小波变换在求解重力测定反问题中的应用

Application of Wavelet Transformation in Solving Gravimetry Inverse Problems

针对重力测定反问题,提出将其离散为线性不适定问题,利用小波变换方法进行数值求解。该方法将小波变换和正则化方法相结合,选取小波函数作为一组基底,将原不适定问题转化为粗子空间上的适定问题,并给出选取粗子空间基的方法。通过数值模拟已有方法和小波变换方法求解结果的比较,表明了小波变换方法的可行性和有效性。

The inverse gravity problem is dispersed to be a linear ill-posed one.A method of wavelet transformation is presented for the solution of the linear ill-posed problem.It combines wavelet transformation with regularization method to solve ill-posed problems,and choices a wavelet function as the base function,which takes full advantage of the wavelet with compact support,and converts the ill-posed problem into a posed one in the coarse space.Compared with existing methods,the numerical results of wavelet transform show the applicability and effectiveness of the proposed method.