ALBERT

Description: Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space $\mathbb {R}^{3}$ is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Description: Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space $\mathbb {R}^{3}$ is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Description: Surveillance of clandestine nuclear tests relies on a global seismic network, but the potential of spaceborne monitoring has been underexploited. We used satellite radar imagery to determine the complete surface displacement field of up to 3.5 meters of divergent horizontal motion with 0.5 meters of subsidence associated with North Korea’s largest underground nuclear test. Combining insight from geodetic and seismological remote sensing, we found that the aftermath of the initial explosive deformation involved subsidence associated with subsurface collapse and aseismic compaction of the damaged rocks of the test site. The explosive yield from the nuclear detonation with best-fitting source parameters for 450-meter depth was 191 kilotonnes of TNT equivalent. Our results demonstrate the capability of spaceborne remote sensing to help characterize large underground nuclear tests.

Description: Volcanic crises are often preceded and accompanied by volcano deformation caused by magmatic and hydrothermal processes. Fast and efficient model identification and parameter estimation techniques for various sources of deformation are crucial for process understanding, volcano hazard assessment and early warning purposes. As a simple model that can be a basis for rapid inversion techniques, we present a compound dislocation model (CDM) that is composed of three mutually orthogonal rectangular dislocations (RDs). We present new RD solutions, which are free of artefact singularities and that also possess full rotational degrees of freedom. The CDM can represent both planar intrusions in the near field and volumetric sources of inflation and deflation in the far field. Therefore, this source model can be applied to shallow dikes and sills, as well as to deep planar and equidimensional sources of any geometry, including oblate, prolate and other triaxial ellipsoidal shapes. In either case the sources may possess any arbitrary orientation in space. After systematically evaluating the CDM, we apply it to the co-eruptive displacements of the 2015 Calbuco eruption observed by the Sentinel-1A satellite in both ascending and descending orbits. The results show that the deformation source is a deflating vertical lens-shaped source at an approximate depth of 8 km centred beneath Calbuco volcano. The parameters of the optimal source model clearly show that it is significantly different from an isotropic point source or a single dislocation model. The Calbuco example reflects the convenience of using the CDM for a rapid interpretation of deformation data.

Description: The advances in modern geodetic techniques such as the global navigation satellite system (GNSS) and synthetic aperture radar (SAR) provide surface deformation measurements with an unprecedented accuracy and temporal and spatial resolutions even at most remote volcanoes on Earth. Modelling of the high-quality geodetic data is crucial for understanding the underlying physics of volcano deformation processes. Among various approaches, mathematical models are the most effective for establishing a quantitative link between the surface displacements and the shape and strength of deformation sources. Advancing the geodetic data analyses and hence, the knowledge on the Earth’s interior processes, demands sophisticated and efficient deformation modelling approaches. Yet the majority of these models rely on simplistic assumptions for deformation source geometries and ignore complexities such as the Earth’s surface topography and interactions between multiple sources. This thesis addresses this problem in the context of analytical and numerical volcano deformation modelling. In the first part, new analytical solutions for triangular dislocations (TDs) in uniform infinite and semi-infinite elastic media have been developed. Through a comprehensive investigation, the locations and causes of artefact singularities and numerical instabilities associated with TDs have been determined and these long-standing drawbacks have been addressed thoroughly. This approach has then been extended to rectangular dislocations (RDs) with full rotational degrees of freedom. Using this solution in a configuration of three orthogonal RDs a compound dislocation model (CDM) has been developed. The CDM can represent generalized volumetric and planar deformation sources efficiently. Thus, the CDM is relevant for rapid inversions in early warning systems and can also be used for detailed deformation analyses. In order to account for complex source geometries and realistic topography in the deformation models, in this thesis the boundary element method (BEM) has been applied to the new solutions for TDs. In this scheme, complex surfaces are simulated as a continuous mesh of TDs that may possess any displacement or stress boundary conditions in the BEM calculations. In the second part of this thesis, the developed modelling techniques have been applied to five different real-world deformation scenarios. As the first and second case studies the deformation sources associated with the 2015 Calbuco eruption and 2013–2016 Copahue inflation period have been constrained by using the CDM. The highly anisotropic source geometries in these two cases highlight the importance of using generalized deformation models such as the CDM, for geodetic data inversions. The other three case studies in this thesis involve high-resolution dislocation models and BEM calculations. As the third case, the 2013 pre-explosive inflation of Volcán de Colima has been simulated by using two ellipsoidal cavities, which locate zones of pressurization in the volcano’s lava dome. The fourth case study, which serves as an example for volcanotectonics interactions, the 3-D kinematics of an active ring-fault at Tendürek volcano has been investigated through modelling displacement time series over the 2003–2010 time period. As the fifth example, the deformation sources associated with North Korea’s underground nuclear test in September 2017 have been constrained. These examples demonstrate the advancement and increasing level of complexity and the general applicability of the developed dislocation modelling techniques. This thesis establishes a unified framework for rapid and high-resolution dislocation modelling, which in addition to volcano deformations can also be applied to tectonic and humanmade deformations.

Description: Fortschritte in modernen geodätischen Techniken wie dem globalen Navigationssatellitensystem (GNSS) und dem Synthetic Apertur Radar (SAR), liefern Messungen der Oberflächenverformung mit einer beispiellosen Genauigkeit sowie zeitlichen und räumlichen Auflösungen, selbst an abgelegensten Vulkanen. Die Modellierung von hochqualitativen geodätischen Daten ist entscheidend für das Verständnis der zugrundeliegenden Physik der Verformungsprozesse an diesen Vulkanen. Um eine quantitative Verbindung zwischen den Oberflächenverschiebungen und der Form und Stärke von Verformungsquellen herzustellen, sind mathematische Modelle am effektivsten. Die Fortschnitte in geodätischen Datenanalysen und damit das Wissen über die Prozesse im Inneren der Erde erfordern ausgefeilte und effiziente Ansätze der Verformungsmodellierung. Die meisten dieser Modelle beruhen jedoch auf vereinfachten Annahmen der Geometrien der Verformungsquellen und ignorieren Komplexitäten wie die Erdoberflächentopographie und Wechselwirkungen zwischen mehreren Quellen. Diese Doktorarbeit befasst sich mit diesem Problem im Kontext der analytischen und numerischen Vulkanverformungsmodellierung. Im ersten Schritt wurden neue analytische Lösungen für dreieckige Dislokationen (triangular dislocation-TD) im gleichförmigen elastischen Voll- und Halbraum entwickelt. Durch eine umfassende Untersuchung wurden die Orte und Ursachen von TDs verbundenen Artefaktsingularitäten und numerischen Instabilitäten identifiziert und diese Problematik gelöst. Dieser Ansatz wurde dann auf rechteckige Dislokationen (rectangular dislocation-RD) mit vollen Rotationsfreiheitsgraden erweitert. Unter Verwendung dieser Lösung in einer Konfiguration von drei orthogonalen RDs wurde ein “Zusammengesetztes Dislokationsmodel” (compound dislocation model-CDM) entwickelt. Das CDM kann verallgemeinerte volumetrische und planare Verformungsquellen effizient darstellen. Somit ist das CDM für schnelle Inversionen in Frühwarnungssystemen relevant und kann auch für detaillierte Verformungsanalysen verwendet werden. Um komplexe Quellengeometrien und eine realistische Topographie in den Verformungsmodellen dieser Untersuchung zu berücksichtigen, wurde die Randelementmethode (REM) auf die neuen Lösungen für TDs angewendet. In diesem Schema werden komplexe Oberflächen als ein kontinuierliches Netz von DVs simuliert, die in den REM-Berechnungen beliebige Verschiebungs- oder Spannungsgrenzbedingungen aufweisen können. Als Beispiele wurden die entwickelten Modellierungstechniken auf fünf verschiedene reale Verformungsszenarien angewendet. Das erste und zweite Beispiel, die Calbuco-Eruption 2015 und die 2013–2016 Copahue-Aufwölbungsperiode, wurden durch die Verwendung des CDM näher beschrieben. Die hoch anisotropen Quellengeometrien in diesen beiden Fällen unterstreichen die Bedeutung der Verwendung verallgemeinerter Verformungsmodelle wie dem CDM für geodätische Dateninversionen. Weitere Fallstudien dieser Doktorarbeit umfassen hochauflösende Versetzungsmodelle und REM-Berechnungen. Die Aufwölbung 2013 am Volcán de Colima wurde simuliert, indem zwei ellipsoidale Quellen verwendet wurden, die Druckzonen im Lavadom des Vulkans lokalisieren. Danach, als Beispiel für Vulkantektonik-Interaktionen, wurde die 3-D-Kinematik einer aktiven Ringstörung am Tendürek-Vulkan durch Modellierung von InSAR-Zeitreihen über die Zeitperiode 2003–2010 simuliert. Als letztes Beispiel wurden die Verformungsquellen, die im Zusammenhang mit Nordkoreas unterirdischem Atomtest im September 2017 stehen, simuliert und der Einsatz der verwendeten Methoden auch in nicht vulkanischen Terrain gezeigt. Diese Beispiele zeigen den Fortschritt und das zunehmende Niveau der Komplexität und die allgemeine Anwendbarkeit der entwickelten Dislokationsmodellierungstechniken. Diese Doktorarbeit unterstreicht die Anwendung von neuer schneller und hochauflösender Dislokationsmodellierung, die neben Vulkanverformungen auch auf tektonische und vom Menschen verursachte Verformungen angewendet werden kann.

Description: This data publication is a high resolution Digital Elevation Model (DEM) generated for the Merapi summit by combining terrestrial laser scanning (TLS) and unmanned aerial vehicles (UAVs) photogrammetry data acquired in 2014 and 2015, respectively. The structures of the data are further analysed in Darmawan et al. 2017 (http://doi.org/10.1016/j.jvolgeores.2017.11.006). The published datasets consist of combined point clouds with ~65 million data points and a DEM with a resampled resolution of 0.5 m. The DEM data covers the complexity of the Merapi summit with area of 2 km2. The coordinate of the datasets is projected to global coordinates (WGS 1984 UTM Zone 49 South). TLS is a topography mapping technique which exploits the travel time of a laser beam to measure the range between the ground-based scanning instrument and the earth’s surface. TLS provides high accuracy, precision, and resolution for topography mapping, however, it requires different scan position to obtain accurate topography model in a complex topography. The TLS dataset was acquired by using a long-range RIEGL VZ-6000 instrument with a Pulse Repetition Rate (PRR) of 30 kHz. The Merapi data includes an observation range of 0.129 – 4393.75 m, a theta range (vertical) of 73 – 120° with a sampling angle of 0.041°, a phi range (horizontal) of 33° - 233° with a sampling angle of 0.05°, and 12 reflectors for each scan. The used TLS dataset was achieved by combining two scan positions, both realized in September 2014. In order to reduce still eminent shadowing, we conducted additionally a UAV photogrammetry survey. The UAV data allows to fill data gaps and generate a complete 3D point cloud. The UAV photogrammetry was conducted by using DJI Phantom 2 quadcopter drone in October 2015. The drone carried GoPro HERO 3+ camera and a H3-3D gimbal to reduce image shaking. We obtained over 300 images which cover the summit area of Merapi. By applying the Structure from Motion algorithm, we are able to generate a 3D point cloud model of Merapi summit. Further details on this procedure are provided in Darmawan et al. (2017). Structure from Motion is a technique to generate a 3D model based on 2D overlapped images. The algorithm detects and matches the same ground features of 2D images, reconstructs a 3D scene, and calculates a depth map for each camera frame. The algorithm used is implemented in Agisoft Photoscan Professional software. After importing the images in Agisoft, we used the ‘align image’ function with high accuracy setting to generate 3D sparse point cloud and ‘build dense cloud’ function with high quality to generate 3D dense point cloud. The 3D point clouds of TLS and UAV photogrammetry were then georeferenced to our georeferenced 3D point cloud which acquired in 2012. The RMS of TLS and UAV photogrammetry during georeferenced is 0.60 and 0.44 m, respectively, as described in Further details on this procedure are provided in Darmawan et al. (2017). After georeferencing, both 3D point clouds were merged and interpolated to a raster format in the ArcMap software.