Related papers: Elastodynamic single-sided homogeneous Green's fun…
We create virtual sources and receivers in a 3D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at…
The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent…
We address an important issue of a dynamic homogenisation in vector elasticity for a doubly periodic mass-spring elastic lattice. The notion of logarithmically growing resonant waves is used in a complete analysis of star-shaped wave forms…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
The methods of time-reversed acoustics and Green's function retrieval are traditionally deployed for classical inhomogeneous, time-invariant materials. The mutual relation between these methods is well-established. Recently, similar methods…
For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is,…
The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…
We report on the passive measurement of time-dependent Green's functions in the optical frequency domain with low-coherence interferometry. Inspired by previous studies in acoustics and seismology, we show how the correlations of a…
The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…
Dynamic homogenization theories are powerful tools for describing and understanding the behavior of heterogeneous media such as composites and metamaterials. However, a major challenge in the dynamic homogenization theory is determining…
In time reversal acoustics experiments, a signal is emitted from a localized source, recorded at an array of receivers-transducers, time reversed, and finally re-emitted into the medium. A celebrated feature of time reversal experiments is…
The forced time harmonic response of a spatiotemporally-modulated elastic beam of finite length with light damping is derived using a novel Green's function approach. Closed-form solutions are found that highlight unique mode coupling…
Directional wave speeds variations in anisotropic elastic solids enables material characterisation capabilities, such as determination of elastic constants and volumetric measurement of crystallographic texture. However, achieving such…
This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation, -the resolvent formula-, Green's…
The geometry of mesoscopic inhomogeneities plays an important role in determining the macroscopic propagation behaviors of elastic waves in a heterogeneous medium. Nonequiaxed inhomogeneities can lead to anisotropic wave velocity and…
We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…
When averaged over sources or disorder, cross-correlation of diffuse fields yield the Green's function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in…
According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the…
Layered media have been studied extensively both for their importance in imaging technologies and as an example of a hyperbolic PDE with discontinuous coefficients. From the perspective of acoustic imaging, the time limited impulse response…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…