基于非负约束的重力向下延拓BTTB-MRNSD方法  

BTTB-MRNSD method for downward continuation of gravity field based on nonnegative constraints

作　　者：刘天佑 曾小牛 李夕海 LIU Tianyou;ZENG Xiaoniu;LI Xihai(School of Nuclear Engineering,Rocket Force University of Engineering,Xi'an 710025,China;National Engineering Research Center of Offshore Oil and Gas Exploration,Beijing 100028,China)

机构地区：[1]火箭军工程大学核工程学院,陕西西安710025 [2]海洋油气勘探国家工程研究中心,北京100028

出　　处：《测绘学报》2024年第8期1552-1563,共12页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41804136)。

摘　　要：向下延拓作为处理与解释重力数据的一项重要技术,因其计算的不适定性而备受研究人员的关注。空间域延拓方法一般延拓精度较高,但通常计算复杂度较大。本文首先根据重力异常数据的特点,借鉴图像复原问题的处理思路,提出了一种重力向下延拓等效数学模型。然后,基于系数矩阵的块-托普利茨-托普利茨-块(BTTB)结构特点,本文提出了一种具有非负约束的空间-波数混合域下延迭代方法。该方法克服了空间域延拓计算复杂度大的问题,计算效率较高。基于理论重力模型和实测异常数据的对比试验表明,本文提出的重力下延方法具有相对较高的下延精度和稳定性,且收敛性较好。As an important technology for processing and interpreting gravity data,downward continuation has attracted the attention of researchers because of its ill-posedness.The space domain continuation method generally has high continuation accuracy,but the computational complexity is usually large.In this paper,firstly,according to the characteristics of gravity anomaly data and the idea of image restoration,an equivalent mathematical model of gravity downward continuation is proposed.Then,based on the block-Toeplitz Toeplitz-block(BTTB)structure of the coefficient matrix,we propose a space-wavenumber mixed domain downward continuation iterative method with nonnegative constraints.The method overcomes the disadvantage of large computational complexity in space domain continuation and has high computational efficiency.The comparison experiments of theoretical gravity model and real anomaly data show that the gravity field downward continuation method proposed in this paper has high downward continuation accuracy and stability,and has good convergence.

关 键 词：重力 非负约束 向下延拓 最速下降法 BTTB矩阵 

分 类 号：P223[天文地球—大地测量学与测量工程]