Open AccessComments on ‘Scattered surface waves from a surface obstacle’ by J. A. Hudson
Author(s) -
Hudson J. A.,
Boore D. M.
Publication year - 1980
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1980.tb02586.x
Subject(s) - surface (topology) , obstacle , surface wave , geology , geophysics , physics , geometry , optics , mathematics , geography , archaeology
The paper ‘Scattered surface waves from a surface obstacle’, published in 1967 (Hudson 1967), contains a theoretical development of the scattering of Rayleigh waves from a region of uneven topography or from a surface inclusion. The slopes of the surface and of the boundary of the inclusion are assumed to be small, and so are the ratios of the elevation of the surface and the thickness of the inclusion to the wavelength of the disturbance. The theory is in fact a straightforward extension to a two-dimensional surface of the method of Gilbert & Knopoff (1960); the unevenness of the surface is replaced by approximately equivalent surface loads. The results of this analysis were used in the latter part of the paper to interpret data which had been collected by Key (1967) and which showed P arrivals at the Eskdalemuir array followed closely by short-period Rayleigh waves. These surface waves appeared to be the result of the scattering of the incident P wave at a nearby deep valley known as Moffatt Water. Comparison of theoretical and observed ratios of P to Rdyleigh wave spectra gave the reasonable result that the scatterer was approximately 5 lun wide. Unfortunately, the paper is marred by three separate errors (only one of which, however, affects the main conclusion) and it seems that, in spite of the long time which has elapsed since its publication, it would be useful to expose and correct these errors here. The ground motion associated with short-period surface waves, strongly guided by sedimentary layers, is of great interest for seismic engineers (see, for instance, Swanger & Boore 1978a,b), and the generation of such waves by uneven topography and by heterogeneous geological structure is quite efficient; the amplitude of the scattered wave from Moffatt Water, for instance,is up to 40 per cent of the surface amplitude of P. Techniques for prediction of the characteristics of such scattered waves are very few apart from the perturbation method (briefly described above) and a straight numerical approach. It is most important to know, therefore, to what extent the results of perturbation theory are accurate.