钻井中首波的共振与衰减

本文从P波首波的严格割线积分出发,首次给出了揭示其共振与衰减特性的渐近展开式,通过数值计算,对这些公式进行了检验,证明它们与严格解符合的相当好.解析的和数值结果一致表明:首波具有共振特性,频谱是连续的;振幅随源距z按1/z规律衰减;各共振峰幅度随岩石泊松比v的增大按[v/（1-v）]2规律增大.时域计算表明,所谓“滤波效应”正是首波共振激发特性的反映,传播过程中不频散.

RESONANCE AND ATTENUATION OF THE HEAD WAVE IN A FLUID-FILLED BOREHOLE

From exact expression of the branch cut integration of P-head wave, asymptotic expressions are first developed for full-P wave train in a fluid-filled borehole. These results obtained are verified with direct numerical integrations and they are in excellent agreement. Analytical and numerical results consistently show that: full-P wave train, possesses the feature of resonance, and the amplitude decays with source-receiver distance z as Inz; the amplitude of each resonant peak increases with Polsson's ratio as [V/（1-v）]2. The calculations in time domain show: so-called "filter-effect" in borehole jast is the reflection of resonance exitation of P wave, but full-P wave train is not dispersive during propagation.