V. Yu. Zaitsev

Nonlinear Interaction of Acoustical Waves Due to Cracks and Its Possible Usage for Cracks Detection

An interaction of a CW acoustic wave and a powerful acoustic pulse due to nonlinear properties of a crack-type discontinuity in a solid is considered. Characteristics of nonstationary variations of the reflected wave amplitude and the phase of the transmitted wave, which are induced by the powerful pulse, are determined. The effects should allow one to distinguish cracks from other scatterers and can be used as a base of a new method of crack detection and positioning. Demonstrative signal estimates based on two simplified crack models are presented.

Pre-avalanche structural rearrangements in the bulk of granular medium: Experimental evidence

Granular avalanches are typical threshold-type phenomena implying the loss of stability of granular packings when their slope exceeds a critical angle. Detection of avalanche precursors is important for both basic studies and numerous applications. In this respect, only surface observations are presently available, whereas other known techniques are not suitable to detect internal pre-avalanche rearrangements expected from physical considerations and numerical simulations. Here, we report the first experimental evidence of avalanche precursors and the long-lasting post-avalanche rearrangements in the bulk of 3D granular packings. We use an original nonlinear-acoustic probing methodology which is selectively sensitive to the state of weakest intergrain contacts. This methodology allowed us to clearly detect transient pre-avalanche rearrangements of the weak-contact network. Those rearrangements get stronger and exhibit quasi-periodicity closer to the avalanche triggering, whereas the statistics of the sounding signal amplitude shows clear transition from Gaussian to power law behavior.

Experimental Study of Nonlinear Acoustic Effects in a Granular Medium

Results of a series of experimental studies of nonlinear acoustic effects in a granular medium are presented. Different effects observed in the experiments simultaneously testify that the nonlinearity of granular media is governed by the weakest intergrain contacts. The behavior of the observed dependences suggests that the distribution function of contact forces strongly increases in the range of forces much smaller than the mean force value, which is inaccessible for conventional experimental measuring techniques. For shear waves in a granular medium, the effects of demodulation and second harmonic generation with conversion to longitudinal waves are studied. These effects are caused by the nonlinear dilatancy of the medium, i.e., by the nonlinear law of its volume variation in the shear stress field. With the use of shear waves of different polarizations, the anisotropy of the nonlinearity of the medium is demonstrated. The observation of the cross-modulation effect shows that the nonlinearity-induced modulation components of the probe wave are much more sensitive to weak nonstationary perturbations of the medium, as compared to the linearly propagating fundamental harmonic. The nonlinear effects under study offer promise for diagnostic applications in laboratory measurements and in seismic monitoring systems.

The equation of state of a microinhomogeneous medium and the frequency dependence of its elastic nonlinearity

In the framework of a rheological model, a nonlinear dynamic equation of state of a microinhomogeneous medium containing nonlinear viscoelastic inclusions is derived. The frequency dependences of the effective nonlinear parameters are determined for the difference frequency and second harmonic generation processes in the case of a quadratic elastic nonlinearity. It is shown that the frequency dependence of the nonlinear elasticity of the medium is governed by the linear relaxation response of the inclusions at the primary excitation frequency, as well as by the relaxation of the inclusions at the nonlinear generation frequencies.

Comparison of linear and nonlinear elastic moduli for reservoir rock by use of a granular medium model

The variations of linear and nonlinear elastic parameters as a function of initial stress and material structure are considered using a model of a granular medium with fluid pore filling. Examples of such variations for some geological conditions interesting for seismoprospecting are presented. It is demonstrated that the nonlinear parameter may be used in exploration seismology as a much more sensitive characteristic compared with conventionally exploited linear moduli.

Relation between the tidal modulation of seismic noise and the amplitude-dependent loss in rock

Geological materials and many other microinhomogeneous media exhibit pronounced nonlinear properties under very small strains, when one may expect an almost linear behavior of the material. These properties are conventionally described on the basis of elastically nonlinear or hysteretic models. The present paper discusses the amplitude-dependent dissipation that is unrelated to hysteretic nonlinearity but is also a universal property of microinhomogeneous media. This property allows the explanation of the effect of correlation between the tidal strains of the Earth’s crust (on the order of 10−8) and the unexpectedly strong (on the order of 10−2–10−1) variations of seismic noise intensity, which has been observed for more than 25 years without being given any adequate interpretation.

Nonlinear Scattering of Acoustic Waves by Discontinuity-like Defects in Application to Crack Detection

Nonlinear sound scattering into higher or combination frequency harmonics on a crack-type dis continuity in a solid due to the intrinsic nonlinearity of the crack is considered. Characteristics of the nonlin early scattered sound are estimated, taking into account the micro-roughness of crack surfaces. Possibilities of the effect of usage for crack detection are discussed, comparison with conventional linear approaches is performed, and the main expected advantages of the nonlinear methods are pointed out.

Interaction of acoustic waves with cracks: Elastic and inelastic nonlinearity mechanisms on different time scales

The interrelated elastic and inelastic fast and slow effects of acoustic wave interaction with cracks are discussed from a unified point of view. Special attention is given to the dissipative manifestations of the presence of cracks and to the effects of the symmetrically time-reversible slow dynamics observed for acoustically activated cracks. These effects can be more pronounced than the conventionally discussed nonlinear elastic effects (such as higher harmonic generation). Taking into account the main geometric features of cracks, a thermoelastic mechanism is proposed to consistently interpret the experimental data. Consequences of the results of these studies for seismics are discussed, and the possibilities of using the observed effects for nonlinear acoustic diagnostics of cracks are discussed.

Giant strain-sensitivity of acoustic energy dissipation in solids containing dry and saturated cracks with wavy interfaces.

Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years, it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismoacoustic loss. In particular, it has been found that strains of order 10(-8) produced by lunar and solar tides are capable of causing variations in the seismoacoustic decrement on the order of several percent. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity of assuming the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains.

Modulation of high-frequency seismic noise by tidal deformations: The features of the phenomenon before strong earthquakes and a probable physical mechanism

A probable physical mechanism of tidal modulation of intensity of the endogenous seismic noise is proposed. The mechanism associates this phenomenon with modulation of the size of the region over which the recorded noise is acquired due to nonhysteresis amplitude-dependent absorption in the Earth’s rocks. The two most important cases, namely dry and fluid-saturated rocks, are considered. In both cases, internal elongated strip-like contacts (even in minor quantities) are found to be of fundamental importance. The proposed mechanism provides an explanation for a variety of features of high-frequency seismic noise modulated by tides, which were revealed in the long-term observations on the Kamchatka Peninsula: (i) the modulation depth on the order of the first few percent; (ii) stabilization of the modulation phase before a strong earthquake; (iii) a frequently observed near jump-like change in the phase to the opposite-sign phase after the earthquake; (iv) the subsequent period of a relatively unstable phase; and (v) temporary predominance of the modulation component on the second harmonic of the fundamental tidal frequency in the vicinity of the time when the earthquake occurred.