Periodic Reporting for period 4 - MATRIX (MAchine for Time Reversal and Immersive wave eXperimentation)
Período documentado: 2021-06-01 hasta 2022-11-30
Seismic waves are still a main source of information when it comes to understanding both the composition of, and the dynamic processes ongoing in, the Earth’s interior, including earthquakes. For example, so-called seismic “coda” waves, because of their large number of scattering interactions with the medium, can be indicative of slight changes in stress fields before catastrophic fracturing that might provide pre-cursory signs of earthquakes. To study such phenomena in the laboratory, current approaches employ experimentation at frequencies (and scales) that are at least 4 orders of magnitude higher (and smaller) than the frequencies at which the phenomena occur in the real-world. This is so, because reflections from the boundaries of the experimental domain would otherwise disturb and invalidate the experiments by virtue of masking the signal of interests. Because of the long wavelengths involved, it is also impractical to build the vast experimental facilities that would be required to otherwise avoid such boundary reflections. However, it is often not known if the physics governing the phenomena stays the same over those 4 orders of magnitude or more. Thus, there is a need for a radically new laboratory experimental approach for studying the interaction of seismic waves with the real complex media of the Earth’s subsurface.
The MATRIX (Machine for Time-Revesal and Immersive eXperimentation) project, aims to establish a fundamentally new approach to seismic wave experimentation that involves fully immersing a physical seismic experiment within a virtual numerical environment. This enormously challenging endeavour, which is relevant to many outstanding issues in seismology, has not been previously attempted. By continuously varying the output of numerous transponders closely spaced around the physical domain using a control algorithm that takes advantage of measurements made by a scanning Laser-Doppler Vibrometer and a novel theory of immersive boundary conditions, waves travelling between the physical and numerical domains will seamlessly propagate back and forth between the two domains without being affected by reflections at the boundaries between the two domains. This will allow us to investigate diverse types of Earth materials using frequencies that are much closer to those of seismic waves propagating through the Earth than previously possible. The novel laboratory enables experimentation under highly controlled conditions.
The MATRIX (Machine for Time-Revesal and Immersive eXperimentation) project, aims to establish a fundamentally new approach to seismic wave experimentation that involves fully immersing a physical seismic experiment within a virtual numerical environment. This enormously challenging endeavour, which is relevant to many outstanding issues in seismology, has not been previously attempted. By continuously varying the output of numerous transponders closely spaced around the physical domain using a control algorithm that takes advantage of measurements made by a scanning Laser-Doppler Vibrometer and a novel theory of immersive boundary conditions, waves travelling between the physical and numerical domains will seamlessly propagate back and forth between the two domains without being affected by reflections at the boundaries between the two domains. This will allow us to investigate diverse types of Earth materials using frequencies that are much closer to those of seismic waves propagating through the Earth than previously possible. The novel laboratory enables experimentation under highly controlled conditions.
A state-of-the-art robotised 3D Scanning Laser Doppler Vibrometer system was purchased and initial experiments were carried on out on a 3D granite rock volume. The wavefield on the six accessible sides of the rock was acquired for a piezo actuator (i.e. a source) on the top surface emitting a high frequency signal, with a frequency just above the audible range [see Figure 1]. As expected, several elastic wave types, including both sound-like compressional (P) waves and the shear (SV) waves propagating directly from the source through the block could be observed (panels 1 and 2). A high amplitude wave, known as the Rayleigh wave, could also be seen propagating along the surface (panels 2 and 3).
An important step in implementing immersive boundary conditions for an elastic medium is the separation of the wave field recorded at the surface of the volume into incident and free-surface reflected waves. This is because the elastic IBC source signals that are needed to cancel the reflections are directly proportional to the so-called outgoing traction (i.e. a force acting across a surface) which can be computed from the outgoing velocity or displacement wavefield measured using the LDV. The small surfaces and sharp corners of the experimentation rock volume represent particular challenges. By injecting an elastic wave field recorded at the free surface of an object into a numerical simulation, it turns out that the incident and reflected fields super-imposed in the measurements naturally separate, propagating away from the injection surface in their respective directions. This means that the presence of sharp corners on or between the free surfaces is no longer problematic and that the incident wave field can be separated, in theory, with almost perfect precision.
Finally, we have performed the first elastic IBC experiments on a one-dimensional beam, successfully cancelling the boundary reflections of both longitudinal and flexural waves using a single 3-axis piezo actuator glued to the open end of the beam. In a first step, so-called dispersion parameters of the flexural waves were estimated. These dispersion parameters were then used to extrapolate wave fields measured “inside” the beam to either end. This was done both to characterize the flexural wave reflection at the beam-end, as well as to characterize the source transfer functions of the used Piezo actuator. This information was then used to compute the IBC wave fields that should be emitted to simultaneously cancel both the incoming non-dispersive longitudinal wave as well as the dispersive flexural waves.
An important step in implementing immersive boundary conditions for an elastic medium is the separation of the wave field recorded at the surface of the volume into incident and free-surface reflected waves. This is because the elastic IBC source signals that are needed to cancel the reflections are directly proportional to the so-called outgoing traction (i.e. a force acting across a surface) which can be computed from the outgoing velocity or displacement wavefield measured using the LDV. The small surfaces and sharp corners of the experimentation rock volume represent particular challenges. By injecting an elastic wave field recorded at the free surface of an object into a numerical simulation, it turns out that the incident and reflected fields super-imposed in the measurements naturally separate, propagating away from the injection surface in their respective directions. This means that the presence of sharp corners on or between the free surfaces is no longer problematic and that the incident wave field can be separated, in theory, with almost perfect precision.
Finally, we have performed the first elastic IBC experiments on a one-dimensional beam, successfully cancelling the boundary reflections of both longitudinal and flexural waves using a single 3-axis piezo actuator glued to the open end of the beam. In a first step, so-called dispersion parameters of the flexural waves were estimated. These dispersion parameters were then used to extrapolate wave fields measured “inside” the beam to either end. This was done both to characterize the flexural wave reflection at the beam-end, as well as to characterize the source transfer functions of the used Piezo actuator. This information was then used to compute the IBC wave fields that should be emitted to simultaneously cancel both the incoming non-dispersive longitudinal wave as well as the dispersive flexural waves.
While we are still constructing the elastic immersive wave experimentation laboratory, we have achieved further expected and unexpected impacts, that we briefly highlight below.
1) Validation of the novel elastic wavefield separation approach on real LDV data for a source inside the rock volume. This allows us to compute the incident traction (vector) wavefield, whose components constitute the values to use to drive the (vector) force sources distributed all over the free surface, both to cancel the incident wavefield and to re-introduce the wavefields scattered back from the virtual domain. This step also includes determining the 3D transfer functions between the ideal IBC point force sources and the multi-component piezo-actuators, similar to what has already been done in 1D.
2) Establishing the iterative/recursive implementation of the immersive boundary condition The wavefield separation, as well as the application of the boundary condition, have to be iterated since the LDV system can only measure the wavefield on the free surface one point at at time. This step also includes implementation of the full elastic boundary condition on at least one full side of the rock volume, so that we can determine appropriate sub-sampled configurations for implementing the boundary condition on all sides from an initially oversampled (in terms of the number of piezo actuators).
3) We have developed an in principle completely passive device that can recognize speech based on simulating MEMS structures to optimize elastic resonances -- a development that was not anticipated at the outset of MATRIX. Such devices have potential applications in low-power alternatives for switching on complex powered dormant systems and therefore contribute to more sustainable technology. This development has led to a further ERC project being funded (ERC Starting grant) for a member of the Matrix team in the Netherlands.
4) We have made some progress on specific applications of the immersive lab. In particular, we understand how we can apply arbitrary 1D, 2D or 3D periodic boundary conditions to the experimentation (rock) volume. This approach (i.e. a periodic boundary) has been applied succesfully to characterization of an elastic meta-material.
1) Validation of the novel elastic wavefield separation approach on real LDV data for a source inside the rock volume. This allows us to compute the incident traction (vector) wavefield, whose components constitute the values to use to drive the (vector) force sources distributed all over the free surface, both to cancel the incident wavefield and to re-introduce the wavefields scattered back from the virtual domain. This step also includes determining the 3D transfer functions between the ideal IBC point force sources and the multi-component piezo-actuators, similar to what has already been done in 1D.
2) Establishing the iterative/recursive implementation of the immersive boundary condition The wavefield separation, as well as the application of the boundary condition, have to be iterated since the LDV system can only measure the wavefield on the free surface one point at at time. This step also includes implementation of the full elastic boundary condition on at least one full side of the rock volume, so that we can determine appropriate sub-sampled configurations for implementing the boundary condition on all sides from an initially oversampled (in terms of the number of piezo actuators).
3) We have developed an in principle completely passive device that can recognize speech based on simulating MEMS structures to optimize elastic resonances -- a development that was not anticipated at the outset of MATRIX. Such devices have potential applications in low-power alternatives for switching on complex powered dormant systems and therefore contribute to more sustainable technology. This development has led to a further ERC project being funded (ERC Starting grant) for a member of the Matrix team in the Netherlands.
4) We have made some progress on specific applications of the immersive lab. In particular, we understand how we can apply arbitrary 1D, 2D or 3D periodic boundary conditions to the experimentation (rock) volume. This approach (i.e. a periodic boundary) has been applied succesfully to characterization of an elastic meta-material.