Biot介质中P波与井孔的耦合

P-WAVE COUPLING TO HOLE IN BIOT SOLID

依据全频域的Ｂｉｏｔ理论，推导了在Ｂｉｏｔ的流体饱和孔隙介质中，平面Ｐ波垂直井轴入时与井孔相互作用所产生的井内声压场的解析表达式．通过数值计算，对井内声压场出现的共振响应进行了分析．重点研究在不同频率段渗透率对井内声压的影响及偏离井轴记录时声压的变化．结果表明，在井内测量地震波声压，全频域都有明显影响；测量大于５００ＨＺ的地震信号，检波器偏离井轴放置以及方位不同的影响不能忽略；渗透率变化对井内声压的影响程度最大不超过弹性固体情况（零渗透率）下相应声压的１／５．

An exact treatment of the Coupling of an external plane P-wave to a fluid-filled hole in a Biot solid is presented.The mechanism of the resonance response of the pressure in a hole is analyzed theoretically and numerically.This theory is compared with a quasi-static derivation from the literature, good at low frequency,and with published theories of coupling of P-waves in a surrounding elastic solid.The effect of permeability in different frequency range on the pressure in a hole and the change of the pressure for off-axis are investigated emphatically.The results show that the well hole has a significant effect on the pressure of seismic wave measured in the hole over the complete frequency range;when the frequency of the seismic signal measured is over 500 Hz,the effect of the off-axis measurement and the difference of azimuth must be considered also; the maximum of the change of pressure caused by permeability is about a fifth of the pressure in elastic solid case corresponding zero permeability limit.