K. Löer
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This work explores how changes in scattering strength in multiply-scattering media can be quantified using synthetic wavefields computed with Foldy's method for isotropic point scatterers. By averaging waves across random realizations, the effective complex wavenumber, which is linked to the scattering strength through the effective attenuation and phase velocity, can be estimated. We estimate the attenuation coefficient from average recordings at different offsets. Simulations show that the attenuation coefficient can be reliably calculated for a wide frequency band around the central frequency of the source wavelet, but that accuracy declines at low and high frequencies due to model and source spectrum limitations. The method currently applies only to 2D isotropic point scatterers with constant scattering amplitude and assumes the scatterer number density to be known, but the extension to estimating relative changes in scattering strength for models with varying scattering amplitudes but equal scatterer number density is straightforward.
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This work explores how changes in scattering strength in multiply-scattering media can be quantified using synthetic wavefields computed with Foldy's method for isotropic point scatterers. By averaging waves across random realizations, the effective complex wavenumber, which is linked to the scattering strength through the effective attenuation and phase velocity, can be estimated. We estimate the attenuation coefficient from average recordings at different offsets. Simulations show that the attenuation coefficient can be reliably calculated for a wide frequency band around the central frequency of the source wavelet, but that accuracy declines at low and high frequencies due to model and source spectrum limitations. The method currently applies only to 2D isotropic point scatterers with constant scattering amplitude and assumes the scatterer number density to be known, but the extension to estimating relative changes in scattering strength for models with varying scattering amplitudes but equal scatterer number density is straightforward.
Conference paper
(2026)
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K. Löer, A. Afanassieva, D. Bowden, F. Munoz Burbano, C. Finger, G. Savard, T. Hudson, M. Lupi
In the GeoHEAT project to advance geothermal exploration in Thurgau, Switzerland, passive seismic imaging plays a major role in mapping the topography of the crystalline basement and identifying potential sedimentary troughs and deep fractured zones. To this end, ambient noise tomography (ANT) is performed, which relies on Green’s function estimates obtained from ambient noise cross-correlations (interferometry). Since the quality of the retrieved Green’s function estimate depends on the properties of the ambient noise wavefield, we use three-component beamforming to analyse the dominant contributions to the wavefield recorded on a temporary nodal network. Deciphering the particle motion allows us to discriminate retro- and prograde Rayleigh waves and shows that the latter dominate a significant part of the frequency range of interest. Frequency-wavenumber analysis further reveals that this prograde motion belongs to the first higher mode Rayleigh wave. We conclude that this higher mode is also controlling the Green’s function estimates retrieved from ambient noise interferometry at the corresponding frequencies. This explains the difficulties encountered when trying to fit dispersion curves retrieved from interferometry for certain station pairs and highlights the need for improved interferometry schemes that use additional wavefield information from beamforming.
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In the GeoHEAT project to advance geothermal exploration in Thurgau, Switzerland, passive seismic imaging plays a major role in mapping the topography of the crystalline basement and identifying potential sedimentary troughs and deep fractured zones. To this end, ambient noise tomography (ANT) is performed, which relies on Green’s function estimates obtained from ambient noise cross-correlations (interferometry). Since the quality of the retrieved Green’s function estimate depends on the properties of the ambient noise wavefield, we use three-component beamforming to analyse the dominant contributions to the wavefield recorded on a temporary nodal network. Deciphering the particle motion allows us to discriminate retro- and prograde Rayleigh waves and shows that the latter dominate a significant part of the frequency range of interest. Frequency-wavenumber analysis further reveals that this prograde motion belongs to the first higher mode Rayleigh wave. We conclude that this higher mode is also controlling the Green’s function estimates retrieved from ambient noise interferometry at the corresponding frequencies. This explains the difficulties encountered when trying to fit dispersion curves retrieved from interferometry for certain station pairs and highlights the need for improved interferometry schemes that use additional wavefield information from beamforming.
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.
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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.
Investigating Rayleigh wave anisotropy in faulted media with three-component beamforming
Insights from numerical models and applications for geothermal exploration
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.
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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.
Subsurface characterisation with three-component ambient noise beamforming
Theory, codes, and applications
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).
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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).
Surface Wave Anisotropy in Fractured Media
Insights from Wavefield Modelling and Applications for Geothermal Exploration
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.
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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.
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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.