Considering three different null hypotheses,this paper has made a comparative analysis about the surrogate data method using six kinds of nonlinear chaotic time series and different nonlinear characteristic quantities.The result shows that the surrogate data method has the best performance while using mutual information as the nonlinear characteristic.With the null hypothesis of a linear correlated stochastic process which is generated by static and nonlinear transform,making 100 amplitude adjusted Fourier transformed(AAFT)surrogates,in accordance with the principle of Sigma test,the nonlinearity test of the H,D,Zcomponents of geomagnetic variation field from Changchun,Kashi,Lasa and Manzhouli geomagnetic station is carried out and we also find that there is nonlinearity in geomagnetic variation field.Simultaneously,the article provides theoretical basis and test method for the determination of nonlinear structure in geomagnetic variation field.