Inverting for a deterministic surface gravity wave using the sensitivity-kernel approach

Abstract

The dynamic imaging of a deterministic gravity wave propagating at an air-water interface requires continuous sampling of every point at this interface. This sampling can be done acoustically using waves that propagate in the water column but have specular reflection points that fully scan the air-water interface. This study aims to perform this complex task experimentally, with identical ultrasonic source and receiver arrays that face each other in a 1-m-long, 5-cm-deep fluid waveguide, and with frequencies in the MHz range. The waveguide transfer matrix is recorded 100 times per second between the source-receiver arrays, while a gravity wave is generated at the air-water interface. Through the beamforming process, a large set of acoustic multi-reverberated beams are isolated and identified that interact with the air-water interface. The travel-time and amplitude modulations of each eigenbeam are measured when the surface gravity wave travels through the source-receiver plane. Linear inversion of the travel-time and amplitude perturbations is performed from a few thousand eigenbeams using diffraction-based sensitivity kernels. Inversion results using travel-times, amplitudes, or these two observables together, lead to accurate spatial-temporal patterns of the surface deformation. The advantages and limitations of the method are discussed.

Surface perturbation inverted from angle variations of eigenbeams in an ultrasonic waveguide

“…(3). The study of the travel-time and amplitude variations dp DBF due to a surface perturbation from the SK approach has been discussed previously (Roux and Nicolas, 2014;Sarkar et al, 2012;van Baarsel et al, 2019).…”

“…For a small surface perturbation, HðpÞ % Hðp 0 Þ means that as a first approximation, the intensity maximum described as the eigenbeam is shifted in time and angles but keeps the same shape and therefore the same curvature in the ½h e ; h r ; t space [for experimental validation, see Fig. 4(b) in Roux and Nicolas, 2014].…”

“…As the purpose of this paper is to invert surface fluctuations from angle variations only, we do not consider from here on the travel-time perturbations in the recovery of the surface perturbation of the waveguide. For discussions about surface fluctuations inverted with travel-time or amplitude perturbations, please refer to previous studies (Roux and Nicolas, 2014;van Baarsel et al, 2019).…”

“…In this paper, we propose to use only the two new angle observables, the emitting and receiving angles of each eigenbeam, to localize and estimate the perturbation of the air-water interface at the surface of an ultrasonic waveguide. This is achieved using the SKs for the two-dimensional (2D) surface approach, which has been used previously for traveltimes and amplitudes (Roux and Nicolas, 2014;Sarkar et al, 2012;van Baarsel et al, 2019), and is here developed for the eigenbeam angles.…”

Timelapse ultrasonic tomography for measuring damage localization in geomechanics laboratory tests

“…As such, the optimal subarray size results from a balance between resolution and robustness. [22][23][24] Large subarrays provide enhanced angular resolution. However, when there are strong heterogeneities close to the transducer arrays, as is often the case for geomaterials (where localized deformations may spread across the entire sample), beamforming performs better with shorter subarrays.…”