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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.
Both horizontal-to-vertical (H/V) spectral ratios and the spatial autocorrelation method (SPAC) have proven to be valuable tools to gain insight into local site effects by ambient noise measurements. Here, the two methods are employed to assess the subsurface velocity structure at the Piano delle Concazze area on Mt Etna. Volcanic tremor records from an array of 26 broadband seismometers is processed and a strong variability of H/V ratios during periods of increased volcanic activity is found. From the spatial distribution of H/V peak frequencies, a geologic structure in the north-east of Piano delle Concazze is imaged which is interpreted as the Ellittico caldera rim. The method is extended to include both velocity data from the broadband stations and distributed acoustic sensing data from a co-located 1.5 km long fibre optic cable. High maximum amplitude values of the resulting ratios along the trajectory of the cable coincide with known faults. The outcome also indicates previously unmapped parts of a fault. The geologic interpretation is in good agreement with inversion results from magnetic survey data. Using the neighborhood algorithm, spatial autocorrelation curves obtained from the modified SPAC are inverted alone and jointly with the H/V peak frequencies for 1D shear wave velocity profiles. The obtained models are largely consistent with published models and were able to validate the results from the fibre optic cable.
The Vogtland, located at the border region between the Czech Republic and Germany, is known for Holocene volcanism, gas and fluid emissions as well as for reoccurring earthquake swarms, pointing towards a high geodynamic activity. During the earthquake swarm in 2008/2009, a temporary array was installed close to Rohrbach (Germany), at an epicentral distance of about 10 km from the Nový Kostel focal zone (aperture ~0.75 km).
22 events of the recorded swarm were selected to set up a source array. Source arrays are spatially clustered earthquakes, which can be used in a similar manner as receiver array recordings of single events (Green’s functions reciprocity). The application of array seismology techniques like beam forming requires similar waveforms and precisely known origin times and locations. The resemblance of waveforms was assured by visual selection of events and quantified with the calculation of cross-correlation coefficients. We observed that the different events recorded at a single station generally show greater resemblances than the recordings of one event at all stations of the receiver array. This indicates a heterogeneous subsurface beneath the receiver array and a comparably homogeneous source array volume with respect to the frequency-dependent resolution of both arrays.
Beam forming was applied on the Z, N and E component recordings of the source array events at 11 stations, and the results were analysed with respect to converted or reflected crustal phases. While the theoretical back azimuth of the direct phases match the beam forming results in case of the source array analysis, in case of receiver array beam forming derivations of 15°-25° are observed.
PS phases, closely following the direct P phase and presumably SP phases, arriving shortly before the direct S phase can be observed on several stations. Based on the time differences to the direct P and S phases we inferred a conversion depth of about 0.6-0.9 km. A second deeper source array was set up in order to interpret a structural phase arriving 0.85 s after the direct P phase on records of deeper events only.
Additionally to the source array beam forming method an analytical method with a fixed medium velocity and a grid search method, both for determining conversion/ reflection locations of phases traveling off the direct line between source and receiver array, were developed and applied to other observed phases.
In conclusion, we think that the distinct beam forming results along with the striking waveform resemblance reveal the opportunities of using source arrays consisting of small swarm events for the analysis of crustal structures.