- The paper demonstrates that elastic TRM leverages scattering-induced multipath to achieve hyper-focusing with a refocused peak width of approximately 3 m.
- The experimental methodology uses dense geophone arrays and sledgehammer sources in dual galleries to accurately reconstruct Green functions via reciprocity.
- The study highlights that sensor mounting conditions and natural heterogeneity critically influence refocusing quality, informing subsurface imaging strategies.
Elastic Time Reversal Mirroring in a Mesoscopic Natural Medium: Experimental Analysis at LSBB
Experimental Context and Methodology
The presented work reports a detailed elastic Time Reversal Mirror (TRM) experiment performed in a natural mesoscopic heterogeneous medium at the LSBB underground facility in Rustrel, France. The LSBB, shielded from anthropogenic and environmental noise at significant depth, provides an ideal site for investigating seismic wave phenomena at mesoscopic scales. Two parallel galleries, separated by 100 meters of fractured and porous carbonate rock, were instrumented with dense, linear arrays of geophones (50 sensors, 1 m spacing, per gallery). The experiment utilizes sledgehammer impacts as impulse sources in one gallery and records responses in the parallel gallery, enabling empirical Green function acquisition.
The experimental procedure involves three steps. The forward experiment establishes the Green function by recording signals from sources in the GAS gallery in the GPR (mirror) gallery. Subsequently, the roles of source and mirror are reversed. Finally, a matched-filter convolution is performed numerically to achieve spatial and temporal refocusing at the original shot location, leveraging the reciprocity of Green functions. The time reversal operation thus exploits the multiple scattered field in the natural medium to focus energy back to its origin without a priori knowledge of the medium's heterogeneous properties.
Theoretical Framework
The study leverages the well-established time reversal invariance of the wave equation and the reciprocity principle for Green functions. The superposition of time-reversed wavefields, recorded and numerically convolved across the receiver array, is shown to act as an optimal matched spatio-temporal filter. This process ideally reconstructs a sharply localized response at the origin of the source in the time-reversed field, with the focusing resolution governed by the physical properties of the medium and the receiver aperture.
A key aspect addressed is the "hyper-focusing" or "super-resolution" effect, where the effective spatial aperture significantly exceeds the physical receiver aperture due to multipath scattering in the heterogeneous medium. This effect is quantified: with a P-wave velocity of 4500 m/s and a characteristic frequency of 200 Hz, the experimental peak width in the refocused image is on the order of 3 meters. This is more than an order of magnitude narrower than the classical expectation for a homogeneous medium, thus empirically validating the theoretical predictions for wavefields in strongly scattering environments.
Data Analysis and Results
Analysis of the TRM experiment reveals marked differences in the quality of energy refocusing between different temporal windows of the recorded waveform: noise, direct field, early coda, and later coda. Only the TRM outputs corresponding to coherent direct and scattered fields (i.e., not the noise window) display the canonical sharp focusing at the original shot location. The temporal progression from direct field to coda windows demonstrates progressive enhancement of spatial refocusing, consistent with increased wavefield complexity and scattering.
A key result is the observation that energy refocusing is significantly sharper in later coda windows compared to the direct field, supporting the proposition that scattering-induced multipath diversity improves time reversal focusing, i.e., hyper-focusing is most pronounced for the coda. At the experimental geometry and chosen frequency content, the effective aperture is estimated to be approximately 750 meters, far exceeding the physical array length of 50 meters, which underscores the crucial role of mesoscopic medium heterogeneity in enabling super-resolution.
The experimental data further reveal asymmetries related to sensor mounting conditions. The GPR gallery, with smooth concrete walls, supports higher-fidelity Green function estimation and thus improved reciprocity. In contrast, the rough, corrugated rock of the GAS gallery induces discrepancies between ideal and real sensor-source orientation, degrading the precision of the focusing peak. Refocusing quality thus shows strong sensitivity to "mirror" aperture properties and mounting topology.
Implications and Future Directions
This study provides robust empirical support for theoretical models predicting enhanced time reversal focusing in complex natural media. The results validate prior laboratory findings and extend them to realistic geophysical settings involving significant scale, real rock fracturing, and natural heterogeneity. The demonstrated refocusing resolution supports the feasibility of employing seismic time reversal techniques for high-precision source localization in subsurface exploration, reservoir characterization, and potentially in monitoring applications where no a priori velocity model is available.
From a theoretical perspective, the findings reinforce the centrality of scattering and medium disorder in realizing hyper-focusing, as predicted by recent models of random media. They also highlight potential limitations of reciprocity in natural, non-ideal experimental geometries, suggesting that practical deployments must carefully consider mirror topology and sensor coupling.
Promising avenues for future research include the extension to 3D sensor arrays, exploration of frequency-dependent focusing behavior, exploitation of in situ environmental fluctuations (e.g., humidity, temperature) for subsurface change detection, and the integration of time reversal with advanced data-driven inversion and imaging frameworks. Practical applications span not only geophysics but also security, monitoring, and potentially biomedical ultrasonics, wherever complex scattering environments are intrinsic.
Conclusion
The experiment establishes that elastic TRM techniques robustly achieve both space and time focusing of seismic energy in a strongly scattering, heterogeneous mesoscale natural medium. Refocusing accuracy is strongly enhanced by medium heterogeneity, with later coda waves yielding superior focusing performance due to increased scattering. Sensor mounting conditions and mirror wall roughness modulate the efficacy of the reversal and focusing processes. The results substantially extend the foundation for deploying time reversal methods for subsurface imaging and source localization in realistic geophysical scenarios, guiding both experimental practices and theoretical development in the field.