Open AccessAmplitude of the Head Wave near the Critical Angle
Author(s) -
Donato R. J.
Publication year - 1963
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1963.tb06284.x
Subject(s) - amplitude , optics , reflection (computer programming) , head (geology) , physics , wavelength , total internal reflection , plane (geometry) , plane wave , boundary (topology) , inverse , mathematics , geometry , mathematical analysis , acoustics , geology , geomorphology , computer science , programming language
Summary A simpler derivation than that given by Brekhovskikh (1960) is given for the amplitude and shape of the head wave produced at the boundary between two semi‐infinite fluids when the distance travelled in the refractor is small. For very small distances the head wave amplitude is shown to vary as the inverse 5/4 power of the ratio of wavelength to ray path distance between source and receiver. A similar expression obtained for the total amplitude produced at the angle of critical reflection shows that a correction term proportional to the inverse quarter power of the above ratio must be added to the plane wave reflection factor corrected for spherical spreading. The analysis is extended from the single frequency case to cover a Lamb pulse. Some measurements are described which support these theoretical predictions.