The main aim of this work was to develop methods to estimate quantitatively, and describe qualitatively, the non-linear behaviour of soft soil in intermediate-scale laboratory experiments. Previous works stated that non-linearity of the soil was found for environments involving a large impedance gradient in the near-surface, e.g., a shallow layer of soft, unconsolidated soil overlying a thick harder layer. It is believed that the micro-grains inside the soft soil, in combination with the geometry, caused the non-linearity, although other laboratory experiments found non-linear behaviour for core samples of different single materials.

The novelty of this thesis project lies in the introduction of a new method for investigating the shallow subsurface that has both the advantages of the laboratory environment (e.g., more control over the parameters and higher resolution measurements) and of the field experiments. Therefore, this new, intermediate-scale laboratory approach could be seen as a missing bridge between the experiments on core samples and the field experiments. To the best of our knowledge, this kind of experiment has not been done before and therefore there have not been any physical definitions or classifications of the observed phenomena, yet.

The research was developed in four experiments. The first two experiments verify the scaling, characterize the chosen analogue materials (Clay and Sand), and investigate the influence of the model boundaries. While, the last two experiments focused on the non-linearity behaviour of the soft soil analogues in response to large voltage (e.g., low 100s of Volts) swept-source signals. Overall, we believe we have observed in these experiments several non-linear behaviours for the constructed two layer model; both in terms of a non-linear dependence of the amplitudes on the voltage level as well as in the form of a slowing of the waves for increasing voltage. In addition, we quantify the non-linearity trough a new parameter called the ``Non-linearity parameter'', $\gamma$, and its magnitude describes the level of non-linearity of the soil. The larger $\gamma$, the more non-linearly the soil behaves, and vice-versa. A model linearized to first order was used to compare the data measured using an laser Doppler vibrometer with other observed data assuming the linear response. Thanks to that model, we could mathematically generalize the amplitude behaviour of the measured velocities of the soil as a function of $\gamma$ and visualize the threshold between the linear and non-linear regimes graphically. It appears it is the first time that such parameter is introduced to describe quantitatively the non-linearity.

The proposed methods for investigating the shallow surface by way of intermediate scale analogue models could breathe new life in the use of the physical modeling for near-surface Geophysics. Both the intermediate scale two layer model and the non-linearity parameter appear to be new in this field. The hope is to open a new path for future research keen in understanding better the non linearity behaviour of soft soils.

With a rapid increase in computational resources two dimensional full-waveform inversion is evolving into a promising tool for near-surface geophysics. However, near-surface applications suffer from local minima due to amplitude errors associated with two dimensional full-waveform inversion. By clever definition of the misfit function, the influence of the amplitude errors can be mitigated. Here, I use a recently proposed misfit function based on the instantaneous-phase coherency. The instantaneous-phase coherency misfit function uses complex trace analysis to create an amplitude unbiased misfit function. First, I compare the new misfit function to a traditional least-squares misfit function by inverting synthetic models where noise is added, a field dataset containing Rayleigh waves and a field dataset containing Love waves. Next, I perform inversions on layer cake models to investigate the accuracy of the full-waveform inversion using the new misfit function and finally, I test the robustness of the inversion by using a complex subsurface model. The inversions performed on the synthetic models show that the instantaneous-phase coherency misfit is more robust when noise is introduced to the data compared to the least-squares misfit. Furthermore the two field datasets, demonstrate the ability of the instantaneous-phase to deliver accurate near-surface results when used on field data. The results from the layer cake inversions where inconclusive, however I did demonstrate that a better selection of the bandwidth did improve the result. Finally, the results from the complex subsurface model show that the instantaneous-phase coherency is able to resolve parts of the complex subsurface model.