This work presents a concrete-specific analytical framework for modelling body-wave scattering by explicitly tailoring multiple-scattering theory to the microstructural characteristics of concrete. Instead of treating scattering parameters as abstract statistical quantities, the framework parameterizes the key inputs of scattering theory in terms of physically measurable concrete attributes, including coarse aggregate size, volume fraction, and the material property contrast between the matrix and the dominant scattering phase, whether coarse aggregates or the interfacial transition zone. By embedding these microstructure-informed parameters into a two-phase spatial statistical formulation, closed-form expressions for total and transport scattering cross-sections are derived and directly linked to ultrasonic diffusivity through diffuse wave theory. Experimental validation using geopolymer concrete members and published data for ordinary concrete demonstrates consistent agreement between theoretical predictions and experimental measurements across a broad frequency range. The proposed framework therefore renders body-wave scattering in concrete quantitatively computable from material composition, providing a physically grounded basis for quantitative interpretation of diffuse wave transport, energy equilibration, and coda-wave velocity changes without reliance on ad hoc fitting parameters.

Rayleigh waves are prevalent in the ambient seismic noise wavefield and are thus often exploited in passive seismic methods to characterise the near subsurface. In fractured or faulted media, Rayleigh waves show anisotropic velocities that could provide information on the fault properties. However, the exact relationship between Rayleigh wave anisotropy and true anisotropic structures is not well known. This study used a three-component (3C) beamforming toolbox to analyse numerical full waveform seismic wave propagation from conceptual models of fractured media, which depict the nonlinear physical behaviour of the wave. We identify Rayleigh waves in the synthetic data produced from a single point source at different locations, compare observed Rayleigh wave anisotropy to structural anisotropy, and assess the effect array design and source distance have on Rayleigh wave analysis and observed anisotropy. Numerical analysis shows that the smaller the velocity contrast between fault and surrounding rock, the more complex the anisotropic response. We find that the slow directions of Rayleigh wave propagation can be a better indicator of fault strike than the fastest direction, when the velocity contrast between the two media is small.

Characterizing faults in geothermal fields is essential for the energy transition, as faults enable efficient heat flow throughout the reservoir. Three-component (3C) beamforming, an ambient seismic noise technique, is a cheap and effective way to analyse fault-related anisotropy by observing surface wave velocities. 3C beamforming extracts the wave type, direction and phase velocities of coherent waves as a function of frequency, which provides an understanding of surface wave velocities. Anisotropic velocities have been shown to be caused by the presence of faults, giving an indication of the maximum depth of permeability within a geothermal reservoir. However, the relationship between faults and surface wave velocities must be examined in more detail. Wavefield modelling using a numerical model was done by propagating a wave through a model of the subsurface with anisotropy applied in the form of a fault at assumed directions. 3C beamforming was then used to analyse this synthetic data, providing information on an identifiable Rayleigh wave and how the velocity of the wave changes depending on fault azimuth. Therefore, indicating the effectiveness of ambient noise methods, like 3C beamforming, compared to that of far more expensive active seismic techniques; the development of which is crucial for the energy transition.

To integrate structural subsurface models and smooth seismic velocity models, they need to share common features and resolutions. Here, we propose a new approach, Depth Assessment from Rayleigh Wave Ellipticities (DARE), for estimating the depth of sudden velocity changes from ambient-noise multi-mode Rayleigh waves applicable to a wide range of frequencies. At frequencies where multi-mode Rayleigh waves have an extremum in ellipticity, the phase velocity can be used to estimate the depth of sudden velocity changes. We test our approach theoretically, numerically, and on real data from two geothermal sites by extracting Rayleigh wave ellipticities and phase velocities from three-component beamforming of ambient noise using the python code package B3AMpy. For a small-scale array, our approach validates the depth of quaternary sediments predicted by geological models. For deeper velocity changes, high uncertainties remain but the general trend of inclining boundaries can be recovered well. We demonstrate that, if impedance contrasts are larger than three, our approach is valid for multiple layers, laterally heterogeneous models, and a wide range of Poisson ratios.

We developed a beamforming toolbox for three-component ambient seismic noise data (B3AM) that enables characterisation and monitoring of the (near) subsurface, and provide a comprehensive overview of its workings and applications. Beamforming is an array technique that analyses phase shifts of the recorded wavefield across the different stations of a seismic array, thereby providing estimates of dominant wave velocities and propagation directions. Measuring phase shifts across the three components of each station further enables us to perform polarisation analysis and identify different wave types and their respective characteristics, for example, Rayleigh wave ellipticity. We explain how these phase shifts are related to a set of intuitive geometric parameters, such as azimuth and dip angle, uniquely describing a specific wave and its propagation properties. As a result, we obtain a quantitative wavefield composition plot as a function of frequency as well as wave type specific dispersion curves and direction of arrival plots. We show examples of B3AM analysis in geothermal fields providing shear-wave velocity profiles and surface wave anisotropy estimates related to the presence and orientation of faults. Examples from ambient noise data in the Groningen area (NL) and the Weisweiler geothermal development (DE) show the potential of the method to improve thickness estimates of sedimentary layers, an important parameter in seismic hazard assessment and reservoir characterisation. Using synthetic data, we demonstrate that B3AM can also be used on transient data and allows us to identify arrival time windows of different waves (in particular Rayleigh waves) in a complex wavefield. The code package is available in both MATLAB and Python (B3AMpy).