Moving-footprint-based large-scale model decomposition method for forward modeling of gravity and gravity gradient anomalies
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摘要: 重力及其梯度异常正演计算效率决定了反演的可行性,也是高效构建足量、多样深度学习样本数据的基础。为了进一步提高重力及其梯度异常正演的计算速度,受航空电磁领域"Moving-footprint"快速正演技术的启发,本文在基于网格点几何格架函数空间域快速正演的基础上,提出了一种"Moving-footprint"大尺度模型分解的重力及其梯度异常正演计算方法。此方法在地下半空间内选择观测点正下方一定有效范围的子空间,该观测点异常近似为其对应子空间内长方体单元的异常和,而忽略子空间外长方体单元产生的异常;当观测点移动,其对应的子空间随之移动,从而可以将地下半空间长方体模型进行大尺度模型分解,为每一个计算点所对应的子空间进行正演计算。模型实验表明,在256x256x15个长方体模型的地下半空间内选取32x32x15的子空间进行计算,重力异常及部分梯度异常的相对平均误差小于10%,计算速度提高19倍;文中方法针对1024x1024x15个长方体模型计算时间约为32min,相比已有算法中存在的超常规计算量的瓶颈问题具有显著的计算优势。
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关键词:
- 重力异常 /
- Moving-footprint /
- 快速正演 /
- 模型分解
Abstract: The computational efficiency of the forward modeling for gravity and gravity gradient anomalies determines the feasibility of inverse modeling. It also forms the basis for the efficient building of sufficient and diverse deep learning sample data. Inspired by the application of moving-footprint—a fast forward modeling method in the aerospace electromagnetic field and based on the fast space-domain forward modeling of geometric lattice functions of grid points, the authors proposed a computation method for the forward modeling of gravity and gravity gradient anomalies by applying ”moving-footprint“, aiming to further improve the speed of the forward calculation for gravity and gravity gradient anomalies. Specifically, this method selects the subspace in a certain effective range directly below an observation point in the underground half-space. The observation point anomaly approximates the total anomalies of the cuboid units in the corresponding subspace while ignoring the anomalies produced by the cuboid units outside the subspace. When the observation point moves, the corresponding subspace moves accordingly. Therefore, the large-scale underground half-space cuboid model can be decomposed into the subspace corresponding to each calculation point for the forward calculation. As shown by the results of a model test, when 32x32x15 subspace was selected in the underground half-space of a 256x256x15 rectangular parallelepiped model for calculation, the relative average error of gravity anomalies and partial gradient anomalies was less than 10% and the calculation speed was increased by 19 times. Moreover, the calculation time of 1024x1024x15 rectangular parallelepiped model is approximately 32 minutes. Compared with the existing algorithms with a bottleneck in the ultra-conventional calculations, the method proposed in this study has significant advantages regarding computation.-
Key words:
- gravity anomaly /
- moving-footprint /
- fast forward modeling /
- model decomposition
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