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本文由系统函数模型H(jω)出发,导出了逐层向下的一维反演公式。该方法的基点是给定频率f处的系统函数值只含有一定深度H以上的构造信息.而更深处的构造信息只影响更低频处的系统函数值。于是从已有最高频率的H(jωmax)出发,以二分层结构作初始假设,可反演第二层的参数。然后,逐步针对较低频率的H(jω),在更深处引入新的离散分层,反演出第三层参数,并依此向深层类推。计算机模拟结果表明,反演方法是有效的,对产P1的初值不敏感,抗噪性能良好。
Starting from the system function model H (jω), this paper deduces the one-dimensional inversion formula from layer to layer. The basic point of the method is that the system function value at a given frequency f only contains the structural information above a certain depth, The deeper structure information affects only system function values at lower frequencies. So starting from the highest frequency of H (jωmax), the initial assumption of the two-layer structure can be used to invert the parameters of the second layer. Then, a new discrete stratification is introduced deeper into H (jω) of lower frequency, the third layer parameters are inverted, and so on. The results of computer simulation show that the inversion method is effective and insensitive to the initial value of P1 and good anti-noise performance.