Research On Born Approximation Imaging Algorithm Of TEM Pseudo Wave-Field And Its Application In The Gobs Detection

The method of transient electromagnetic is widely used in hydrogeological exploration of coal field,resource exploration,geological disaster investigation and other fields with its advantages of high construction efficiency,sensitivity to low resistivity body and strong abnormal response,and it has achieved good results.As a result,it is considered as a promising method in geophysical methods.At present,the method of deep prospecting and detailed exploration has put forward higher requirements for this method.However,this method faces difficulties in large amount of calculation and slow speed due to threedimensional inversion interpretation.In addition,transient electromagnetic field satisfies the diffusion equation,which describes the diffusion characteristics of eddy current field,and its propagation velocity and propagation energy attenuation are both fast,which is not conducive to imaging.It is well known that the wave field on the earthquake satisfies the wave equation and is convenient for imaging,and seismic exploration methods are relatively mature in theoretical research and data interpretation.The predecessors have proved that there is a mathematical conversion relationship between the diffusion equation satisfied by the transient electromagnetic field and the wave equation that the wave field satisfies.According to the relationship between the two fields,the electromagnetic field response is converted into a virtual wave field,and the method of borrowing on seismic interpretation ways can be realized.The purpose of transient electromagnetic quasi-seismic interpretation is to obtain information on the underground target body that can not be obtained by the method of transient electromagnetic.Given that the product decomposition of the wave equation is non-linear,a certain approximation method must be adopted to solve it.The Born approximation algorithm based on inverse scattering theory can realize the linearization of the wave equation,in addition,the Born approximation algorithm has advantages such as fast calculation speed and does not require accurate speed analysis to obtain the accurate velocity.Therefore,transforming the transient electromagnetic field into a virtual wave field,and then researching the Born approximation imaging algorithm is of great significance in realizing the transient electromagnetic quasi-seismic interpretation.Firstly,according to the mathematical relation between diffusion field and wave field,the technique of sweeping time wave field transform is used to improve the unsuitability of wave field transform.Set a time window first,and then make it slide on the time series,apply the singular value decomposition method to the diffusion field value in each time window,and use the regularization method to perform the wave field transformation in the whole time period to obtain the virtual field.The wave field value is then used to determine the correlation between the wave field of each window and the full-time wave field.If the correlation is greater than the set smaller correlation threshold,the wave field value and the full-time wave field value are superimposed.Thereby,a virtual wave field with strong antinoise ability is obtained.In this paper,based on the virtual wave field conditions,the velocity of the subsurface medium is divided into the background velocity and the perturbation velocity,and the total wave field can be divided into radiation field and the scattering field,and the equation of scattering is established.Then Born approximation is used to change the integral equation to be linearized,and the expression of the time domain Green’s function is introduced to establish an equation based on the constant background velocity and the self-excited selfcollecting scattering field,ie the virtual wavefield with respect to the velocity perturbation.According to the form of the equation,the equation belongs to the first kind of Fredholm integral equation,which has characteristically ill-posed.This paper analyzes the curve characteristics of the kernel function in different discrete modes,and then adopt the appropriate numerical discrete method.Finally,velocity disturbance quantity is obtained by singular value decomposition method.Finally,based on the theoretical derivation formula,the Born approximation imaging algorithm is applied to the theoretical model and the actual production of gobs detection.The validity and practicability of the Born approximation imaging algorithm are verified by comparing the imaging results with the theoretical model and the measured geological data.