Karel N. van Dalen

In-Situ Permeability from Integrated 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 behavior for different seismic wavetypes can differ in such a way that their combination gives unique estimates of in?situ permeability and porosity simultaneously. This is utilized in the integration of angle? and frequency?dependent poroelastic reflection coefficients in a cost function. Realistic numerical simulations show that the estimated values of permeability and porosity are robust against uncertainties in the employed poroelastic mechanism and in the data. Potential applications of this approach exist in hydrocarbon exploration, hydrogeology, and geotechnical engineering.

Retrieving surface waves from ambient seismic noise using seismic interferometry by multidimensional deconvolution

Retrieving virtual source surface waves from ambient seismic noise by cross correlation assumes, among others, that the noise field is equipartitioned and the medium is lossless. Violation of these assumptions reduces the accuracy of the retrieved waves. A point-spread function computed from the same ambient noise quantifies the associated virtual sources spatial and temporal smearing. Multidimensional deconvolution (MDD) of the retrieved surface waves by this function has been shown to improve the virtual sources focusing and the accuracy of the retrieved waves using synthetic data. We tested MDD on data recorded during the Batholiths experiment, a passive deployment of broadband seismic sensors in British Columbia, Canada. The array consisted of two approximately linear station lines. Using 4 months of recordings, we retrieved fundamental-mode Rayleigh waves (0.05–0.27 Hz). We only used noise time windows dominated by waves that traverse the northern line before reaching the southern (2.5% of all data). Compared to the conventional cross-correlation result based on this subset, the MDD waveforms are better localized and have significantly higher signal-to-noise ratio. Furthermore, MDD corrects the phase, and the spatial deconvolution fills in a spectral (f, k domain) gap between the single-frequency and double-frequency microseism bands. Frequency whitening of the noise also fills the gap in the cross-correlation result, but the signal-to-noise ratio of the MDD result remains higher. Comparison of the extracted phase velocities shows some differences between the methods, also when all data are included in the conventional cross correlation.

The significance of the evanescent spectrum in structure-waveguide interaction problems

Modal decomposition is often applied in elastodynamics and acoustics for the solution of problems related to propagation of mechanical disturbances in waveguides. One of the key elements of this method is the solution of an eigenvalue problem for obtaining the roots of the dispersion equation, which signify the wavenumbers of the waves that may exist in the system. For non-dissipative media, the wavenumber spectrum consists of a finite number of real roots supplemented by infinitely many imaginary and complex ones. The former refer to the propagating modes in the medium, whereas the latter constitute the so-called evanescent spectrum. This study investigates the significance of the evanescent spectrum in structure-waveguide interaction problems. Two cases are analysed, namely, a beam in contact with a fluid layer and a cylindrical shell interacting with an acousto-elastic waveguide. The first case allows the introduction of a modal decomposition method and the establishment of appropriate criteria for the truncation of the modal expansions in a simple mathematical framework. The second case describes structure-borne wave radiation in an offshore environment during the installation of a pile with an impact hammer-a problem that has raised serious concerns in recent years due to the associated underwater noise pollution.

Combined Particle Motion And Fluid Pressure Measurements of Surface Waves

In this paper we investigate the use of combined particle motion and fluid pressure measurements of surface waves. In particular, we show that the surface-wave impedance of the pseudo-Rayleigh (pR) wave, excited at a water/aluminum interface, can be successfully extracted from such a combined experiment at ultrasonic frequencies. The displacement is measured using a laser Doppler vibrometer (LDV) and the pressure with a needle hydrophone. The impedance of the pR-wave can be clearly distinguished in the wavenumberfrequency domain. Our results suggest that the surface-wave impedance can also be extracted from measurements on seismic or borehole logging scales. Further, the excellent agreement between the observed and predicted pR-waveforms in both the particle displacement and fluid pressure shows that laboratory scale experiments using laser ultrasonics and small pressure detectors can offer a useful link between theoretical models and real field experiments.

Semi-analytical Solution for the Dynamic Response of a Cylindrical Structure Embedded in a Homogeneous Half-Space

This paper addresses the dynamic response of an infinitely long cylindrical structure embedded in an elastic half-space. The structure has a circular cross-section and its axis is parallel to the half-space surface. Excitation can be incident body waves or forces applied on the surface of the half-space and/or the structure. The model can be used to assess the integrity of structures when acted upon by seismic waves, to predict ground-borne vibration due to circulation of vehicles, and to infer about the safety of vehicles during earthquake events. Because the half-space and the structure surfaces possess different symmetries, the solution is not straightforward. In order to circumvent this difficulty, the physical domain is conformally mapped onto an auxiliary domain with a cylindrical symmetry, in which the free surface of the half-space and the surface of the structure are located at concentric cylindrical surfaces. The solution of the original boundary value problem is finally obtained by solving a set of algebraic equations. Truncation of the summation over circumferential modes is needed in the numerical implementation. Convergence tests, validations and comparisons of stresses and motions for two- and three-dimensional cases are presented and discussed as well as the advantages and disadvantages of the proposed method. Additionally, the effect of the presence of the tunnel is analysed by considering a limiting case of the half-space with just a cylindrical cavity of the same radius as the outer radius of the tunnel.

Green’s Tensors for Wave Propagation in a Fluid-Saturated Porous Medium

We derive the infinite-space Green’s tensors (the impulse responses) for wave propagation in a fluid-saturated porous medium by straightforward application of the Fourier transform. Low- and high-frequency approximations and numerical examples are used to illustrate the frequency dependence of the attributes (i.e., velocity, attenuation, relative fluid-solid motion) of the possible wavemodes, of the corresponding transient waveforms as excited by point sources, and of the difference between the waveforms in the particle velocity and fluid pressure. The latter difference is captured by the “coupling impedance” and is shown to be significant particularly for the slow compressional mode.

Governing Equations for Wave Propagation in a Fluid-Saturated Porous Medium

In this chapter the governing equations for wave propagation in a fluid-saturated porous medium are derived and the involved physical mechanisms and acoustic parameters are discussed. It is shown that the stress-strain relations associated with Biot’s theory can be straightforward obtained from constitutive and continuity equations. Equations of motion are derived by combining these stress-strain relations with momentum equations. We present the equations of motion in the two different formulations that are known in the literature.