K.N. Van Dalen

On Wavemodes at the Interface of a Fluid and a Fluid-Saturated Poroelastic Solid

Pseudo interface waves can exist at the interface of a fluid and a fluid-saturated poroelastic solid. These waves are typically related to the pseudo-Rayleigh pole and the pseudo-Stoneley pole in the complex slowness plane. It is found that each of these two poles can contribute (as a residue) to a full transient wave motion when the corresponding Fourier integral is computed on the principal Riemann sheet. This contradicts the generally accepted explanation that a pseudo interface wave originates from a pole on a nonprincipal Riemann sheet. It is also shown that part of the physical properties of a pseudo interface wave can be captured by loop integrals along the branch cuts in the complex slowness plane. Moreover, it is observed that the pseudo-Stoneley pole is not always present on the principal Riemann sheet depending also on frequency rather than on the contrast in material parameters only. Finally, it is shown that two additional zeroes of the poroelastic Stoneley dispersion equation, which are comparable with the P-poles known in nonporous elastic solids, do have physical significance due to their residue contributions to a full point-force response.

Assessing the small-strain soil stiffness for offshore wind turbines based on in situ seismic measurements

In this contribution, in situ seismic measurements are used to derive the small-strain shear modulus of soil as input for two soil-structure interaction (SSI) models to assess the initial soil stiffness for offshore wind turbine foundations. This stiffness has a defining influence on the first natural frequency of offshore wind turbines (OWTs), which is one of the most important design parameters of these structures. The fundamental natural frequency as measured on installed OWTs is significantly higher than its designed value, and it is expected that the explanation for this can be found in the currently adopted modeling of soil-structure interaction. In this paper a method is suggested to improve the accuracy of estimating the small-strain soil stiffness. The field data used in this study is measured with a seismic cone penetration test. A method is suggested to identify the shear moduli, which together with the measured in situ mass densities and estimated Poisson’s ratios are input for two static 3D SSI models. The first model is a linear elastic finite element model of a half-space of solids attached to a pile (shell). This is a straightforward and fast approach in which a static horizontal force and a bending moment are applied at the top of the pile. The second model extends the first one by introducing contact elements at the interface between pile and soil, where a contraction of the soil towards the pile is not allowed and maximum friction forces on the interface can be prescribed. Finally a method is suggested to translate the global response of a 3D model into an engineering model of a 1D beam laterally supported by uncoupled distributed springs. When comparing the deflections, those derived with the global 3D models, are smaller than deflections derived with the p-y curve design code. The deflections of the global models behave more rigidly, and especially the upper 10m deflections are smaller. The presented work is a small part of the research that still needs to be done before any conclusion can be drawn.

Multi-component acoustic characterization of porous media

The characterization of porous materials (e.g., sandstone) is very important for geotechnical and reservoir engineers. For this purpose, often use is made of acoustic waves that are sent through the medium. The desired material parameters can then be estimated from the measured signals. However, often only the velocity or the attenuation of the acoustic waves is employed, and much information that is carried by the waves remains untouched. Therefore, in this thesis we investigate the feasibility of the characterization of porous media using information contained in full acoustic waveforms as observed in different components (e.g., particle motion and fluid pressure). We subsequently address the mathematical description of pseudo interface waves, their experimental detection and the estimation of medium parameters. In the latter part, we show that it is possible to obtain unique and stable estimates of the permeability and porosity of a porous medium by simultaneously exploiting either different waveform attributes of a pseudo interface wave, or the reflection coefficients of different body waves.

Medium characterization from interface-wave impedance and ellipticity using simultaneous displacement and pressure measurements.

The interface-wave impedance and ellipticity are wave attributes that interrelate the full waveforms as observed in different components. For each of the fluid/elastic-solid interface waves, i.e., the pseudo-Rayleigh (pR) and Stoneley (St) waves, the impedance and ellipticity are found to have different functional dependencies on Youngs modulus and Poissons ratio. By combining the attributes in a cost function, unique and stable estimates of these parameters can be obtained, particularly when using the St wave. In a validation experiment, the impedance of the laser-excited pR wave is successfully extracted from simultaneous measurements of the normal particle displacement and the fluid pressure at a water/aluminum interface. The displacement is measured using a laser Doppler vibrometer (LDV) and the pressure with a needle hydrophone. Any LDV measurement is perturbed by refractive-index changes along the LDV beam once acoustic waves interfere with the beam. Using a model that accounts for these perturbations, an impedance decrease of 28% with respect to the plane wave impedance of the pR wave is predicted for the water/aluminum configuration. Although this deviation is different for the experimentally extracted impedance, there is excellent agreement between the observed and predicted pR waveforms in both the particle displacement and fluid pressure.

Characterization of Subsurface Parameters with Combined Fluid-pressure and Particle-velocity Measurements

The idea of combined 3C-geophones and hydrophones (4C-receivers) often used in marine Ocean-Bottom Cables, can also be used for seismic surveying on land in saturated soils. The fluid-pressure data can be used to interpret the particle-velocity data. It can, however, also be used to extract more information about the subsurface, e.g., information about 2-phase behaviour. To gain insight in the behaviour of various wave modes in the different components, the three-dimensional point-force response of a homogeneous isotropic half-space has been calculated. Because the subsurface is considered as a poroelastic medium in 4C-experiments, Biot’s theory for poroelastic media needs to be used; this explicitly accounts for 2-phase behaviour. The responses show strong dependence on porosity and permeability. It is the combination of particle velocity and fluid pressure that reveals poroelastic characteristics of the subsurface, especially for the Rayleigh wave. Its dispersive behaviour, met in 4C-experiments, is not entirely understood yet. Furthermore, it is shown that it makes sense to use Biot’s theory to model seismic responses when dealing with 4C-measurements. The slow compressional mode may even contribute significantly to the Rayleigh wave.

Higher-order homogenization for one-dimensional wave propagation in poroelastic composites

An effective model is derived for periodically layered poroelastic media, where layers represent mesoscopic-scale heterogeneities that are larger than the pore and grain sizes but smaller than the wavelength. Each layer is homogeneous, described by Biot’s equations of poroelasticity. The proposed model has only real-valued frequencyindependent effective coefficients determined analytically exclusively by the physical parameters of the layers. It serves as an alternative to the existing models with frequency-dependent effective elastic properties. Homogenization is based on asymptotic expansions with multiple spatial scales and results in equations of motion containing higher-order derivatives. It is valid for wavelengths much larger than the period of the system. This approach, being widely used in elasticity, is extended to poroelasticity in this work. The exact analytical solution, obtained by the application of Floquet’s theory to poroelastic composites, is used to validate the model.

Coupled flap and edge wise blade motion due to a quadratic wind force definition

The wind force on turbine blades, consisting of a drag and lift component, depends nonlinearly on the relative wind velocity. This relative velocity comprises mean wind speed, wind speed fluctuations and the structural response velocity. The nonlinear wind excitation couples the flap wise and edge wise response of a turbine blade. To analyze this motion coupling, an isolated blade is modelled as a continuous cantilever beam and corresponding nonlinear expressions for the drag and lift force are defined. After reduction of the model on the basis of its principal modes, the nonlinear response up to the second order is derived with the help of a Volterra series expansion and the harmonic probing technique. This technique allows for response analysis in the frequency domain, via which the combined flap and edge wise responses can easily be visualized. As a specific case, the characteristics of the NREL5 turbine blades are adopted. For both non-operating and operating conditions, blade responses in a turbulent wave field, based on a Kaimal spectrum, are determined. The second-order responses are shown to cause additional motion coupling, and moreover, are proven not to be negligible straightforwardly.

Retrieving higher-mode surface waves using seismic interferometry by multidimensional deconvolution

Virtual-source surface-wave responses can be retrieved using the crosscorrelation of wavefields observed at two receivers. Higher-mode surface waves cannot be properly retrieved when there is a lack of subsurface sources, which is often the case. In this paper, we present a multidimensional-deconvolution scheme that introduces an additional processing step in which the crosscorrelation result is deconvolved by a point-spread function. The scheme is based on an approximate convolution theorem that includes pointforce responses only, which is advantageous for applications with contemporary field-acquisition geometries. The point-spread function captures the imprint of the lack of subsurface sources and quantifies the associated smearing of the virtual source in space and time. The function can be calculated from the same wavefields used in the correlation method, provided that one or more vertical arrays of subsurface receivers are present and the illumination is from one side. We show that the retrieved surface-wave response, including the higher modes, becomes much more accurate. The waveforms are properly reconstructed and there is only a small amplitude error, which is due to non-canceling cross terms in the employed approximate convolution theorem. The improved retrieval of the multi-mode surface waves can facilitate dispersion analyses and near-surface inversion algorithms.

In-situ permeability from physics-based integration of poroelastic reflection coefficients

A reliable estimate of the in-situ permeability of a porous layer in the subsurface is extremely difficult to obtain. We have observed that at the field seismic frequency band the poroelastic behaviour for different seismic wave modes can differ in such a way that their combination can give unique estimates of in-situ permeability and porosity simultaneously. We have integrated the angle- and frequency-dependent poroelastic reflection coefficients of different seismic wave modes, and have tested the results through numerical simulations. The estimated values of permeability and porosity appear to be robust against uncertainties in the employed poroelastic attenuation mechanism. Potential applications of this approach exist in hydrocarbon exploration, hydrogeology, and geotechnical engineering.