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We present SEA99, a revised predictive relation for geometric mean horizontal peak ground acceleration and 5%-damped pseudovelocity response spectrum, appropriate for estimating earthquake ground motions in extensional tectonic regimes, which we demonstrate to have lower ground motions than other tectonic regimes. SEA99 replaces SEA96, a relation originally derived by Spudich et al. (1996, 1997). The data set used to develop SEA99 is larger than that for SEA96, and minor errors in the SEA96 data set have been corrected. In addition, a one-step regression method described by Joyner and Boore (1993, 1994) was used rather than the two-step method of Joyner and Boore (1981). SEA99 has motions that are as much as 20% higher than those of SEA96 at short distances (5-30 km), and SEA99's motions are about 20% lower than SEA96 at longer periods (1.0-2.0 sec) and larger distance (40-100 km). SEA99 dispersions are significantly less than those of SEA96. SEA99 rock motions are on the average 20% lower than motions predicted by Boore et al. (1994) except for short distances at periods around 1.0 sec, where SEA99 motions exceed those predicted by Boore et al. (1994) by as much as 10%. Comparison of ground motions from normal-faulting and strike-slip events in our data set indicates that normal-faulting horizontal ground motions are not significantly different from extensional regime strike-slip ground motions.

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.

Recent interest in finite‐difference modeling of the wave equation has raised questions regarding the degree of match between finite‐difference solutions and solutions obtained by the more classical analytical approaches. This problem is studied by means of a comparison of seismograms computed for receivers located in the vicinity of a 90-degree wedge embedded in an infinite two‐dimensional acoustic medium. The calculations were carried out both by the finite‐difference method and by a more conventional eigenfunction expansion technique. The results indicate the solutions are in good agreement provided that the grid interval for the finite‐difference method is sufficiently small. If the grid is too coarse, the signals computed by the finite‐difference method become strongly dispersed, and agreement between the two methods rapidly deteriorates. This effect, known as “grid dispersion,” must be taken into account in order to avoid erroneous interpretation of seismograms obtained by finite‐difference techniques. Both second‐order accuracy and fourth‐order accuracy finite‐difference algorithms are considered. For the second‐order scheme, a good rule of thumb is that the ratio of the upper half‐power wavelength of the source to the grid interval should be of the order of ten or more. For the fourth‐order scheme, it is found that the grid can be twice as coarse (five or more grid points per upper half‐power wavelength) and good results are still obtained. Analytical predictions of the effect of grid dispersion are presented; these seem to be in agreement with the experimental results.