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.

Broadband acoustic invisibility and illusions.

Rendering objects invisible to impinging acoustic waves (cloaking) and creating acoustic illusions (holography) has been attempted using active and passive approaches. While most passive methods are inflexible and applicable only to narrow frequency bands, active approaches attempt to respond dynamically, interfering with broadband incident or scattered wavefields by emitting secondary waves. Without prior knowledge of the primary wavefield, the signals for the secondary sources need to be estimated and adapted in real time. This has thus far impeded active cloaking and holography for broadband wavefields. We present experimental results of active acoustic cloaking and holography without prior knowledge of the wavefield so that objects remain invisible and illusions intact even for broadband moving sources. This opens previously inaccessible research directions and facilitates practical applications including architectural acoustics, education, and stealth.

Seismological Processing of Six Degree-of-Freedom Ground-Motion Data.

Recent progress in rotational sensor technology has made it possible to directly measure rotational ground-motion induced by seismic waves. When combined with conventional inertial seismometer recordings, the new sensors allow one to locally observe six degrees of freedom (6DOF) of ground-motion, composed of three orthogonal components of translational motion and three orthogonal components of rotational motion. The applications of such 6DOF measurements are manifold-ranging from wavefield characterization, separation, and reconstruction to the reduction of non-uniqueness in seismic inverse problems-and have the potential to revolutionize the way seismic data are acquired and processed. However, the seismological community has yet to embrace rotational ground-motion as a new observable. The aim of this paper is to give a high-level introduction into the field of 6DOF seismology using illustrative examples and to summarize recent progress made in this relatively young field. It is intended for readers with a general background in seismology. In order to illustrate the seismological value of rotational ground-motion data, we provide the first-ever 6DOF processing example of a teleseismic earthquake recorded on a multicomponent ring laser observatory and demonstrate how wave parameters (phase velocity, propagation direction, and ellipticity angle) and wave types of multiple phases can be automatically estimated using single-station 6DOF processing tools. Python codes to reproduce this processing example are provided in an accompanying Jupyter notebook.

Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves.

We analyze a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook as well as the general multirelaxation-time collision operators. By calculating the dispersion relation for various 2D lattices, we show that the D2Q5 lattice is the most suitable model for the linear acoustic problem. We also implement a grid-refinement algorithm for the LB scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts. Our results show that the LB scheme performance is comparable to the classical second-order finite-difference schemes. Given its efficiency for parallel computation, the LB method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media.

Characterization of interface reflection coefficients using a finite-difference injection technique.

In this paper, a numerical wave field injection technique for characterizing the reflection coefficient of a planar medium interface is proposed. By injecting recorded wave field quantities into a three-dimensional (3D) finite-difference calculation, two key objectives are addressed: first, the recorded wave field is separated into its incident and reflected constituents without the need of spatial Fourier transforms or a temporal separation of incident and reflected parts in the recorded data. Second, the separated constituents are independently extrapolated to the location of the reflecting interface to determine its reflecting properties. The methodology is experimentally validated on 3D laboratory data consisting of reflections from the water-air interface in a water tank and is shown to give accurate results for incidence angles of up to 60°.

Broadband cloaking and holography with exact boundary conditions.

Broadband cloaking and holography are achieved by creating an exact boundary condition on a surface enclosing an object or free space. A time-recursive, discrete version of the Kirchhoff-Helmholtz integral predicts the wavefield impinging on the surface, as well as its transmission through an arbitrary embedding or replacement medium. Surface source distributions proportional to the predicted wavefield cancel the incident waves and radiate the desired response. The fields inside and outside the surface can be controlled independently. A two-dimensional numerical example shows that cloaking and holography can be achieved to within numerical precision across the frequency range of the incident radiation.

Immersive experimentation in a wave propagation laboratory.

A wave propagation laboratory is proposed which enables the study of the interaction of broadband signals with complex materials. A physical experiment is dynamically linked to a numerical simulation in real time through transmitting and recording transducer surfaces surrounding the target. The numerical simulation represents an arbitrarily larger domain, allowing experiments to be performed in a total environment much greater than the laboratory experiment itself. Specific applications include the study of non-linear effects or wave propagation in media where the physics of wave propagation is not well understood such as the effect of fine scale heterogeneity on broadband propagating waves.

Exact wave field simulation for finite-volume scattering problems.

An exact boundary condition is presented for scattering problems involving spatially limited perturbations of arbitrary magnitude to a background model in generally inhomogeneous acoustic media. The boundary condition decouples the wave propagation on a perturbed domain while maintaining all interactions with the background model, thus eliminating the need to regenerate the wave field response on the full model. The method, which is explicit, relies on a Kirchhoff-type integral extrapolation to update the boundary condition at every time step of the simulation. The Green's functions required for extrapolation through the background model are computed efficiently using wave field interferometry.

Modeling of wave propagation in inhomogeneous media.

We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium. Following a predictable initial computational effort, Green's functions between arbitrary points in the medium can be computed as needed using a simple cross-correlation algorithm.