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Study of effects of focal depth on the characteristics of Rayleigh waves using finite difference method

This paper presents a relationship between the focal depth in terms of Rayleigh-wave wavelength and the dominant frequency of Rayleigh waves generated in a homogeneous half-space. Rayleigh waves were simulated using a (2, 4) staggered grid P-SV wave finite difference algorithm with VGR-stress imaging technique as a free surface boundary condition. VGR is an acronym for vertical grid-size reduction. The simulated seismic responses using P-wave and SV-wave sources at different focal depths revealed Rayleigh-wave generation up to certain focal depth only for the considered frequency bandwidth. A shift of normalized spectral shape of Rayleigh wave towards lower frequency with increasing focal depth was inferred. Largest spectral amplitude was obtained in the wavelength for which the ratio of focal depth to the wavelength of Rayleigh wave was around 0.17 in the case of P-wave source and 0.9 in the case of SV-wave source. An exponential decrease of spectral amplitude of Rayleigh wave with the departure of the ratio of focal depth to Rayleigh wave wavelength from the above mentioned values was obtained.