Errata to the paper ‘Rayleigh wave scattering by a wedge. II’ [Wave Motion 24 (1996) 307–317]
✍ Scribed by B.V. Budaev; D.B. Bogy
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 26 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0165-2125
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✦ Synopsis
In our recent paper [1], it was acknowledged that computations of Rayleigh wave reflection and transmission coefficients reported in our previous paper [2] were inaccurate for wedges larger than 180 • . Here we would like to disclose the technical cause of that error.
Errors in [2] were introduced for some wedge angles by the selection of constants a and b, and of the auxiliary function σ (ω) appearing in Eq. ( 1) of [2]. All computations in [2] were made with a = -π , b = π , and with the 2π -periodic σ (ω) = 1 2 cot( 1 2 ω), which was correct for wedges smaller than 180 • , e.g. in cases with α < π/2. But, in cases with α > π/2 these selections for a, b and σ (ω) caused the functions Φ * (ω) and Ψ * (ω) defined by Eq. ( 1) of [2] to have extraneous poles in the strip |Re ω -π/2| < α, which led to numerical errors. In the paper [1], the auxiliary function σ (ω) is defined by (3.16) differently than in [2], and the extraneous poles, and hence the numerical errors, no longer occur. Results plotted in Fig. 6 of [1] agree with existing experimental and numerical data. However, the phase of the reflected wave for the angles from 160 • to 200 • is not plotted because their computation was not stable, which is not surprising because of the small absolute values of the corresponding reflection coefficients.