Wavelets Applied In Forward Of Normal Resistivity Well Logging Using Numerrical Mode-Matching Mrthod

The forward and inversion modeling of normal resistivity well logging in old wells has greatly practical value.In this paper we will make a study the inversion of normal resistivity logging. Numerical mode-matching method is a partly analytical and partly numerical method that could quickly solve forward modeling of normal resistivity well logging, and that widely used in electrical method logging positive calculation. This paper will focus on the seletction of the basic functions applied in numerical mode-matching method which can influent the precision and the speed and stability of numerical result.Wavelet basic functions have many good qualities such as compactly supported sets and orthogonality and so on.Therefore, introducing Daubechies wavelet and Hermite multiwavelet basis functions into numerical mode- matched method in the normal resistivity logging ,we put forward a new method- seletction wavelet basis functions in numerical mode- matched method in normal resistivity well logging, studying the calculated speed of the influence of well logging response.First of all, in view of the present numerical calculation always having to use a mass of basic functions which are generally Lagrange linear interpolation function or triangle function as basic functions that can achieve the required precision.Concequetly we will introduce Daubechies wavelet into the finite element method. The Daubechies wavelets are the orthogonality and short supportive, which can make the character of sparseness matrix greatly improved. The experimental results show that the algorithm can effectively reduce the computation time.Secondly, since the Daubenchies wavelets don't have analytical expressions, and don't have the interpolation property, and the transition matrix must be used in the process of computation. As a result ,we put forward a new method that the Hermite finite element mulitscalet with interpolation and multiscale characteristics as numerical mode-matching method basis functions and Hermite finite element multiscalet functions were improved which makes the linear combination meet boundary conditions. Experimental results show that the improved Hermite multiscale basis functions can improve the calculation precision significantly.Finally, in order to further improve the calculation accuracy and make the matrix sparse, we construct Hermite finite element multiscale functions corresponding 2 multiplitity finite element multiwavelet, and gives the pattern matching method of numerical solutions unit shape functions. Experimental results show that the algorithm used, the accuracy of results is greatly improved and sparseness matrix is also greatly improved.