A fast 3D gravity forward algorithm based on circular convolution

Xianzhe Yin

doi:10.1016/j.cageo.2023.105309

2023-03-01

PRE

DOI：10.1016/j.cageo.2023.105309

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摘要

En 中文

The dominant approach for calculating the gravity field from density sources is discretizing the density source into a collection of rectangular prisms with a regular grid distribution. In the case of an enormous number of model cells for large-scale data, however, the efficiency and storage requirements for calculation are usually confronted with challenges. In this paper, we propose an improved spatial domain convolutional forward al-gorithm for 3D fast and accurate gravity modeling. Compared with previous discrete-convolution-based algo-rithms, our approach inherits converting discrete convolution operations into frequency-domain dot products for an efficient forward process and features two improvements. (1) Generating the circular gravity kernel sensitivity matrix directly by padding the edges of the measurement grid and the model grid, which is based on the translational equivalence property of the potential field, leads the forwarding implementation process more concise. In previous methods, the construction of the circular kernel matrix is achieved by circular shifts of the original matrix only from the mathematical perspective, so we provide an alternative option, omitting matrices transformation. (2) The approach enables more flexible position relationships between the observed points and the model by introducing the distance vector between them, making the approach more practical and requiring less storage space. The accuracy and speed of our algorithm are comparable to the analytical solution and fre-quency domain methods, respectively. The presented algorithm efficacy and practicality are demonstrated by comparing it with the analytical formulation and the 3D traditional frequency domain method for synthetic models, as well as a real example for seawater correction. Our analysis indicates that the new algorithm is also applicable to fast-forward modeling for the magnetic field.

Keyword:

Geopotential theory

Circular convolution

Numerical solution

Gravity anomalies