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.

Motivated by environmental concern, the industry has been developing an alternative marine seismic source, in particular a marine vibrator. By spreading the emitted energy out over time, vibrator sources are perceived to be less intrusive to marine mammals. It is also believed that vibrators have greater control of the emitted source wavelet than can be achieved with traditional airguns. With the added control, it is possible to only emit portions of the frequency spectrum, which in turn allows for many applications such as deblending and the ability to avoid masking mammal communications. To effectively implement these, two methodologies are proposed to interpolate the frequency data that are not emitted. The first is a deep learning approach utilizing a U-Net architecture, with a custom frequency loss function. The second is a sparse optimization method that approximates the reflectivity series of the subsurface using known frequency content. By assuming that the signal can be represented sparsely and that all frequencies interact with the subsurface interfaces similarly at all frequencies, the frequency spectrum can be reconstructed. Both of the presented methods are tasked to interpolate the missing frequency band(s) in North Sea shot data. It is found that both methods are able to interpolate narrow 2.5 Hz bands, but are unable to accurately reconstruct wider (ex. 10 Hz), frequency bands. Overall, the U-Net shows better results than the sparse optimization method when the frequency gaps are positioned closely.

Unconsolidated granulates exhibit complex, nonlinear behaviour when subjected to dynamic forces. The presence of granular contacts gives this type of material a relatively low stiffness and provides hysteretic energy losses. These features make unconsolidated granulates suitable for railway ballast as it provides dissipation of vibrational energy from passing trains which is important to minimise vibrational disturbance. However, simulating the response of the railway superstructure under dynamic loads becomes difficult due to then onlinearity of the ballast. In order to develop better prediction tools, the elastic behaviour of unconsolidated rocks is first investigated experimentally by quasi-static and dynamic stress-strain experiments yielding the Young's modulus, nonlinear resonance shift and analysis of harmonic generation. In addition, the transmission of structural waves through granulates is investigated by assessing the transfer function for different thicknesses of granulates, different
particle sizes and different materials with varying viscous damping. Three granulates are used, small-scale ballast, a gravel, and two sizes of uniform steel spheres. All three materials exhibit a combination of classical and hysteretic nonlinearity where the strain depends on the stress amplitude and history.

A completely new finite element approach is taken to model the hysteretic nonlinearity, based on an existing phenomenological static model. Multiple spring-slider elements with gaps are used, as opposed to implementing a homogenised material model. It is shown that only 50 elements can reproduce the hysteretic nature of the material, which is a significant advantage to a traditional material model requiring the discretisation of the entire ballast volume. Each spring-slider element is parameterised by two springs constants, a yield force and an initial gap. A distribution of these parameters across the 50 elements is found that reproduces the quasi-static stress cycles acquired experimentally. In addition, a parametric study of the model parameters during dynamic excitation reveals that key indicators of nonlinearity can be simulated. The finite element simulations prove that using a set of spring-slider elements
to model the behaviour of unconsolidated granulates is viable method. With experimental tests performed on true ballast and further work on the finite element model to understand optimal parameter distributions, a more accurate and efficient railway superstructure model can be produced.