Anisotropic Diffusion And Its Application Research In Electromagnetic Data Processing

The anisotropic diffusion(AD) based on the partial differential equations is one of the extensive used method in the image processing due to possess the directional diffusivity from twenty century ninety years. Especially the anisotropic diffusion, as a nonlinear method, possesses of computing facility, moreover, the partial differential equations can be regard as local filter iteration of exiguity neighbour, and make a new filter method by combined with existing filter method in the image de-noise and segment processing. The directional diffusivity of anisotropic diffusion is introduced to geophysical data processing, and achieves the nonlinear processing of electromagnetic signal.The first the relation of AD model and the energy variety of image is educed by thermal diffusion and the diffusion equations based energy flux, and proves the image processing by energy flux sufficing maximum-minimum principle, the variety of image energy is equivalent to that of image intensity. The variety character of image and noise energy are studied. The concept of image diffusion balance is defined and achieves the efficient estimation of diffusion time scale by diffusion balance of thermal diffusion introduced to anisotropic diffusion. The result of simulation test indicates the method proposed in the paper can remove noise and protects the character of signal and achieves preferable vision effect. The novel method need not estimate intensity of noise and can adapt image relatively with MSE method. The results of test indicate its validity.The second the anisotropic diffusion is introduced to the impedance estimation of electromagnetic measurement by the relation of Bayes statistic, Robust statistic and anisotropic diffusion, the anisotropic diffusion equation is modified to adapt to impedance estimation, the modification equation improves the stability of estimation, and the convergence of general Robust estimation is one of ADR result.The third the curve smoothing of electromagnetic measurement based anisotropic diffusion and local monotony diffusion is proposed. In order to remove "outliers" noise and instability in the diffusion, the application of rational function in the signal smoothing and the relation with linear and nonlinear filter is studies, the stability of diffusion and the ability of removing outliers noise is improved by altering grads estimation method.The fourth estimation method of diffusion time scale is proposed in order to remove the effect of time scale to filter result. The results of simulation and field data test indicate: (1) the noisy simulation curve can approach to the free curve highly precision by diffusion time scale. (2)the DB minimum or zero value point is existence obviously in the anisotropic diffusion smoothing.The fifth the correction method of station effect in electromagnetic measurement is studied by the directional diffusivity of anisotropic diffusion and the character of asymmetry in the shallow earth, and a new diffusion model and diffusion coefficient function are proposed. The computer method of grads operator is discussed. The field data test indicates that the proposed method can remove the interference of shallow asymmetry, extract trend information in deep earth and local information shallow earth and precede the classical EMAP method.