Kasper van Wijk

The Virtual Refraction: Useful Spurious Energy in Seismic Interferometry

Seismic interferometry is rapidly becoming an established technique to recover the Green’s function between receivers, but practical limitations in the source-energy distribution inevitably lead to spurious energy in the results. Instead of attempting to suppress all such energy, we use a spurious wave associated with the crosscorrelation of refracted energy at both receivers to infer estimates of subsurface parameters. We named this spurious event the virtual refraction. Illustrated by a numerical two-layer example, we found that the slope of the virtual refraction defines the velocity of the faster medium and that the stationary-phase point in the correlation gather provides the critical offset. With the associated critical time derived from the real shot record, this approach includes all of the necessary information to estimate wave speeds and interface depth without the need of inferences from other wave types.

Surface-wave inversion limitations from laser-Doppler physical modeling

Surface-wave dispersion inversion is growing in popularity for geotechnical applications, due to its noninvasive character, relative straightforward field procedures and interpretation, especially when the subsurface structure is locally assumed to be one-dimensional (1D). Here, laser-Doppler physical modeling of surface-wave propagation is used to address issues of surface-wave depth penetration, the presence of dipping layers, and the associated limitations and systematic errors propagated in conventional 1D surface-wave inversion. Flat-layered models show that, with an active source and linear spread, the maximum resolvable wavelength of the Rayleigh-wave fundamental mode is on the order of 40% of the spread length. Linearised inversions confirm the rule of thumb that the depth penetration is 20–25% of the spread length, and that correct a priori layer interface depths from refraction analysis allow more accurate results. However, even under optimal conditions, failing to account for a dominant higher mode at low frequency when a stiff shallow layer is present, causes an overestimate of deeper layer shear-wave velocity. Moreover, a layer dip of only a few degrees can significantly bias the surface-wave inversion. If the incorrect a priori information from a single-shot refraction analysis is incorporated in the inverse problem, estimated interface depth depends on the shot position and deeper layer shear-wave velocity is underestimated. Even if correct a priori constraints are used, an underestimate of half-space shear-wave velocity of up to 25% remains.

Imaging and suppressing near-receiver scattered surface waves

When traveling through a complex overburden, upcoming seismic body waves can be disturbed by scattering from local heterogeneities. Currently, surface-consistent static and amplitude corrections correct for rapid variations in arrival times and amplitudes of a reflector, but these methods impose strong assumptions on the near-surface model. Observations on synthetic and laboratory experiments of near-surface scattering with densely sampled data suggest that removing noise from near-receiver scattering requires multichannel approaches rather than single-channel, near-surface corrections. In this paper we develop a wavefield-based imaging method to suppress surface waves scattered directly beneath the receivers. Using an integral-equation formulation, we account for near-surface heterogeneities by a surface impedance function. This impedance function is used to model scattered surface waves, excited by upcoming wavefronts. The final step in our algorithm is to subtract the scattered surface waves. We succes...

Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group effective attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles from 0° to 90° with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient A governed by the Thomsenstyle attenuation-anisotropy parameters Q and Q. Whereas the symmetry axis of the angle-dependent coefficient A practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor Q increases more than tenfold from the symmetry axisslow direction to the isotropy planefast direction. Inversion of the coefficient A using the Christoffel equation yields large negative values of the parameters Q and Q. The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO amplitude-variation-with-offset analysis, amplitude-preserving migration, and seismic fracture detection.

Analysis of strong scattering at the micro-scale

Exploiting the fine structure of strongly scattered waves could provide a wealth of new information in seismology, ultrasonics, acoustics, and other fields that study wave propagation in heterogeneous media. Therefore, noncontacting laser-based measurements of ultrasonic surface waves propagating in a strongly disordered medium are performed in which the ratio of the dominant surface wavelength to the size of a scatterer is large, and waves that propagate through many scatterers are recorded. This allows analysis of scattering-induced dispersion and attenuation, as well as the transition from ballistic to diffusive propagation. Despite the relatively small size of the scatterers, multiple scattering strikingly amplifies small perturbations, making changes even in a single scatterer visible in the later-arriving waveforms. To understand the complexity of the measured waveforms, elastic spectral-element numerical simulations are performed. The multiple-scattering sensitivity requires precise gridding of the...

Multicomponent wavefield characterization with a novel scanning laser interferometer

The in-plane component of the wavefield provides valuable information about media properties from seismology to nondestructive testing. A new compact scanning laser ultrasonic interferometer collects light scattered away from the angle of incidence to provide the absolute ultrasonic displacement for both the out-of-plane and an in-plane components. This new system is tested by measuring the radial and vertical polarization of a Rayleigh wave in an aluminum half-space. The estimated amplitude ratio of the horizontal and vertical displacement agrees well with the theoretical value. The phase difference exhibits a small bias between the two components due to a slightly different frequency response between the two processing channels of the prototype electronic circuitry.

Observation and modeling of source effects in coda wave interferometry at Pavlof volcano

Sorting out source and path effects for seismic waves at volcanoes is critical for the proper interpretation of underlying volcanic processes. Source or path effects imply that seismic waves interact strongly with the volcanic subsurface, either through partial resonance in a conduit (Garces et al., 2000; Sturton and Neuberg, 2006) or by random scattering in the heterogeneous volcanic edifice (Wegler and Luhr, 2001). As a result, both source and path effects can cause seismic waves to repeatedly sample parts of the volcano, leading to enhanced sensitivity to small changes in material properties at those locations. The challenge for volcano seismologists is to detect and reliably interpret these subtle changes for the purpose of monitoring eruptions.

Theory and Laboratory Experiments of Elastic Wave Scattering by Dry Planar Fractures

Remote sensing of fractures with elastic waves is important in fields ranging from seismology to nondestructive testing. In many geophysical applications, fractures control the flow of fluids such as water, hydrocarbons or magma. While previous analytic descriptions of scattering mostly deal with very large or very small fractures (compared to the dominant wavelength), we present an analytic solution for the scattering of elastic waves from a fracture of arbitrary size. Based on the linear slip model for a dry fracture, we derive the scattering amplitude in the frequency domain under the Born approximation for all combinations of incident and scattered wave modes. Our analytic results match laser-based ultrasonic laboratory measurements of a single fracture in clear plastic, allowing us to quantify the compliance of a fracture. Copyright

Tunable multiple-scattering system

To study the propagation of multiply scattered waves, it is useful to have a medium in which the scattering properties can be easily controlled. Here, we describe such a system; it involves the propagation of ultrasonic surface waves in a medium with an aligned, disordered pattern of grooves. Waves propagating parallel to the grooves see a homogeneous medium; waves propagating perpendicular to the grooves are strongly scattered. By varying the source–receiver distance and orientation with respect to the grooves, we are able to map out the transition from ballistic to diffusive propagation. In addition, by using an optical detection system we are able to measure the wave motion inside the scattering medium. We measure the angle-dependent macroscopic properties of the medium, such as the group velocity as well as the mean-free path and the diffusion constant in the strong-scattering regime.

Analyzing the coda from correlating scattered surface waves

The accuracy of scattered Rayleigh waves estimated using an interferometric method is investigated. Summing the cross correlations of the wave fields measured all around the scatterers yields the Greens function between two excitation points. This accounts for the direct wave and the scattered field (coda). The correlations themselves provide insights into the location of the scatterers, as well as which scatterer is responsible for particular parts of the coda. Furthermore, these measurements confirm a constant-time arrival in the correlations, not part of the Greens function, but which has previously been derived as a result of the generalized optical theorem.