The dynamic response of a fluid‐filled borehole under a normal point load on the free surface |
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| Authors: | Andrei M Ionov |
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| Institution: | Department of Computer Modelling and the Physics of Nanostructures and Superconductors (National Research Nuclear University, MEPhI), 31 Kashirskoe Shosse, 115409 Moscow, Russia |
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| Abstract: | 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. |
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| Keywords: | Borehole seismics Stoneley wave Wave propagation |
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