利用余弦变换的重力梯度Parker正演方法及其应用

重力测量数据存在地形数据产生的高频分量的影响，高精度地形数据正演重力梯度也能较好地反映重力局部高频特征。为获得高精度重力梯度数据，实现基准梯度数据库精确快速构建，研究了利用数字高程模型正演重力梯度的频率域快速计算方法，推导出基于余弦变换的Parker正演重力梯度理论公式。数值实验结果表明，余弦变换频率域正演方法平均绝对误差可达到0.5E左右精度要求，与傅里叶变换正演方法相比误差可减小3dB左右，与棱柱法等空间域正演方法相比，该方法计算规模小，速度优势明显。

Gravity Gradient Parker’s Forward Method and Application Based on Cosine Transform

Topographical data have significant influence on the high frequency component in gravimetry data. The high precision of terrain data forward method can basically reflect local gravity characteristics. In order to obtain accurate gradient data and build the gravity gradient reference database quickly, the fast frequency method for digital elevation model forward gravity gradient was investigated in detail. A novel Parker’s forward formula based on cosine transform has been deduced to calculate the full tensor gravity gradient, and then discusses accuracy and calculation time of the frequency method by numerical experiment. The simulation tests and analysis show that, the mean abstract error of gradient data forwarded by our Parker’s forward method is estimated to be less than 0.5E precision. The errors of this solution decreased by 3dB in comparison to Fourier transform Parker’s forward method. Comparing with spatial domain rectangular prism numerical methods, it gives better apparent advantages over calculating scale and efficiency.