三维重力梯度局部光滑约束反演

针对重力勘探中光滑反演存在的分辨率较低的问题，本文提出一种基于地质体埋深、地层倾向等一定先验信息的局部光滑约束三维反演算法，并提出了一种光滑反演中粗糙度矩阵的存储方式，该存储方式可以将M×N维粗糙度矩阵存储为M×2维，减少了计算机计算内存，且详细介绍了该存储方式下粗糙度矩阵与其他矩阵相乘时，粗糙度矩阵所存储的位置信息的读取方式以及与其他矩阵逐列逐步相乘最终得到计算结果的过程。最后，利用文中提出的算法对理论模型和实测数据进行反演试算，结果表明局部光滑反演算法相比于全局光滑反演结果更加准确，且该算法在一定噪声水平下依然稳定，在实际生产中有效可行。

Local Smooth Inversion of 3D Gravity Gradient

Aiming at the low resolution problem of smooth inversion in gravity exploration, the authors proposed a local smooth constrained three-dimensional inversion algorithm based on certain prior information such as the depth of geological bodies and stratum inclination, and a storage method of roughness matrix in smooth inversion. By this method the computer’s calculation memory can be reduced through storing the M×N dimension roughness matrix as M×2 dimension, and when the roughness matrix is multiplied by other matrices in this storage mode, the position information stored in the roughness matrix can be read, and the calculating results can be obtained. The theoretical model and measured data were used to perform inversion trial calculations using the algorithm proposed in this study. It is shown that the result of the local smooth inversion algorithm is more accurate than the result of the global smooth inversion, and the algorithm is still stable, effective, and feasible under a given noise level in production.