The dynamic response of a fluid-filled borehole under a normal point load on the free surface . Geophysical Prospecting Volume 61, Issue 1, January 2013, Pages 104-119

The dynamic response of a semi-infinite fluid-filled borehole embedded in an elastic half-space under a concentrated normal surface load is analysed in the long-wavelength limit. The solution of the problem is obtained with integral transforms in the form of a double integral with respect to the slowness and frequency. The partial P- and SV-wave responses are further transformed to path integrals along Cagniard paths in the complex slowness plane. Unlike the traditional Cagniard-de Hoop technique based on the Laplace transform of time dependence, this paper is based on the Fourier transform. The tube-wave response is presented as a causal integral over a slowness range. The resultant representation in the time-domain is suitable for the numerical evaluation of the complete response in the fluid-filled borehole, especially at large distances. Asymptotic analysis of seismic phases arising in the borehole is performed on the basis of the obtained solution. The complete asymptotic wavefield consists in P- and SV-waves, the Rayleigh wave and the low-frequency Stoneley (tube) wave. Pressure synthetics obtained by the use of the asymptotic formulas are shown to be in good agreement with straightforward calculations. © 2012 European Association of Geoscientists