瞬变电磁虚拟波场Born近似算法研究

Study on Born approximation algorithm of TEM pseudo wave-field

根据瞬变电磁场所满足的扩散方程与波动场所满足的波动方程之间的数学关系,运用扫时波场变换技术,得到稳定的虚拟波场.在虚拟波场的基础上,借用地震勘探中的Born近似逆散射技术实现对电性界面进行成像的目的.在理论推导中,直接从时间域波动方程出发,运用格林定理、引入均匀半空间的Green函数建立散射场关于速度扰动量的表达式;在数值求解中,运用奇异值分解的方法实现对第一类Fredholm积分方程的求解.通过对理论模型的计算以及实例应用,均表明瞬变电磁虚拟波场Born近似算法对地下电性界面具有良好的分辨能力.

According to the mathematical relation between the diffusion equation satisfied by the transient electromagnetic field and the wave equation satisfied by the wave field,the technology of'sweep time'and'correlation superposition'is introduced to obtain the stable pseudo wave-field.Based on the pseudo wave-field,the technique of Born approximate inverse scattering in seismic exploration is used to image the electrical interface.In the theoretical derivation,the expression of velocity perturbation of scattering field is obtained by Green’s theorem and Green function of uniform half-space.In the process of numerical solution,the first class of Fredholm integral equation is solved by singular value decomposition.Through the calculation of the theoretical model and practical application,it is shown that the Born approximation algorithm of Transient Electromagnet(TEM)pseudo wave-field has a good resolution capability for the underground electrical interface.