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Goforth 1976
Goforth, T.T. (1976). A model study of the effect on the Rayleigh spectrum of lateral heterogeneity in eathquake source regions. Journal of Geophysical Research 81: doi: 10.1029/JB081i020p03599. issn: 0148-0227.

Theory has been previously developed to determine the spectrum of Rayleigh waves which have been excited and propagated through laterally homogeneous layered media. The spectral shape is a complicated function of the source and medium properties, but in general there is a shift of spectral energy in a relative sense toward the longer periods as the source depth is increased. Studies of Rayleigh wave spectra obtained from a high-gain, long-period seismograph at Grand Saline, Texas, show that for earthquakes occuring in some Pacific island are regions such as the New Hebrides, New Britain, and the Solomons, the relative spectral shift to longer periods with increasing sources depth is indeed observed. However, for the relative spectral shift to longer periods with increasing source depth is indeed observed. Howerver, for earthquakes originating in certain other island are regions, such as Tonga-Kermadec, the Phillipines, and the Marianas, no corresponding spectral shift was observed. In the first group of island arcs the lithospheric plate dips more or less toward the recording site at Grand Saline; in the second group the plate dips away from Grand Saline. It is suggested that lateral heterogeneity in the earthquake source regions is at least partially responsible for the spectral differences and that, in particular, the downward bent lithosphere acts as a wave guide at some azimuths for some Rayleigh wavelengths. To test this hypothesis for the case in which the lithosphere dips directly away from a recording position, a two-dimensional scale model of an assumed island arc source region was designed and constructed. The model was scaled such that Rayleigh energy was in the frequency range 20--200 kHz. The signals were converted to digital form for spectral analysis. Sources were first located at scaled depths of 0.50, and 250 km in the laterally homogeneous portion of the model. Sources were then located at similar depths in the dipping portion of the model lithosphere. Comparison of these spectra with those from sources at the same depth in the laterally homogeneous portion indictes a significant shift of the spectral peak to shorter periods for the sources in the dipping lithosphere. It is concluded that wavelengths as long as twice the width of the lithosphere are being enhanced in a direction opposite to the dip of the lithosphere.

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Journal of Geophysical Research
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