位场的footprint分析及footprint-FFT快速正演方法

doi:10.11720/wtyht.2025.2424

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Abstract

Conventional inversion and forward modeling of large-scale potential field data from gravity and magnetic exploration, demanding high computer performance, exhibit low efficiency. Hence, this study defined a footprint determination method for potential fields, analyzed the influencing factors, and innovatively proposed a footprint-FFT strategy for forward modeling of potential fields. The footprint-FFT algorithm improved the forward modeling process from three aspects: (1) Kernel matrices were calculated based on the potential field-derived properties, significantly reducing their size; (2) A footprint concept for potential fields was introduced and defined, decoupling data scales from kernel matrix sizes, thus improving the kernel matrix computing efficiency and reducing the hardware cost; (3) Based on the above, the computing area was divided into subspaces, and the footprint-FFT strategy was first proposed for the batch computing of potential fields in subspaces, accelerating the forward modeling process. By reducing the computational complexity and storage of the kernel matrix, the method proposed in this study significantly improved the operational speed while ensuring computational accuracy. This method enabled the fast forward modeling of potential fields with more than 1 billion grids on a laptop computer within a few minutes. Theoretical examples demonstrate that this method has high efficiency and moderate requirements for computer configuration, manifesting considerable potential in the forward modeling and inversion of large-scale potential field data.

Key words： kernel matrix footprint FFT potential field forward modeling

Received: 13 October 2023 Published: 26 February 2025

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	Si-Yuan SUN
	Xiu-He GAO
	Xue-Feng CAO

Cite this article:

Si-Yuan SUN,Xiu-He GAO,Xue-Feng CAO. Footprint analysis and footprint-FFT-based fast forward modeling of potential fields[J]. Geophysical and Geochemical Exploration, 2025, 49(1): 63-72.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2025.2424 OR https://www.wutanyuhuatan.com/EN/Y2025/V49/I1/63

The equivalent diagram for footprint of potential field

The relationship between radiuses of footprint and calculation

Curves of contributions for fields with calculation radius
(color dots represent radius of footprint for different fields)

Footprint radius of V_z and V_xx varies with (a) depth of region, (b) observation height, and (c) grid dimension

The Schematic of footprint-FFT method

The forward modeling results of rectangular anomalies
a—gravity field;b—magnetic field in perpendicular magnetization mode;c—magnetic field in incline magnetization mode

The absolute errors between our method and analytical solution
a—gravity field;b—magnetic field in perpendicular magnetization mode;c—in incline magnetization mode

Depth variations of basement for Bishop complex model

Variations of magnetic susceptibility for basement of Bishop model

The forward modeling results of Bishop model for (a) gravity field and (b) magnetic field

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