ALBERT

Description: 〈span〉〈div〉Abstract〈/div〉In wave physics, the geometrical limit is defined as a propagation regime where the scattering cross‐section σ of an object becomes independent of its internal structure and tends to twice its geometrical cross section σg as the frequency goes to infinity. This is a result that is particularly well documented in the field of optics. Following the classification of 〈a href="https://pubs.geoscienceworld.org/bssa#rf20"〉Wu and Aki (1985b)〈/a〉, we study the high‐frequency scattering limit for velocity‐type and impedance‐type elastic perturbations. Although velocity‐type scatterers do follow the geometrical limit of σ→2σg, the scattering cross section of any impedance‐type scatterer depends on both its density and elastic properties at all frequencies. These results are illustrated using the example of a spherical inclusion that exhibits a small contrast of properties with its environment. We derive simple asymptotic formulas that show good agreement with exact solutions of the boundary value problem (BVP). Our results confirm the distinct behavior of velocity‐type versus impedance‐type perturbations at all frequencies.〈/span〉

Description: 〈span〉〈div〉Abstract〈/div〉In wave physics, the geometrical limit is defined as a propagation regime where the scattering cross‐section σ of an object becomes independent of its internal structure and tends to twice its geometrical cross section σg as the frequency goes to infinity. This is a result that is particularly well documented in the field of optics. Following the classification of 〈a href="https://pubs.geoscienceworld.org/bssa#rf20"〉Wu and Aki (1985b)〈/a〉, we study the high‐frequency scattering limit for velocity‐type and impedance‐type elastic perturbations. Although velocity‐type scatterers do follow the geometrical limit of σ→2σg, the scattering cross section of any impedance‐type scatterer depends on both its density and elastic properties at all frequencies. These results are illustrated using the example of a spherical inclusion that exhibits a small contrast of properties with its environment. We derive simple asymptotic formulas that show good agreement with exact solutions of the boundary value problem (BVP). Our results confirm the distinct behavior of velocity‐type versus impedance‐type perturbations at all frequencies.〈/span〉

Description: The coda quality factor of short-period S waves ( Q c ) excited by local earthquakes in the Pyrenees has been measured as a function of the length of the coda window ( L W ) for different choices of the onset time of the coda ( t W ). In the 2–16 Hz frequency band, we observe a transient regime characterized by an increase of Q c with L W , followed by a stabilization around a plateau the value of which depends on the central frequency of the signal. Using Monte Carlo simulations of wave transport in a variety of random media (1200 models), we demonstrate that the lapse-time dependence of Q c in the Pyrenees may be modeled by multiple anisotropic scattering of seismic waves, without invoking any depth dependence of the attenuation properties in the crust. In our model, anisotropic scattering is quantified by the ratio between the transport mean free path and the mean path ( l */ l ). At 6 Hz, the data require an anisotropy factor l */ l ≥5, a transport mean free path l *400 km, and an intrinsic quality factor Q i 800. From the frequency-dependent plateau of Q c at large lapse time, we infer an intrinsic quality factor of the form Q i 400 f 0.4 in the Pyrenees. We also show how the rapid increase of the lapse-time dependence of Q c with frequency may be exploited to put constraints on the power spectrum of heterogeneities in the crust.

Description: We compare different methods to estimate frequency-domain amplification and duration lengthening of earthquake ground motion in the Mygdonian basin (Greece). Amplification is measured by standard spectral ratios (SSRs) of horizontal component or by single-station earthquake horizontal-to-vertical ratios (EHVRs). Duration lengthening is measured either by the group delay method ( Beauval et al. , 2003 ) and labeled GDDL, or based on the significant duration ( Trifunac and Brady, 1975 ) and labeled TBDL. The methods are applied both to high-quality recordings of the European experimental site EUROSEISTEST array and to a large set of 3D synthetics computed in a new basin model for 1260 sources regularly distributed in depth, distance, and azimuth from the center of the array. The analysis of the recordings in the center of the basin shows an anticorrelation between amplification and duration lengthening, that is, maxima (resp. minima) of GDDL correspond to minima (resp. maxima) of SSR. The maxima of GDDL are also found to coincide with those of SSR variability. This is confirmed by the analysis of the synthetics, which also reveals a pronounced north–south asymmetry of both amplification and duration lengthening caused by nonisotropic excitation of surface waves at the basin edges. We find that all estimates of site response depend on source location and that EHVR is also strongly sensitive to energy partitioning in the analyzed wavefield. We quantify the source-related variability of each estimate, discuss the biases in site response estimation using incomplete source catalogs, and investigate whether the azimuthal dependence of site response can be identified in the recordings. Electronic Supplement: Movies of simulated wave propagation, figures of surface-to-downhole standard spectral ratio (SSR), group delay duration lengthening (GDDL), earthquake horizontal-to-vertical ratio (EHVR), and synthetic waveforms.