ALBERT

Beschreibung: Cross-correlation of ambient seismic noise recorded by two seismic stations may result in an estimate of the Green's function between those two receivers. Several authors have recently attempted to measure attenuation based on these interferometric, receiver–receiver surface waves. By now, however, it is well established that the loss of coherence of the cross-correlation as a function of space depends strongly on the excitation of the medium. In fact, in a homogeneous dissipative medium, uniform excitation is required to correctly recover attenuation. Applied to fundamental-mode ambient seismic surface waves, this implies that the cross-correlation will decay at the local attenuation rate only if noise sources are distributed uniformly on the Earth's surface. In this study we show that this constraint can be relaxed in case the observed loss of coherence is due to multiple scattering instead of dissipation of energy. We describe the scattering medium as an effective medium whose phase velocity and rate of attenuation are a function of the scatterer density and the average strength of the scatterers. We find that the decay of the cross-correlation in the effective medium coincides with the local attenuation of the effective medium in case the scattering medium is illuminated uniformly from all angles. Consequently, uniform excitation is not a necessary condition for the correct retrieval of scattering attenuation. We exemplify the implications of this finding for studies using the spectrally whitened cross-correlation to infer subsurface attenuation.

Beschreibung: Time-reversal modelling provides a simple and robust solution to source-imaging problems. However, for recovering a well-resolved image of the source, time-reversal requires a balanced illumination of the target from all angles. When acquisition is incomplete and a balanced illumination is not possible, the time-reversal solution may not be adequate. We present an inversion algorithm for computing the signals to be back propagated by an array of receivers with a given configuration in order to optimally image an unknown source in an elastic medium. This approach is based on minimizing the difference between the back-propagated wavefield and the time-reversed displacement field of the source in the near source region. The proposed method requires knowledge of the propagation medium and an estimate of the source location. Other information related to the source (e.g. source mechanism) is encoded within the data and not explicitly required by the method. The method is applicable in both elastic and acoustic media. We use synthetic examples to test the performance of our method, to analyse its sensitivities, potentials and limitations and to demonstrate its potential advantages over the time-reversal source-imaging technique.

Beschreibung: Passive seismic methods using earthquakes can be applied for extracting body waves and obtaining information of subsurface structure. In this study, we retrieve direct and reflected plane waves by applying seismic interferometry to the recorded ground motion from a cluster of regional earthquakes. We apply upgoing/downgoing P/S wavefield decomposition, time windowing, and multidimensional deconvolution to improve the quality of the extraction of reflected waves with seismic interferometry. The wavefield separation and seismic interferometry based on multidimensional deconvolution allow us to reconstruct PP, PS, SP and SS reflected waves without unwanted crosstalk between P and S waves. From earthquake data, we obtain PP, PS and SS reflected plane waves that reflect off the same reflector, and estimate P - and S -wave velocities.

Beschreibung: Remotely sensing the properties of fractures has applications ranging from exploration geophysics to hazard monitoring. Newly developed capabilities to measure the in-plane component of dense laser-based ultrasound wave fields allow us to test the applicability of a linear slip model to describe fracture properties. In particular, we estimate the diameter, and the normal and tangential compliance of a fracture from the measured scattering amplitudes of P and S waves in the laboratory. Finally, we show that the normal compliance decreases linearly with increasing uniaxial static stress in the plane of the fracture, but that our measurements of the SV scattered field do not show significant changes in the tangential compliance.

Beschreibung: We detect time-lapse changes in P - and S -wave velocities (hereafter, V P and V S , respectively) and shear wave splitting parameters associated with the 2011 Tohoku earthquake, Japan, at depths between 0 and 504 m. We estimate not only medium parameters but also the 95 per cent confidence interval of the estimated velocity change by applying a new least squares inversion scheme to the deconvolution analysis of KiK-net vertical array records. Up to 6 per cent V S reduction is observed at more than half of the analysed KiK-net stations in northeastern Japan with over 95 per cent confidence in the first month after the main shock. There is a considerable correlation between the S -wave traveltime delay and the maximum horizontal dynamic strain (MDS) by the main shock motion when the strain exceeds 5 x 10 – 4 on the ground surface. This correlation is not clearly observed for MDS at the borehole bottom. On the contrary, V P and shear wave splitting parameters do not show systematic changes after the Tohoku earthquake. These results indicate that the time-lapse change is concentrated near the ground surface, especially in loosely packed soil layers. We conclude that the behaviour of V P , V S and shear wave splitting parameters are explained by the generation of omnidirectional cracks near the ground surface and by the diffusion of water in the porous subsurface. Recovery of V S should be related to healing of the crack which is proportional to the logarithm of the lapse time after the main shock and/or to decompaction after shaking.

Beschreibung: Measuring attenuation on the basis of interferometric, receiver–receiver surface waves is a non-trivial task: the amplitude, more than the phase, of ensemble-averaged cross-correlations is strongly affected by non-uniformities in the ambient wavefield. In addition, ambient noise data are typically pre-processed in ways that affect the amplitude itself. Some authors have recently attempted to measure attenuation in receiver–receiver cross-correlations obtained after the usual pre-processing of seismic ambient-noise records, including, most notably, spectral whitening. Spectral whitening replaces the cross-spectrum with a unit amplitude spectrum. It is generally assumed that cross-terms have cancelled each other prior to spectral whitening. Cross-terms are peaks in the cross-correlation due to simultaneously acting noise sources, that is, spurious traveltime delays due to constructive interference of signal coming from different sources. Cancellation of these cross-terms is a requirement for the successful retrieval of interferometric receiver–receiver signal and results from ensemble averaging. In practice, ensemble averaging is replaced by integrating over sufficiently long time or averaging over several cross-correlation windows. Contrary to the general assumption, we show in this study that cross-terms are not required to cancel each other prior to spectral whitening, but may also cancel each other after the whitening procedure. Specifically, we derive an analytic approximation for the amplitude difference associated with the reversed order of cancellation and normalization. Our approximation shows that an amplitude decrease results from the reversed order. This decrease is predominantly non-linear at small receiver–receiver distances: at distances smaller than approximately two wavelengths, whitening prior to ensemble averaging causes a significantly stronger decay of the cross-spectrum.

Beschreibung: The material properties of earth materials often change after the material has been perturbed (slow dynamics). For example, the seismic velocity of subsurface materials changes after earthquakes, and granular materials compact after being shaken. Such relaxation processes are associated by observables that change logarithmically with time. Since the logarithm diverges for short and long times, the relaxation can, strictly speaking, not have a log-time dependence. We present a self-contained description of a relaxation function that consists of a superposition of decaying exponentials that has log-time behaviour for intermediate times, but converges to zero for long times, and is finite for t = 0. The relaxation function depends on two parameters, the minimum and maximum relaxation time. These parameters can, in principle, be extracted from the observed relaxation. As an example, we present a crude model of a fracture that is closing under an external stress. Although the fracture model violates some of the assumptions on which the relaxation function is based, it follows the relaxation function well. We provide qualitative arguments that the relaxation process, just like the Gutenberg–Richter law, is applicable to a wide range of systems and has universal properties.