各向同性固体介质中的高阶非线性系数

High-order nonlinear coefficients in isotropic solid media

到目前为止,人们对自然界岩石非线性系数的量级范围甚至它们的符号都没有确定的结论。本文作者对他以前的理论作了进一步研究,结果表明,奇阶非线性系数只与奇阶非线性谐波的振幅有关;偶阶非线性系数只与偶阶谐波振幅有关,各阶谐波存在积累解,它的振幅与距离一次方成正比的。应用已发表的波谱测量数据对Berea砂石样品的2~5阶非线性系数做了计算。结果表明,2阶和3阶非线性系数的符号为负,4阶和5阶非线性系数的符号为正。由于非线性系数与声场频谱测量的精度密切相关,本文认为对测得的声场频谱需要作探针接收器灵敏度和测量位置变化的修正。

Abstract Up to now,there is no definite conclusion about the magnitude range or even the sign(positive or negative) of nonlinear coefficients of rocks in nature.In this paper,a further analysis was conducted on the previously published theory by this author and the result reveals that the odd order nonlinear coefficients only depend on the amplitude of the odd order nonlinear harmonics,while the even order nonlinear coefficients only depend on the amplitude of the even order harmonics.There is an accumulated solution for each harmonic,of which the amplitude is proportional to the first power of distance.The 2 nd-5 th order nonlinear coefficients of Berea sandstone samples were calculated using the published spectrum measurement data.The results show that the signs of the 2 nd and 3 rd order nonlinear coefficients are negative,and the signs of the 4 th and 5 th order nonlinear coefficients are positive.Since the nonlinear coefficients are closely related to the accuracy of the measurement of the sound field spectrum,it is necessary to make corrections to the receiving sensitivity and the directivity of the pinducers.