基于凸集投影的重力同时填充扩边和去噪方法

实测重力数据经常因工区不规则导致数据存在空缺。在波数域进行重力数据处理和转换前必须对原始数据进行填充和扩边处理。数据中存在的高频噪声往往是造成数据后续处理不稳定的主要原因。常规重力数据处理一般将数据的填充、去噪和扩边这三个步骤独立进行。为此，将这三个问题统一考虑，提出一种基于改进凸集投影方法的规则网格重力数据同时填充、去噪和扩边迭代方法。首先通过计算并拟合重力数据的径向平均功率谱确定迭代的最终截止波数，然后利用数据低于截止波数的谱对数据同时进行填充、扩边和去噪，直至达到预设的迭代次数。对理论重力模型和阿富汗实测均衡重力数据进行了扩充和去噪实验，结果表明，所提方法原理简单、操作方便，填充和扩边结果的数据衔接处光滑无畸变，且具有较好的填充和去噪效果，处理结果优于经典的最小曲率和Kriging插值法及小波去噪和余弦扩边组合法。

Simultaneous interpolation,edge padding and denoising method for gravity data based on the projection onto convex sets

Gravity exploration blocks are often irregular,which causes the vacancy in the acquired gravity data.Before the processing and transformation of gravity data in wavenumber domain,the original data must be interpolated and processed with edge padding.High-frequency noise in gravity data is the main factor which causes the instability in later processing.Conventional gravity data processing generally performs interpolation,denoising and edge padding independently. These three issues were considered integrally,and an iterative method for simultaneous interpolation,denoising and edge padding of gravity data based on the projection onto convex sets was proposed.Firstly,the final cutoff wavenumber of the iterative method was determined through calculating and fitting the radial average power spectrum of the gravity data.Secondly,interpolation,edge padding and denoising were applied to gravidy data using the spectrum with the wavenumber lower than the cutoff wavenumber,until the preset iteration number was reached.Theoretical gravity model test and the application in real isostatic gravity data acquired in Afghanistan showed that the method proposed is simple theoretically and convenient to be applied.The splicing of the interpolation and edge padding results is smooth without distortion,and the method achieved good interpolation and denoising effect.The results of the method proposed in this paper are better,compared with those of the conventional joint processing method based on minimum curvature,Kriging interpolation,wavelet denosing and cosine edge padding.