}, year = {2020}, abstract = {A comet is a highly dynamic object, undergoing a permanent state of change. These changes have to be carefully classified and considered according to their intrinsic temporal and spatial scales. The Rosetta mission has, through its contiguous in-situ and remote sensing coverage of comet 67P/Churyumov-Gerasimenko (hereafter 67P) over the time span of August 2014 to September 2016, monitored the emergence, culmination, and winding down of the gas and dust comae. This provided an unprecedented data set and has spurred a large effort to connect in-situ and remote sensing measurements to the surface. In this review, we address our current understanding of cometary activity and the challenges involved when linking comae data to the surface. We give the current state of research by describing what we know about the physical processes involved from the surface to a few tens of kilometres above it with respect to the gas and dust emission from cometary nuclei. Further, we describe how complex multidimensional cometary gas and dust models have developed from the Halley encounter of 1986 to today. This includes the study of inhomogeneous outgassing and determination of the gas and dust production rates. Additionally, the different approaches used and results obtained to link coma data to the surface will be discussed. We discuss forward and inversion models and we describe the limitations of the respective approaches. The current literature suggests that there does not seem to be a single uniform process behind cometary activity. Rather, activity seems to be the consequence of a variety of erosion processes, including the sublimation of both water ice and more volatile material, but possibly also more exotic processes such as fracture and cliff erosion under thermal and mechanical stress, sub-surface heat storage, and a complex interplay of these processes. Seasons and the nucleus shape are key factors for the distribution and temporal evolution of activity and imply that the heliocentric evolution of activity can be highly individual for every comet, and generalisations can be misleading.}, language = {en} } @misc{BoeckmannRitterCappelletti2018, author = {B{\"o}ckmann, Christine and Ritter, Christoph and Cappelletti, David}, title = {Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data}, series = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium}, journal = {IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium}, publisher = {IEEE}, address = {New York}, isbn = {978-1-5386-7150-4}, issn = {2153-6996}, doi = {10.1109/IGARSS.2018.8518674}, pages = {5575 -- 5578}, year = {2018}, abstract = {We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example.}, language = {en} } @article{GoeritzBergerGegeetal.2018, author = {G{\"o}ritz, Anna and Berger, Stella A. and Gege, Peter and Grossart, Hans-Peter and Nejstgaard, Jens C. and Riedel, Sebastian and R{\"o}ttgers, R{\"u}diger and Utschig, Christian}, title = {Retrieval of water constituents from hyperspectral in-situ measurements under variable cloud cover}, series = {Remote sensing / Molecular Diversity Preservation International (MDPI)}, volume = {10}, journal = {Remote sensing / Molecular Diversity Preservation International (MDPI)}, number = {2}, publisher = {MDPI}, address = {Basel}, issn = {2072-4292}, doi = {10.3390/rs10020181}, pages = {19}, year = {2018}, abstract = {Remote sensing and field spectroscopy of natural waters is typically performed under clear skies, low wind speeds and low solar zenith angles. Such measurements can also be made, in principle, under clouds and mixed skies using airborne or in-situ measurements; however, variable illumination conditions pose a challenge to data analysis. In the present case study, we evaluated the inversion of hyperspectral in-situ measurements for water constituent retrieval acquired under variable cloud cover. First, we studied the retrieval of Chlorophyll-a (Chl-a) concentration and colored dissolved organic matter (CDOM) absorption from in-water irradiance measurements. Then, we evaluated the errors in the retrievals of the concentration of total suspended matter (TSM), Chl-a and the absorption coefficient of CDOM from above-water reflectance measurements due to highly variable reflections at the water surface. In order to approximate cloud reflections, we extended a recent three-component surface reflectance model for cloudless atmospheres by a constant offset and compared different surface reflectance correction procedures. Our findings suggest that in-water irradiance measurements may be used for the analysis of absorbing compounds even under highly variable weather conditions. The extended surface reflectance model proved to contribute to the analysis of above-water reflectance measurements with respect to Chl-a and TSM. Results indicate the potential of this approach for all-weather monitoring.}, language = {en} } @misc{GoeritzBergerGegeetal.2018, author = {G{\"o}ritz, Anna and Berger, Stella A. and Gege, Peter and Grossart, Hans-Peter and Nejstgaard, Jens C. and Riedel, Sebastian and R{\"o}ttgers, R{\"u}diger and Utschig, Christian}, title = {Retrieval of water constituents from hyperspectral in-situ measurements under variable cloud cover}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {941}, issn = {1866-8372}, doi = {10.25932/publishup-45983}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-459837}, pages = {21}, year = {2018}, abstract = {Remote sensing and field spectroscopy of natural waters is typically performed under clear skies, low wind speeds and low solar zenith angles. Such measurements can also be made, in principle, under clouds and mixed skies using airborne or in-situ measurements; however, variable illumination conditions pose a challenge to data analysis. In the present case study, we evaluated the inversion of hyperspectral in-situ measurements for water constituent retrieval acquired under variable cloud cover. First, we studied the retrieval of Chlorophyll-a (Chl-a) concentration and colored dissolved organic matter (CDOM) absorption from in-water irradiance measurements. Then, we evaluated the errors in the retrievals of the concentration of total suspended matter (TSM), Chl-a and the absorption coefficient of CDOM from above-water reflectance measurements due to highly variable reflections at the water surface. In order to approximate cloud reflections, we extended a recent three-component surface reflectance model for cloudless atmospheres by a constant offset and compared different surface reflectance correction procedures. Our findings suggest that in-water irradiance measurements may be used for the analysis of absorbing compounds even under highly variable weather conditions. The extended surface reflectance model proved to contribute to the analysis of above-water reflectance measurements with respect to Chl-a and TSM. Results indicate the potential of this approach for all-weather monitoring.}, 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} } @article{Hassler2016, author = {Haßler, Gerda}, title = {La inversiones del orden de palabras}, series = {Revista de Investigaci{\´o}n Ling{\"u}{\´i}stica}, volume = {19}, journal = {Revista de Investigaci{\´o}n Ling{\"u}{\´i}stica}, issn = {1989-4554}, pages = {35 -- 60}, year = {2016}, abstract = {Las teor{\´i}as sobre el orden de las palabras del siglo XVII han encontrado mucha repercusi{\´o}n en las investigaciones actuales sobre la estructura de la informaci{\´o}n. No obstante, estas alusiones tienden a ser inconscientes. ?'C{\´o}mo deben evaluar los histori{\´o}grafos tales similitudes, mucho m{\´a}s all{\´a} de determinar su continuidad? ?'Se pueden derivar tal vez conclusiones sobre este tema complejo, que es relevante en la discusi{\´o}n de hoy en d{\´i}a, tomando en cuenta las diversas posiciones opuestas y el intenso discurso del siglo XVIII?}, language = {es} } @article{LeyCooperViezzoliGuillemoteauetal.2015, author = {Ley-Cooper, Alan Yusen and Viezzoli, Andrea and Guillemoteau, Julien and Vignoli, Giulio and Macnae, James and Cox, Leif and Munday, Tim}, title = {Airborne electromagnetic modelling options and their consequences in target definition}, series = {Exploration geophysics : the bulletin of the Australian Society of Exploration Geophysicists}, volume = {46}, journal = {Exploration geophysics : the bulletin of the Australian Society of Exploration Geophysicists}, number = {1}, publisher = {CSIRO}, address = {Clayton}, issn = {0812-3985}, doi = {10.1071/EG14045}, pages = {74 -- 84}, year = {2015}, abstract = {Given the range of geological conditions under which airborne EM surveys are conducted, there is an expectation that the 2D and 3D methods used to extract models that are geologically meaningful would be favoured over ID inversion and transforms. We do after all deal with an Earth that constantly undergoes, faulting, intrusions, and erosive processes that yield a subsurface morphology, which is, for most parts, dissimilar to a horizontal layered earth. We analyse data from a survey collected in the Musgrave province, South Australia. It is of particular interest since it has been used for mineral prospecting and for a regional hydro-geological assessment. The survey comprises abrupt lateral variations, more-subtle lateral continuous sedimentary sequences and filled palaeovalleys. As consequence, we deal with several geophysical targets of contrasting conductivities, varying geometries and at different depths. We invert the observations by using several algorithms characterised by the different dimensionality of the forward operator. Inversion of airborne EM data is known to be an ill-posed problem. We can generate a variety of models that numerically adequately fit the measured data, which makes the solution non-unique. The application of different deterministic inversion codes or transforms to the same dataset can give dissimilar results, as shown in this paper. This ambiguity suggests the choice of processes and algorithms used to interpret AEM data cannot be resolved as a matter of personal choice and preference. The degree to which models generated by a ID algorithm replicate/or not measured data, can be an indicator of the data's dimensionality, which perse does not imply that data that can be fitted with a 1D model cannot be multidimensional. On the other hand, it is crucial that codes that can generate 2D and 3D models do reproduce the measured data in order for them to be considered as a plausible solution. In the absence of ancillary information, it could be argued that the simplest model with the simplest physics might be preferred.}, 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} }