以复模两相饱和介质Biot动力学方程为基础，根据该方程D'Alembert解的Fourier变换所属的Homholtz方程特性，由Biot方程解的相容性条件及δ函数性质较好地解决了快、慢纵波位势的耦合问题.较为简便地得到了两相饱和介质在集中力作用下低频(ω＜ωc)时的频域和时域的Green函数.%The Green function on two-phase saturated medium by concentrated force is useful and important in seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. Therefore, after Biot put forward the two-phase saturated medium equation,there are a series of research on the Green function on two-phase saturated medium by concentrated force from 1970's (Cleary[1] (1977), Burrdge & Vargas[21 (1979), Norris[a] (1985), Kynia[4] (1992),J.Chen[a,6] (1994)). Among them, Norris's work was more famous. He firstly showed the dynamic equition on two-phase saturated medium by concentrated force. According to Burrdge's work,he found the formal solution of the quick and slow dilation spectrum and distortion spectrum of Green function on two-phase saturated medium by concentrated force by the property of δfunction, and gave detailed discussion on the approximate solutions of various conditions (low frequency, high frequency, near field, far field, big porosity and small porosity). Norris's work was exquisite, yet we should point out the complete close solution of Green function can be found on condition of low frequency. The close solution has very important uses in geophysics, especially in dislocation inversion theory of focus in seismology. Otherwise, when two-phase saturated medium acted by a concentrated force, the contributions of quick, slow dilation wave and distortion wave to Green function can be gained with their amplitude. In 1987, by making use of that coupling eigin equation equal to zero, Philippacopoulis got the result of low frequency, which is correct for quick and slow dilation wave amplitude ratio, and is also correct for distortion wave amplitude value. The problem is when use quick, slow dilation amplitude value, he use amplitude ratio as substitute, i.e. Philippacopoulos's solution merely consider the interaction of quick and slow dilation wave, it did not consider the restrict of distortion wave displacement field to quick and slow dilation wave displacement field. The thesis's work was on the basis of complex modular two-phase saturated medium Biot's equation by the characteristic of Homholtz's equation it is suitable for the Fourier transform of D'Alembert solution, using the compatibility condition of Biot's equation and the property of δ function, the authors solved the coupling problem of quick, slow dilation wave potential, gained the Green function on two-phase saturated medium in low frequency (ω ＜ ωe),and discussed on its forms in various special conditions.
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