【摘要】 旨在构造一种新的地震波散射非线性反演方法.将函数论中的不动点理论引入到地震波散射非线性反演中,并构造出了波相空间里关于速度参数的具体的压缩映射算子,从而从理论上保证了速度参数不动点的存在性和寻找途径.在此基础上还证明了利用此速度参数的不动点和正演所得到的相应的波值也是波函数本身的不动点,并利用不动点的稳定属性得出此不动点是一个最优的点.最后,文中还用该方法给出了具体的数值算例,间接地证实了本方法的实用性.更多还原

【Abstract】 The work described in this paper focuses on making a new method of nonlinear inversion for seismic scattering. The fixed-point theory is incorporated into the nonlinear seismic scattering inversion and the method to create a series of contractive mappings of velocity parameter’s in the mapping space of wave is given. The existence of fixed point of velocity parameter is testified by the results and the method to find it is given. Furthermore, it is proved that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Because of the stabilities quality of the fixed point, it is the global optimum. The given numerical example shows the validity of the method.更多还原