中文摘要：

分形守恒定律是一种基于偏微分方程的滤波方法.方程最显著的特征是将互为矛盾的两项——分形反扩散项与经典的扩散项结合在一起.反扩散项起信号增强的作用,而去噪的作用在扩散项中体现.通过分形指数,扩散与反扩散的系数可实现滤波器的调节.本文应用这个新颖的滤波模型来实现地震资料中随机噪声的消减,同时又能增强有效的地震信号.方程的求解基于傅里叶变换.对合成地震记录的测试表明。本算法在不同强度的噪声环境中（信噪比为-5 dB至10 dB）都能很好地恢复同相轴,提高信噪比.通过对实际共炮点资料的处理结果表明,基于分形守恒定律的新滤波方法能有效的压制随机噪声并改善同相轴的连续性.

英文摘要：

The fractal conservation law is based on the partial differential equation filtering. The main advantage of the equation is the combined use of fractal anti-diffusion and classical diffusion, which are two antagonistic terms. The nonloeal anti diffusion is used to enhance the contrast, whereas the diffusion is used to reduce the noise. The tuning of the filter can be achieved by controlling the fractal exponent, the amount of anti-diffusion and diffusion. This paper applied this new filtering method for the simultaneous noise reduction and enhancement of seismic signals. Numerical simulations based on the FFT are given. The properties of this novel method are tested on synthetic seismic data. The experimental results show that our method can recover the seismic events and improve the SNR in the different noise levels （the SNR is from 5 dB to 10 riB）. In real common shot point （CSP） seismic records, the experimental results illustrate the superior performance of our method in the improvement the continuity and clarity of reflection events by removing random noise.