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利用离散水平波数域中复频平面的性质,对三维声波方程解的复振幅和相位之间的联系进行了研究。对于一般的三维不均匀介质声波方程的解来说,在某种技术性假设条件下,推导出震源谱范围内相位均值和取对数的振幅均值之间的关系。这种关系表明:在记录到的振幅响应中,整个震源谱范围上的起伏变化,当相位成分中不存在相似数量级的起伏变化时,这种起伏变化不是由声波方程解的性质直接引起的。这种结果包括地下地层横向特征发生任意变化那种情况。对于横向变化大地层模型,通过对二维声学响应的数值模拟,用边界积分模型技术
By using the property of complex frequency plane in discrete horizontal wave number domain, the connection between complex amplitude and phase of three-dimensional acoustic wave equation is studied. For the solution of the general three-dimensional inhomogeneous media acoustic equation, under certain technical assumptions, the relationship between the phase mean value in the source spectral range and the average amplitude of the logarithm is deduced. This relationship shows that in the recorded amplitude response, fluctuations in the entire source spectral range are not directly caused by the nature of the acoustic wave equation solution when there is no fluctuation of similar magnitude in the phase components. This result includes the situation where the horizontal characteristics of the subsurface strata change arbitrarily. For the lateral variation of the formation model, through the numerical simulation of two-dimensional acoustic response, with the boundary integral model