Three-dimensional Forward And Inversion Of Frequency Domain Airborne Electromagnetic Method Based On The Localized Quasi-linear (LQL) Approximation

Frequency-domain airborne electromagnetic measurements (AEM) can obtain large amounts of electromagnetic data in remote areas where terrestrial electrical methods can not be reached. A typical airborne electromagnetic measurement is a sampling point every few meters, so it may contain hundreds of sample points.Quantitative calculations for these large-scale data are very time-consuming and challenging.Forward modeling is the basis of inversion, so fast and accurate forward modeling numerical simulation is the key to inversion to achieve good results. Integral equation(IE) method is an effective method in numerical simulation, because it only has the advantages of fast computation speed. However,the main difficulty of the integral equation technique lies in the size of the linear equation matrix. If the linear equation matrix is too large, it will consume a lot of memory and the computation time will increase much. This limitation of the integral equation technique becomes more serious in the inversion problem, since multiple forward modeling is required for different iterative model parameters in the inversion.In order to solve this problem, several approximate solutions are introduced into the full integral solution. Foreign scholars Zhdanov and Fang (1996a, 1997) developed a quasi-linear approximation algorithm based on the electrical reflection coefficient. In this approximation, the anomalous electric field in the anomalous region is proportional to the background field through an electrical reflection tensor. This electric reflection tensor is obtained by solving the problem of the minimum value of the integral equation based on the scattered current. The advantage of this method is that if you want to simplify and speed up the calculation, the electrical reflection tensor can be assumed to be a scalar or diagonal tensor instead of the total tensor.However, a problem with QL approximation is that its electrical reflection tensor needs to be recalculated once every new excitation source. This means that this approximation method is not suitable for multi-source data arrangement in the inversion scheme, especially the three-dimensional inversion method of these data becomes extremely unrealistic. To solve this problem, Zhdanov developed a new quasi-linear approximation (QL) method based on the so-called "localized" electric reflection tensor,which is independent of the source position. This new method is called the local quasi-linear approximation (LQL) method, which combines the idea of local nonlinear approximation (LN) and primitive quasi-linear approximation (QL).In this paper, the local quasi-linear approximation (LQL) method is applied to the synthetic data inversion of the frequency domain airborne method. The inversion results show that this method is stable and effective in solving the multi-source frequency domain airborne method.