Temporal changes in the lunar soil from correlation of diffuse vibrations

A Reconstruction Algorithm for Temporally Aliased Seismic Signals Recorded by the InSight Mars Lander

In December 2018, the NASA InSight lander successfully placed a seismometer on the surface of Mars. Alongside, a hammering device was deployed at the landing site that penetrated into the ground to attempt the first measurements of the planetary heat flow of Mars. The hammering of the heat probe generated repeated seismic signals that were registered by the seismometer and can potentially be used to image the shallow subsurface just below the lander. However, the broad frequency content of the seismic signals generated by the hammering extends beyond the Nyquist frequency governed by the seismometer's sampling rate of 100 samples per second. Here, we propose an algorithm to reconstruct the seismic signals beyond the classical sampling limits. We exploit the structure in the data due to thousands of repeated, only gradually varying hammering signals as the heat probe slowly penetrates into the ground. In addition, we make use of the fact that repeated hammering signals are sub-sampled differently due to the unsynchronized timing between the hammer strikes and the seismometer recordings. This allows us to reconstruct signals beyond the classical Nyquist frequency limit by enforcing a sparsity constraint on the signal in a modified Radon transform domain. In addition, the proposed method reduces uncorrelated noise in the recorded data. Using both synthetic data and actual data recorded on Mars, we show how the proposed algorithm can be used to reconstruct the high-frequency hammering signal at very high resolution.

Impacts of Reservoir Water Level Fluctuation on Measuring Seasonal Seismic Travel Time Changes in the Binchuan Basin, Yunnan, China

An airgun source in a water reservoir has been developed in the past decade as a green active source that had been proven effective to derive short-term subsurface structural changes. However, seasonal water level fluctuation in the reservoir affects the airgun signal, and thus whether the airgun signals can be used to derive robust seasonal variation in subsurface structure remains unclear. We use the airgun data observed in the Binchuan basin to estimate the seasonal variation of seismic travel time and compare the results with those derived from ambient noise data in the same frequency band. Our main observation is that seasonal change δt/t from airgun is negatively correlated to the variation of dominant frequency and water table fluctuation in the reservoir. One possible explanation is that water table fluctuation in the reservoir affects the dominant frequency of the airgun signal and causes significant phase shift. We also compute the travel time changes in P-wave from the empirical Green’s function after deconvolving the waveforms from a reference station that is 50 m from the airgun source. The dominant frequency after deconvolution still shows seasonal variation and correlates inversely to the travel time changes, suggesting that deconvolution cannot completely eliminate the source effect on travel time changes. We also use ambient noise cross-correlation to retrieve coda waves and then derive travel time changes in monthly stacked cross-correlations relative to a yearly average cross-correlation. We observe that seismic travel time increases to its local maximum in the end of August. The travel time changes lag behind the precipitation for about one month. We apply a poroelastic physical model to explain seismic travel time changes and find that a combined effect from precipitation and evaporation might induce the seasonal changes as shown in the ambient noise data. However, the pattern of travel time changes from the airgun differs from that from ambient noise, reflecting the strong effects of airgun source property changes. Therefore, we should be cautious to derive long-term subsurface structural variation from the airgun source and put more attention on stabilizing the dominant frequency of each excitation in the future experiments.

Onset of energy equipartition among surface and body waves

We derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a two-dimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the axis of the waveguide: those that are almost trapped in the thin layer, and thus model surface waves, and those that penetrate deep in the waveguide, and thus model body waves. The remaining modes are evanescent waves. We introduce a mathematical theory of mode coupling induced by scattering in the thin layer, and derive a radiative transfer equation which quantifies the mean mode power exchange. We study the solution of this equation in the asymptotic limit of infinite width of the waveguide. The main result is a quantification of the rate of convergence of the mean mode powers toward equipartition.

Probing the in situ Elastic Nonlinearity of Rocks with Earth Tides and Seismic Noise

Heterogeneous materials such as rocks, concrete, and granular materials exhibit a strong elastic nonlinearity. The sensitivity of the elastic nonlinearity to the applied stress and pore pressure in principle allows the use of seismic waves for remote observations of stress or pore pressure changes. Yet the nonlinearity of rocks is difficult to quantify in situ as active deformation tests are not possible in the field. We investigate the elastic nonlinearity in a fully natural experiment using the ambient seismic noise of a single seismic station to sense changes of the seismic velocity in the subsurface reaching 0.026% in response to the minute deformation caused by various constituents of the tidal forces exerted by the Sun and Moon.

Sensitivity of coda wave interferometry to fluid migration through rock

The sound speed of a porous medium changes with fluid substitution when the fluids have different acoustic properties. The authors demonstrate that coda wave interferometry is capable of sensing subtle local sound speed changes associated with minute fluid displacements, Δh. In fact the resolution on fluid motion is given by a simple scaling relationship, Δh_min/λ∼t^-γe^2αt, where t is the waveform time, λ is the wavelength, γ is a constant that varies based on the nature of the acoustic propagation, and α is a system specific acoustic attenuation coefficient. In contrast to the conventional notion that later arrivals (further into the coda) give greater sensitivity to fluid movement, this scaling relationship suggests that there is a temporal optimum in sensitivity to Δh. This is the case even though later arrivals exhibit signal intensities well above the noise floor. The authors elucidate the physical basis for determining the waveform time at which the sensitivity is optimal.

Coda-wave monitoring of continuously evolving material properties and the precursory detection of yielding

The nominally incoherent coda of a scattered wavefield has been shown to be a remarkably sensitive quantitive monitoring tool. Its success is, however, often limited to applications where only moderate or localised changes in the scattering properties of the medium can be assumed. However, the compressional deformation of a relatively homogeneous rock matrix towards failure represents for a monitoring wavefield pronounced changes in both velocity and scattering power often due to a distribution of inelastic changes. A rolling reference wavefield is implemented when applying coda-wave interferometry (CWI) and coda-wave decorrelation (CWD), allowing relative velocity and material scattering power monitoring for such applications. It is demonstrated how this modification enables the qualitative monitoring of stages in material deformation common to unconfined compressive strength tests. In addition, the precursory/subtle onset of material yielding is identifiable in both the CWI and CWD methods, which was not possible when comparing to a fixed reference wavefield. It is, therefore, expected that this approach will enable these coda-based methods to robustly monitor continuous, destructive processes at a variety of scales. Possible applications include critical infrastructure, landslide, and reservoir compaction monitoring where both the subtle continuous and sudden large changes in a material's scattering properties occur.

Nonlinear coda wave interferometry for the global evaluation of damage levels in complex solids

A nonlinear acoustic method to assess the damage level of a complex medium is discussed herein. Thanks to the highly nonlinear elastic signatures of cracks or, more generally, internal solid contacts, this method is able to distinguish between contributions from linear wave scattering by a heterogeneity and contributions from nonlinear scattering by a crack or unbounded interface. The coda wave interferometry (CWI) technique is applied to reverberated and scattered waves in glass plate samples featuring various levels of damage. The ultrasonic coda signals are recorded in both the absence and presence of an independent and lower-frequency elastic "pump" wave, before being analyzed by CWI. The monitored CWI parameters quantifying changes in these coda signals, which therefore quantify the nonlinear wave-mixing effects between the coda and pump waves, are found to be dependent on the damage level in the sample. A parametric study is also performed to analyze the influence of sensor positions and average temperature on the method's output. The reported results could be applied to the non-destructive testing and evaluation of complex-shape materials and multiple scattering samples, for which conventional ultrasonic methods show strong limitations.

Diffuse ultrasound monitoring of stress and damage development on a 15-ton concrete beam

This paper describes the use of an ultrasonic imaging technique (Locadiff) for the Non-Destructive Testing & Evaluation of a concrete structure. By combining coda wave interferometry and a sensitivity kernel for diffuse waves, Locadiff can monitor the elastic and structural properties of a heterogeneous material with a high sensitivity, and can map changes of these properties over time when a perturbation occurs in the bulk of the material. The applicability of the technique to life-size concrete structures is demonstrated through the monitoring of a 15-ton reinforced concrete beam subject to a four-point bending test causing cracking. The experimental results show that Locadiff achieved to (1) detect and locate the cracking zones in the core of the concrete beam at an early stage by mapping the changes in the concrete's micro-structure; (2) monitor the internal stress level in both temporal and spatial domains by mapping the variation in velocity caused by the acousto-elastic effect. The mechanical behavior of the concrete structure is also studied using conventional techniques such as acoustic emission, vibrating wire extensometers, and digital image correlation. The performances of the Locadiff technique in the detection of early stage cracking are assessed and discussed.

Locating and characterizing a crack in concrete with diffuse ultrasound: A four-point bending test

This paper describes an original imaging technique, named Locadiff, that benefits from the diffuse effect of ultrasound waves in concrete to detect and locate mechanical changes associated with the opening of pre-existing cracks, and/or to the development of diffuse damage at the tip of the crack. After giving a brief overview of the theoretical model to describe the decorrelation of diffuse waveforms induced by a local change, the article introduces the inversion procedure that produces the three dimensional maps of density of changes. These maps are interpreted in terms of mechanical changes, fracture opening, and damage development. In addition, each fracture is characterized by its effective scattering cross section.

Validation of a thermal bias control technique for Coda Wave Interferometry (CWI)

The Coda Wave Interferometry (CWI) analysis serves to monitor the variation of propagation velocity in a heterogeneous medium with high precision (10(-3)% in relative terms). In combination with acoustoelastic theory, this type of analysis offers an NDT method for stress evaluation and/or damage detection. Since the CWI method is intended to evaluate extreme levels of accuracy, the presence of bias under certain circumstances can undermine evaluation results and/or test repeatability. In this paper, we offer a bias control technique involving the use of a second (reference) specimen for CWI analysis that is designed to compensate: (1) the thermally-induced velocity variation due to environmental temperature fluctuations; and (2) bias originating from experimental procedures. The presentation of this technique contains both a theoretical analysis and experimental protocol for the purpose of implementation. Furthermore, comparisons of experimental results have been included in order to demonstrate the utility of this bias control technique under laboratory conditions.

Study of stress-induced velocity variation in concrete under direct tensile force and monitoring of the damage level by using thermally-compensated Coda Wave Interferometry

In this paper, we describe an experimental study of concrete behavior under a uniaxial tensile load by use of the thermally-compensated Coda Wave Interferometry (CWI) analysis. Under laboratory conditions, uniaxial tensile load cycles are imposed on a cylindrical concrete specimen, with continuous ultrasonic measurements being recorded within the scope of bias control protocols. A thermally-compensated CWI analysis of multiple scattering waves is performed in order to evaluate the stress-induced velocity variation. Concrete behavior under a tensile load can then be studied, along with CWI results from both its elastic performance (acoustoelasticity) and plastic performance (microcracking corresponding to the Kaiser effect). This work program includes a creep test with a sustained, high tensile load; the acoustoelastic coefficients are estimated before and after conducting the creep test and then used to demonstrate the effect of creep load.

Monitoring stress changes in a concrete bridge with coda wave interferometry

Coda wave interferometry is a recent analysis method now widely used in seismology. It uses the increased sensitivity of multiply scattered elastic waves with long travel-times for monitoring weak changes in a medium. While its application for structural monitoring has been shown to work under laboratory conditions, the usability on a real structure with known material changes had yet to be proven. This article presents experiments on a concrete bridge during construction. The results show that small velocity perturbations induced by a changing stress state in the structure can be determined even under adverse conditions. Theoretical estimations based on the stress calculations by the structural engineers are in good agreement with the measured velocity variations.

Stability of monitoring weak changes in multiply scattering media with ambient noise correlation: laboratory experiments

Previous studies have shown that small changes can be monitored in a scattering medium by observing phase shifts in the coda. Passive monitoring of weak changes through ambient noise correlation has already been applied to seismology, acoustics, and engineering. Usually, this is done under the assumption that a properly reconstructed Green function (GF), as well as stable background noise sources, is necessary. In order to further develop this monitoring technique, a laboratory experiment was performed in the 2.5 MHz range in a gel with scattering inclusions, comparing an active (pulse-echo) form of monitoring to a passive (correlation) one. Present results show that temperature changes in the medium can be observed even if the GF of the medium is not reconstructed. Moreover, this article establishes that the GF reconstruction in the correlations is not a necessary condition: The only condition to monitoring with correlation (passive experiment) is the relative stability of the background noise structure.