This thesis delves into glacier dynamics using the 2D Shallow Ice Approximation enriched by satellite remote sensing data on glacier surface velocities and ice thickness, aiming to refine empirical laws for better predicting glacier movements. The integration of such data has been pivotal, markedly enhancing model calibration despite challenges like steady-state assumptions necessitated by data scarcity. This underscores the critical role of high-quality, temporally resolved data in modeling glacier dynamics accurately.
A significant advancement was the implementation of spatial stratification, which notably improved model performance—reducing Root Mean Square Error (RMSE) by up to 30% and elevating the coefficient of determination (R²) by 0.2 to 0.4 across different regions. This highlights the potential of fully distributed inversions to capture the complex variability of glaciers. Employing Julia for its computational efficiency proved effective for large-scale modeling tasks, setting a promising foundation for future research aimed at understanding and predicting glacier responses to climate change. It is recommended to utilize geostatistical interpolation methods for inverting glacier characteristics from sparse data, in order to acquire these characteristics across the entire glacier area.

A model is designed for solving gravitational profiles of self-gravitating and rotating planets via the use of Poisson's equation for total gravity, i.e., the sum of the gravitational and rotational potential. Poisson's equation is a partial differential equation that is solved with the usage of Green's functions. This is a major advantage because Earth's surface is an equipotential, which leads to a Dirichlett boundary condition. We apply this methodology to a spherical Earth, where the Green's function is closed. It is demonstrated that, when this Green’s functions based methodology is applied to a homogeneous density, a linear spherical density and the PREM density profiles (where all density profiles are spherically symmetric), then discontinuities occur in the accelerationof gravitation across the surface of the Earth, in the range of 0.01 %- 0.13 %. Such an effect is a symptom of incompatibility with the laws of physics for geostaticalequilibrium, and it is certainly significant as compared to the numerical accuracy of the solution. Moreover, the discrepancy is dependent on geographical latitude, as was to be expected, because it somehow reflects the centrifugal effect. The conclusion is made that this method is indeed capable of detecting, and even quantifying, the incompatibility of spherically symmetric mass distributions with the fundamental laws of physics for self-gravitating and rotating planets. This opens a way -and this is one of the main results- to computing corrections to spherically symmetric mass distributions, such as the PREM model. Based on this method, a further way forward to this end is suggested.

Creating accurate engineering models for predicting the response of large structures often requires geotechnical modelling of soil behaviour. Soil material damping is an important input parameter for modelling the structural response and energy dissipation, especially for embedded and lightly damped structures, as in particular for offshore wind turbines. Non-invasive in-situ measurements like the multichannel analysis of surface waves, offer cost-effective solutions and estimations over a wider volume of soil. This research aims to demonstrate that MASW technique can be used to generate a reliable in-situ estimation of the soil damping in marine environments in the depth range of 0-30m.
A unique and high-quality dataset has been made available through a collaboration with the Norwegian Geotechnical Institute (NGI). Shear wave data are rarely available for offshore site investigations and have not been used before for a damping inversion from real surface waves measurements. Moreover, also the horizontal soil response was recorded in this measurements which allow for reducing the uncertainties of the results obtained by using the Scholte wave model. Therefore, two forward waves models are implemented in Matlab to reproduce both the in-line and cross-line measurements.
A reliable shear wave velocity profile is derived via the stiffness inversion method, after which the damping inversion is performed. A modal damping inversion method is developed and it uses a novel modified random search algorithm in order to estimate the material damping profile over depth. The attenuation coefficient is chosen as the reference parameter for the damping inversion and the misfit function for the damping inversion is defined as the normalized difference per frequency of the attenuation curves. The measured attenuation coefficient is extracted based on a modified half-power bandwidth method. The modelled attenuation curve is retrieved as the imaginary part of the complex wavenumber. The wavelet compression technique is employed to reduce the number of roots used in the inversion for both the experimental and the theoretical curves. The identification requires solving an inverse problem with a global optimization method. To get a better understanding of the model and computational time, a combination of sensitivity studies, behaviours of the phase damping ratio curves and layer reduction were performed. Then, synthetic
inversions are run to verify the validity of the proposed technique. Finally, the
method is applied to the aforementioned collected data and two damping profiles (Scholte and Love models) are computed and they show good agreement in terms of both trend and magnitude.
The frequency dependence of the material damping ratio of the soil is analysed
from the use of measured surface wave data. A novel technique is proposed for retrieving this relation starting from the results of the damping inversion and it shows that the material damping ratio is independent from frequency. Then, two new alternative approaches are proposed, which are based on a simplification of the traditional dependency relation. The first confirms the frequency independence of damping while, although it seems very promising, the second one cannot be tested due to computational limitations. The demonstrated frequency independence of the material damping is only valid based on the frequency ranges available in the dataset and cannot be generalized to cover all scenarios.

This work determines whether the amount of frequency components present in the data can be reduced, whilst still retaining image quality, whereas most efforts in seismological research are done in reducing spatial sampling. It is shown using a PCA on the frequency spectra of several data sets that indeed a large redundancy in frequency content is present in onshore seismic data, and an attempt is made to generate a distribution of frequencies in order of importance. Given this redundancy in the frequency spectrum of onshore seismic data, it has been attempted to reconstruct the missing frequencies by applying the Fourier transformation iteratively to the data. However, this transform does not take spatial sampling into account, which is aimed at to compensate for the missing frequencies. Therefore it has been elected to use a linear Radon transformation instead, which keeps components which are connected in space-time connected in the transform domain. A CGNE scheme has been set up to reconstruct the data, which performs very well along the almost linear asymptots in the shot records, up to a reduction of 70% of frequency components. This scheme iteratively applies the linear Radon transform to a shot record, weighing the data in the transform domain with an amplitude based norm. The energy that was spread out due to aliasing because of the missing frequencies is refocused to the main reflectors, especially along the asymptots of the reflection hyperbola. Missing frequencies are reconstructed, up to a scaling factor, and band gaps of up to 6Hz get filled in very well. Next, it is attempted in this work to give quantitative quality metrics, to make comparison between seismic images easier and based on data, rather than subjective visual inspection. Treating migration as a black box, several quality metrics have been devised for the migrated sections: correlation to the ground truth, contrast within an image, average length of found lines, and local SNR. Contrast is not a very good metric to compare between images as its average across an image is almost constant with reduction percentage. The other parameters are good metrics and show a clear trend that the fewer frequency components present in the shot records, the worse the quality of the final image. An increase in deterioration of image quality is observed around 70% reduction, which is in correspondence with the earlier found value for the shot records.