瞬变电磁虚拟波场二阶Born近似成像算法

依据瞬变电磁扩散场与虚拟波动场之间的数学表达式,通过波场反变换得到虚拟波场,进而借用地震勘探上成熟的成像方法定位地质界面的位置以及形态.本文首先将时间域波动方程转换为频率域波动方程,将总波动场分为背景场和散射场、总波速分为背景速度和扰动速度,然后运用Green定理得到了散射场关于地质界面速度扰动量的表达式,并使用Bor...

Second-order Born approximation imaging algorithm for transient electromagnetic pseudo wave-field

According to the mathematical expression between the transient electromagnetic diffusion field and the pseudo wave-field,the pseudo wave-field can be obtained by the inverse transformation and then realizing imaging the electrical interface using the mature imaging methods in seismic exploration.In this paper,converting the wave equation in the time domain into the frequency domain firstly,and then dividing the total wave-field into the background field and the scattered field,the total wave-velocity into the background velocity and the disturbance velocity.Then,Green′s theorem is used to obtain the expression between the scattering field and the disturbance velocity of the geological interface and using Born approximation algorithm to linearize the integral equation,finally,the value of the disturbance velocity can be quickly obtained by Fourier transform.By analyzing the morphology of the step function and the Delta function in different frequency bands,it can be seen that the Delta function is almost not affected by the frequency band.Therefore,the first derivative of the disturbance velocity can be used to obtain the reflectance function that is not affected by the frequency band,realizing accurately positioning the underground electrical interface.It can be seen from the expression of the scattering sequence that the Born approximation algorithm only retains the first item in the scattering sequence and loses part of useful information,so it cannot accurately image the underground electrical interface.The first two items of the scattering sequence are preserved according to the recursive relationship between the items,and the second-order Born approximation expression is derived.By comparing the influence of resistivity changes and layer thickness changes on the imaging accuracy,this paper finds that the second-order Born approximation algorithm has a higher resolution than the conventional Born approximation imaging method.Through the calculation of the two-dimensional model and the three-dimensional low-resistance thin plate model,compared with the Born approximation algorithm,the second-order Born approximation algorithm can accurately locate and quickly image the position of the underground electrical interface and even the shape of the abnormal body.