EGU23-13540
https://doi.org/10.5194/egusphere-egu23-13540
EGU General Assembly 2023
© Author(s) 2023. This work is distributed under the Creative Commons Attribution 4.0 License.
Back and Through the Looking Glass - Space-time scattering of elastic waves
- 1ETH Zurich, Institute of Geophysics, Zurich, Switzerland (johannes.aichele@rwth-aachen.de)
- 2AMOLF, Amsterdam, The Netherlands
Due to causality wave scattering in time is simpler than scattering in space: In
contrast to multiple spatial boundaries, there are no infinite reflections between
temporal boundaries. Salem and Caloz, 2015 [1] showed that wave scatter-
ing can be simplified by constructing a time-space cross-mapping. We identify
the cross-mapped wavefields as the Focusing functions developed in data-driven
geophysical imaging. Experimentally, Bacot et al, 2016 [2] have shown that
time modulation of the medium properties of a capillary-gravity wave results in
time-refraction and time-reflection of the original wave. This experimental re-
sult should hold true for any system obeying Alembert’s equation. This should
in principle allow us to physically compute wavefields for the single-sided inverse
scattering problem through forward scattering experiments. We set up a sim-
ple comb-like discrete system for time-modulated 1D elastic wave propagation.
Elastic beams act as the masses and an electrostatic force as the springs of our
system. The effective coupling stiffness between the beams is modulated in time
through a variation of the electrostatic force. A Galerkin based wave propaga-
tion model shows that an experimental realization of hundreds of beams can be
achieved through micro-machining. Through time-modulations of the system’s
wavespeed a broadband excitation is refracted and reflected everywhere in space.
Time-scattering preserves the wave vector k, which implies that the frequency
ω is not conserved. To elucidate the dispersion relation at time boundaries,
we employ a correction method for spatial dispersion. Herefore, a correction
method for time-dispersion in finite difference simulations developed by Koene
et al 2018 [3] is mapped to the spatial dimension of our meta-material.
[1] Salem, Mohamed A., and Christophe Caloz. “Space-Time Cross-Mapping
and Application to Wave Scattering.” ArXiv:1504.02012 [Physics], April 7, 2015.
http://arxiv.org/abs/1504.02012. [2] Bacot, Vincent, Matthieu Labousse, An-
tonin Eddi, Mathias Fink, and Emmanuel Fort. “Time Reversal and Holography
with Spacetime Transformations.” Nature Physics 12, no. 10 (October 2016):
972–77. https://doi.org/10.1038/nphys3810. [3] Koene, Erik F M, Johan O A
1
contrast to multiple spatial boundaries, there are no infinite reflections between
temporal boundaries. Salem and Caloz, 2015 [1] showed that wave scatter-
ing can be simplified by constructing a time-space cross-mapping. We identify
the cross-mapped wavefields as the Focusing functions developed in data-driven
geophysical imaging. Experimentally, Bacot et al, 2016 [2] have shown that
time modulation of the medium properties of a capillary-gravity wave results in
time-refraction and time-reflection of the original wave. This experimental re-
sult should hold true for any system obeying Alembert’s equation. This should
in principle allow us to physically compute wavefields for the single-sided inverse
scattering problem through forward scattering experiments. We set up a sim-
ple comb-like discrete system for time-modulated 1D elastic wave propagation.
Elastic beams act as the masses and an electrostatic force as the springs of our
system. The effective coupling stiffness between the beams is modulated in time
through a variation of the electrostatic force. A Galerkin based wave propaga-
tion model shows that an experimental realization of hundreds of beams can be
achieved through micro-machining. Through time-modulations of the system’s
wavespeed a broadband excitation is refracted and reflected everywhere in space.
Time-scattering preserves the wave vector k, which implies that the frequency
ω is not conserved. To elucidate the dispersion relation at time boundaries,
we employ a correction method for spatial dispersion. Herefore, a correction
method for time-dispersion in finite difference simulations developed by Koene
et al 2018 [3] is mapped to the spatial dimension of our meta-material.
[1] Salem, Mohamed A., and Christophe Caloz. “Space-Time Cross-Mapping
and Application to Wave Scattering.” ArXiv:1504.02012 [Physics], April 7, 2015.
http://arxiv.org/abs/1504.02012. [2] Bacot, Vincent, Matthieu Labousse, An-
tonin Eddi, Mathias Fink, and Emmanuel Fort. “Time Reversal and Holography
with Spacetime Transformations.” Nature Physics 12, no. 10 (October 2016):
972–77. https://doi.org/10.1038/nphys3810. [3] Koene, Erik F M, Johan O A
1
Robertsson, Filippo Broggini, and Fredrik Andersson. “Eliminating Time Dis-
persion from Seismic Wave Modeling.” Geophysical Journal International 213,
no. 1 (April 1, 2018): 169–80. https://doi.org/10/gcz9wb.
persion from Seismic Wave Modeling.” Geophysical Journal International 213,
no. 1 (April 1, 2018): 169–80. https://doi.org/10/gcz9wb.
How to cite: Aichele, J., Müller, J., Nissar, Z., van Manen, D.-J., and Serra-Garcia, M.: Back and Through the Looking Glass - Space-time scattering of elastic waves, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-13540, https://doi.org/10.5194/egusphere-egu23-13540, 2023.
