Modified Parker's Method for Gravitational Forward and Inverse Modeling Using General Polyhedral Models

Abstract

Parker's method (Parker, 1973), initially introduced by the author for the rapid calculation of gravitational and magnetic anomalies, of 2D and 3D complexly layered models based on the FFT algorithm, is by no doubt one of the most widely applied algorithms in potential field data processing and interpretation (Nabighian, Ander, et al., 2005;. By raising the interface functions of a layered model to the E n th power and transforming into Fourier series using the FFT algorithm, potential anomalies on a horizontal plane above the layered model can be computed much more efficiently than using space-domain numerical integration techniques. The method has been proved particularly useful in solving forward problems such as gravimetric terrain correction and isostatic correction (

Modelling and computation of gravitational attraction, gradient tensors, rotational and horizontal invariants of Asteroid Bennu (101955), Itokawa (25143) and Eros (433) via 2D Non-Uniform FFT

“…Then, the 2D Gaussian quadrature rule is applied to the modelled triangular surfaces with NU-FFT ( Lee and Greengard, 2005;Greengard and Lee, 2006;Keiner et al, 2009;Wu, 2016;Barnett et al, 2019;Barnett, 2021). A combination of the Gaussian quadrature rule and NU-FFT was introduced by (Wu, 2021a).…”

“…where 𝑛𝑛 1 , … , 𝑛𝑛 1 , 𝑛𝑛 2 , … , 𝑛𝑛 2 and 𝑛𝑛 𝑁𝑁 𝐹𝐹 , … , 𝑛𝑛 𝑁𝑁 𝐹𝐹 are repeated by 𝐽𝐽 1 , 𝐽𝐽 2 and 𝐽𝐽 𝑁𝑁 𝐹𝐹 times, respectively. Hence vertical component of the gravitational vector (𝑔𝑔 𝑧𝑧 (𝑟𝑟)) can be written as (Wu, 2021a):…”

Gravity‐Derived Antarctic Crustal Thickness Based on the Gauss‐FFT Method

“…Therefore, deficiencies in numerical accuracy related to traditional FFT methods are properly solved, while superiority in efficiency well retained. Recently, Wu (2021) further extended Parker's method to general polyhedron models based on non‐uniform fast Fourier transform algorithms (Barnett et al., 2019). G. Zhao et al.…”

“…Compared with the study of G. Zhao et al (2020), a more simple and effective way would be a direct combination of Parker's formula, evaluated using new Fourier techniques, with Bott's iterative process (Bott, 1960), which we refer to as the Bott-Parker's formulas throughout the paper. This alternative approach has several advantages, including improved agreement between calculated and observed gravity values, avoiding of the low-pass filtering preprocessing required by the Parker-Oldenburg approach, and better adaptability for direct inversion of observation values on undulating surfaces without additional reduction-toplane operation (Wu, 2021).…”

“…Therefore, deficiencies in numerical accuracy related to traditional FFT methods are properly solved, while superiority in efficiency well retained. Recently, Wu (2021) further extended Parker's method to general polyhedron models based on non-uniform fast Fourier transform algorithms (Barnett et al, 2019). G. Zhao et al (2020) applied the Gauss-FFT method to reformulate the Parker-Oldenburg expression (Oldenburg, 1974;Parker, 1973) for mapping the Moho structure of the Tibetan Plateau.…”