一种基于改进凸集投影原理的航空重力数据插值与去噪方法

Simultaneous Interpolation and Denoising Method for Airborne Gravity Data Based on Improved Projection onto Convex Sets Theory

航空实测重力数据不仅噪声含量大,而且由于各种因素的限制,数据常常需要插值加密。常规航空重力数据处理一般将数据的插值和去噪这两个步骤独立进行,将这两个问题统一考虑,借鉴地震数据处理方法,提出一种基于改进凸集投影原理的规则网格重力数据同时插值和去噪迭代方法。基于EGM2008重力场模型仿真一组重力数据,验证了该迭代法的插值和去噪效果优于4种经典插值方法和部分小波阈值去噪方法。并通过某区域的实测航空重力数据进一步验证了方法的有效性。

The areas of airborne gravity measurement are often irregular and the gravitational measurement data often have vacancy and high frequency noise interference. Conventional airborne gravity data processing generally performs the two steps of interpolation and denoising independently. In this paper, we consider these two problems in a unified way. Learning from seismic data processing methods, we propose an iterative method for interpolation and denoising of airborne gravity data based on the projection onto convex sets method. Using the simulative airborne gravity data based on the EGM2008, the results of numerical calculation examples have clearly demonstrated that our proposed iterative method for interpolation and denoising of gravity data is better than the four classical interpolation methods and some wavelet threshold denoising methods. And the effectiveness of the method is further verified by the measured aerial gravity data of a certain area.