Generation of acoustic waves by an impulsive line source in a fluid/solid configuration with a plane boundary

Abstract

The space–time acoustic wave motion generated by a two-dimensional, impulsive, monopole line source in a fluid/solid configuration with a plane boundary is calculated with the aid of the modified Cagniard technique. The source is located in the fluid, and numerical results are presented for the reflected-wave acoustic pressure, especially in those regions of space where head wave contributions occur. There is a marked difference in time response in the different regimes that exist for the wave speed in the fluid in relation to the different wave speeds (compressional, shear, Rayleigh) in the solid. These differences are of importance to the situation where the reflected wave in the fluid is used to determine experimentally the elastic properties of the solid.

Transient Analysis of a Line-Focus Transducer Probing a Liquid/Solid Interface

“…Because of the one-dimensional degeneracy of an infinite line source, a two dimensional Green's function is sufficient to model the waves generated by a line source. Both have been studied and reported by de Hoop and van der Hijden [9,10]. Our derived formulas are much simpler, can be progranuned easily, and give the same numerical results.…”

“…The Green's function of a planar liquid/solid interface represents the transient pressure at any point in the liquid due to a sudden expansion at another point in the liquid near a planar solid. This Green's function is derived and described in great detail in the geophysics literature [7,8,9,10]. We have developed a simplified algorithm which is easy to program and computationally efficient [11].…”

Multi-Component Acoustic Characterization of Porous Media

“…Here, the "poroelastic Stoneley-wave denominator" (see Section 4.3) is defined as (4.35) which is associated with interface waves along the fluid/poroelastic-medium interface. It is very similar to the "Scholte-wave denominator" for a fluid/elastic-solid interface (de Hoop & van der Hijden, 1983), and equivalent to the one as given by Denneman et al (2002). It contains the "poroelastic Rayleigh-wave denominator" that is associated with interface waves along a vacuum/poroelastic-medium interface (4.36) which is very similar to the one for a vacuum/elastic-solid interface (Achenbach, 1973;Aki & Richards, 1980).…”

“…The Green's functiong − only contains the fluid (F ) compressional mode. Both Green's functions have the "Stoneley-wave denominator" ∆ St = ∆ St (p r , ω) that is associated with interface waves along the fluid/poroelastic-medium interface, which is very similar to the "Scholte-wave denominator" for a fluid/elastic-solid interface (de Hoop & van der Hijden, 1983). Here, p r = (p The body-wave slownesses s α , α = {P 1 , P 2 , F, S}, are defined in Appendix A (Table 4.3).…”

Propagation of Transient Elastic Waves in Stratified Anisotropic Media

“…The head waves and interface waves that can be present in the wave forms in a stratified medium lead to the possibility of having more ar rivals in a generalized ray than just a body-wave arrival. For the case of a fluid/solid interface the occurrence of the compressional and shear head waves and the Scholte wave at the interface has been studied using the Cagniard-de Hoop method by de Hoop and van der Hijden (1983Hijden ( , 1985 and . These papers contain ample numerical results that elucidate how the head waves and interface wave arrivals show up in the Green's functions and convolution results if the propagation path is mostly parallel to an interface.…”