X. Jia

Nonlinear dynamics, granular media and dynamic earthquake triggering

The 1992 magnitude 7.3 Landers earthquake triggered an exceptional number of additional earthquakes within California and as far north as Yellowstone and Montana. Since this observation, other large earthquakes have been shown to induce dynamic triggering at remote distances—for example, after the 1999 magnitude 7.1 Hector Mine and the 2002 magnitude 7.9 Denali earthquakes—and in the near-field as aftershocks. The physical origin of dynamic triggering, however, remains one of the least understood aspects of earthquake nucleation. The dynamic strain amplitudes from a large earthquake are exceedingly small once the waves have propagated more than several fault radii. For example, a strain wave amplitude of 10-6 and wavelength 1 m corresponds to a displacement amplitude of about 10-7 m. Here we show that the dynamic, elastic-nonlinear behaviour of fault gouge perturbed by a seismic wave may trigger earthquakes, even with such small strains. We base our hypothesis on recent laboratory dynamic experiments conducted in granular media, a fault gouge surrogate. From these we infer that, if the fault is weak, seismic waves cause the fault core modulus to decrease abruptly and weaken further. If the fault is already near failure, this process could therefore induce fault slip.

Transitional nonlinear elastic behaviour in dense granular media

[1] Nonlinear sound propagation in a stressed glass bead pack is investigated via amplitude measurements of harmonic generation. We evidence two distinct regimes of sound-matter interaction: reversible and irreversible, as a function of the ratio rs between dynamic strain and static one. In the reversible regime, the higher harmonics generated agree well with a mean-field model based on the Hertz contact theory, and the coefficient of nonlinearity b deduced from the measured amplitude of second-harmonic is consistent with that deduced from the acoustoelastic measurement. Beyond a certain threshold (rs > 3%), the interaction of sound wave with granular matter becomes irreversible, accompanied by a small compaction of the medium. Citation: Brunet, T., X. Jia, and P. A. Johnson (2008), Transitional nonlinear elastic behaviour in dense granular media, Geophys. Res. Lett., 35, L19308, doi:10.1029/2008GL035264.

Anisotropic nonlinear elasticity in a spherical-bead pack: influence of the fabric anisotropy.

Stress-strain measurements and ultrasound propagation experiments in glass bead packs have been simultaneously conducted to characterize the stress-induced anisotropy under uniaxial loading. These measurements realized, respectively, with finite and incremental deformations of the granular assembly, are analyzed within the framework of the effective-medium theory based on the Hertz-Mindlin contact theory. Our work shows that both compressional and shear wave velocities and consequently the incremental elastic moduli agree fairly well with an effective-medium model developed by Johnson [J. Appl. Mech. 65, 380 (1998)] for the oedometric test, but the anisotropic stress ratio resulting from finite deformation does not at all. As indicated by numerical simulations, the discrepancy may arise from the fact that the model does not properly allow the grains to relax from the affine motion approximation. Here we find that the interaction nature at the grain contact could also play a crucial role for the relevant prediction by the model; indeed, such discrepancy can be significantly reduced if the frictional resistance between grains is removed. Another main experimental finding is the influence of the inherent anisotropy of granular packs, realized by different protocols of the sample preparation. Our results reveal that compressional waves are more sensitive to the stress-induced anisotropy, whereas the shear waves are more sensitive to the fabric anisotropy.

DETECTION OF IN-PLANE AND OUT-OF-PLANE ULTRASONIC DISPLACEMENTS BY A TWO-CHANNEL CONFOCAL FABRY-PEROT INTERFEROMETER

Simultaneous detection of in‐plane and out‐of‐plane ultrasonic displacements by a two‐channel confocal Fabry–Perot optical receiver is described. Accuracy is tested by measuring the in‐plane and out‐of‐plane displacements produced by Rayleigh surface waves generated by a piezoelectric transducer and a laser.

Analysis of optical interferometric measurements of guided acoustic waves in transparent solid media

Guided acoustic waves propagating in transparent and isotropic solids are studied by optical interferometry via the photoelastic effect. Unlike the photoelastic technique, the interferometric method permits the measurement of the phase shift rather than the polarization change of the light passing through an acoustic field. By analyzing the acoustically induced change in the index ellipsoid of refraction, it is demonstrated that the optical phase shift is proportional to the dilatation or the relative change in volume of the material. The dilatation fields of the symmetric and antisymmetric Lamb modes S0 and A0, as well as that of the Rayleigh wave, were calculated. Experiments performed in fused quartz by the interferometric method are in good agreement with theoretical predictions. Compared to the conventional photoelastic technique, the interferometric measurement of acoustic wave is phase sensitive and quantitative.

Laser interferometric detection of ultrasonic waves propagating inside a transparent solid

Ultrasonic waves propagating inside a transparent solid have been investigated by using a combination of laser interferometry and photoelastic effect. In comparison with the classical photoelastic technique, the present heterodyne method is sensitive not only to the amplitude but also to the phase of acoustic strains. Pulsed strains of longitudinal, shear, and Rayleigh waves have been experimentally achieved. The phase changes of ultrasonic pulses reflected at the different interfaces were investigated. In addition, the polarization states of shear waves have been observed using the heterodyne detection.

Softening of stressed granular packings with resonant sound waves.

We perform numerical simulations of a two-dimensional bidisperse granular packing subjected to both a static confining pressure and a sinusoidal dynamic forcing applied by a wall on one edge of the packing. We measure the response experienced by a wall on the opposite edge of the packing and obtain the resonant frequency of the packing as the static or dynamic pressures are varied. Under increasing static pressure, the resonant frequency increases, indicating a velocity increase of elastic waves propagating through the packing. In contrast, when the dynamic amplitude is increased for fixed static pressure, the resonant frequency decreases, indicating a decrease in the wave velocity. This occurs both for compressional and for shear dynamic forcing, and is in agreement with experimental results. We find that the average contact number Zc at the resonant frequency decreases with increasing dynamic amplitude, indicating that the elastic softening of the packing is associated with a reduced number of grain-grain contacts through which the elastic waves can travel. We image the excitations created in the packing and show that there are localized disturbances or soft spots that become more prevalent with increasing dynamic amplitude. Our results are in agreement with experiments on glass bead packings and earth materials such as sandstone and granite, and may be relevant to the decrease in elastic wave velocities that has been observed to occur near fault zones after strong earthquakes, in surficial sediments during strong ground motion, and in structures during earthquake excitation.

Direct experimental investigations of acoustic modes guided by a solid–solid interface using optical interferometry

This paper presents direct field measurements of acoustic modes guided by the interface between two transparent solids. The measurement technique is based on the acousto-optical interaction inside the solid between the acoustic field and the probe laser beam of an interferometer. The main advantage of the method is its ability to measure acoustic strain fields in areas of difficult access with the classic detection methods. Moreover, it gives complete information about the dilatation strain field inside the solid, e.g., amplitude and phase. The propagation of a real velocity mode (Stoneley wave) is first illustrated. Then the situation of complex velocity modes is investigated for a Plexiglas–fused quartz slip interface. This material combination supports two possible interface modes theoretically. These modes are simultaneously observed and the differences between their behavior are measured.

Evolution of granular packings by nonlinear acoustic waves

We investigate the nonlinear response of pulsed high-amplitude sound transmission in weakly compressed granular materials, simultaneously probing sound amplitude, time-of-flight velocity and harmonic generation. We observe that weakly compressed packings can both exhibit weakening and strengthening when driven by high-amplitude sound, and that weakening/strengthening of the sound velocity and transmission amplitude go hand in hand. We find that strengthening is associated with the generation of second harmonics, whereas for weakening, no appreciable second harmonics are generated. All these findings point to changes in the contact network; effective medium theory can describe these effects qualitatively, but fails to account for them quantitatively.

Normal-mode theory of nonspecular phenomena for a finite-aperture ultrasonic beam reflected from layered media

A normal-mode formalism is developed to describe the nonspecular effects of a finite-aperture ultrasonic beam incident onto layered elastic media. Analytical expressions for the reflected field have been obtained for various structures. This model proposed a unique physical picture and resolved the conflict between various explanations made for the nonspecular reflection phenomena. Novel features of leaky wave fields were observed at interfaces of liquid-solid and liquid-solid-liquid structures. These results may be helpful for nondestructive evaluation of layered structures and determination of material signatures in the acoustic microscope.