On wave splitting, source separation and echo removal with absorbing boundary conditions

Abstract

Starting from classical absorbing boundary conditions (ABC), we propose a method for the separation of time-dependent wave fields given measurements of the total wave field. The method is local in space and time, deterministic, and makes no prior assumptions on the frequency spectrum and the location of sources or physical boundaries. By using increasingly higher order ABC, the method can be made arbitrarily accurate and is, in that sense, exact. Numerical examples illustrate the usefulness for source separation and echo removal.

Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

“…Collectively, these stipulations and suppositions constitute the foundational framework upon which the problem's analysis and resolution are predicated. The constitutive relation for a second-grade fluid satisfies [45]:…”

“…Muhr et al [43] applied the ABC to address the Westervelt wave equation related to sound velocity potential, and the effectiveness and efficiency were confirmed. Further information on ABC is available in [44][45][46].…”

How to solve inverse scattering problems without knowing the source term: a three-step strategy

“…except in a zone D S around the obstacle O), see figure 1. First, we shall split the signal on the boundary Γ by the method developed in [10][11][12]. Then using twice the TRAC method [13][14][15], we shall compute the field u I in Ω \ D I and the u S in Ω \ D S .…”

“…The goal of wave splitting is to isolate different components of a complex wavefield, which we know is the result of the sum of several signals [12,[16][17][18]. In the context of our work, the total wavefield recorded by the transducers is actually the sum of the incident wavefield, which coincides with u I , and the scattered wavefield corresponding to u S .…”