High-order nonlinear coefficients in isotropic solid media

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.