| The wavelets have many good properties such as multi-scale and multi-resolution which is a very powerful tool for the analysis of non-stationary signals,and the traditional finite element method(FEM) have the advantages of adaptability and high accuracy. This paper devotes to ground penetrating radar (GPR) two-dimensional forward by Daubechies-wavelet finite element method(DWFEM)which combining their respective advantages of Daubechies wavelet function with traditional finite element method.and realize the complex model of GPR efficient forward,provides a high precision algorithm,and also have a very attractive prospect to the large gradient,singularity engineering.The paper is funded by a joint support of the National Natural Science Fund "The complex GPR element-free method forward simulation and multi-parameter hybrid intelligent optimization inversion"(41074085) and "The research of GPR’s forward modeling and migration based on finite element of wavelet"(40804027).The main content of this paper is as follow:1.This paper research of wavelet finite element method especial-ly, Daubechies wavelet finite element are briefly introduced.then the basi-c principle of ground penetrating radar(GPR) is introduced and the influe nee of electrical parameters of media on the transmission mechanism of g round penetrating radar (GPR) is discussed in detail, especially the relatio nship between electric conductivity, relative permittivity and speed,frequ ency of electromagnetic wave The resolution and measuring methods of GPR are discussed.2.Considering the mathematical expressions of Daubechies wavelet deos not exsit and some problems of numerical calculation will be exsit when combines Daubechies wavelet with FEM, the construction method of Daubechies wavelet function and the solution of its derivative value and integral valueare introduced and the contact coefficient of Daubechies wavelet-finite element(DWFEM) is deduced in detail. Since connection coefficient is calculated by adding complex equations currently, this paper combined the Compound Trapezoid Quadrature Method (CTQM) with filter coefficient equations without additional conditions in traditional method to obtained the initial value of several connection coefficients firstly, then combining with generalized least squares (GLS) theory to deduce the calculation formula of Daubechies wavelet finite element connection coefficient,and get better result.3. Started from the Maxwell equation which met the GPR, and based on the Galerkin Principle, used the basis function which is a linear combined of the Daubechies wavelet into the conventional finite element method,detailed infers the wave equation of the GPR wave equation Daubechies wavelet finite element method,then based on transmission mechanism and attenuation mechanism expounding the transmission absorbing boundary,sarma absorbing boundary and improved sarma absorbing boundary.Through the Degrees of cohesion technology,making the degresss freedom of wavelet unit from [2N-1]×[2N-1] to only4,greatly reducing the freedom of wavelet unit,and reducing the amount of computing storage.4. Based on theses algorithms GPR forward simulation program is prepared. By using this program a number of typical geoelectric model was simulated.Compared with conventional finite element method with Wavelet finite element method for simulation results.From the corresponding forward simulation profile, snapshot of wave field and Single-channel data comparison chart,we can obtain the result that either in a simple model or in combination model,wavelet finite element method for simulation speed and accuracy compared to conventional finite element method has a certain improvement.The wavelet finite element method of GPR forward simulation results are valid,and more helpful to guide the geological interpretation in the GPR data. |
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