Computation of geophysical magnetic data for a buried 3‐D hexahedral prism using the Gauss–Legendre quadrature method

Abstract

A new method is presented for the 3‐D forward modelling of the magnetic effects (induced magnetization) of a hexahedral (trilinear) prism using the Gauss–Legendre quadrature method. The 3‐D forward modelling provides an improved application to geological problems. The magnetic effect has been evaluated via the summation of the effects of the point dipole that fills the volume. The 3‐D volume is divided into smaller prisms using an appropriate number of nodes. The algorithm is tested on two synthetic examples, and the results are compared against calculated data from a common program developed at the University of British Columbia–Geophysical Inversion Facility, with both tests showing positive results. The results of testing the algorithm against two synthetic slab models are also given. Finally, the program is applied to a field data set from Aynak‐Logar Valley region in Afghanistan. Using this program, complex 3‐D model bodies may be constructed from hexahedral prisms to facilitate the calculation of their magnetic anomalies and magnetic susceptibility. Interpretation of the results shows that 3‐D constructed models are successful in recovering the shape and location of the true model.

Structural architecture of the Middle Niger Basin, Nigeria based on aeromagnetic data: An example of a non-volcanic basin

“…Since a general understanding of sedimentary basin features can be achieved through the interpretation of aeromagnetic anomaly data ( Farhi et al., 2016 ; Mohamed et al., 2020 ), we have deployed geophysical data to provide further information needed to address the internal geometry of the basin. This is with the aim of locating structural features and estimating depths to magnetic sources by various processing techniques that have been established to aid the interpretation of magnetic data such as the estimation of source depth with the aid of source parameter imaging method ( Thurston and Smith 1997 ).…”

EMT simulation and effect of TTI anisotropic media in EMT signal

“…(See "Appendix 2") In practice, the integrand is seldom smooth. However, this issue is addressed in Gaussian quadrature by using weighting function, which results in removal of integrable singularities (Mahesh and Sucharitha 2018;Piqueras et al, 2019;Hassan et al 2020). Therefore, for higher accuracy calculation, we used the explicit Legendre-Gauss-Lobatto (LGL), Legendre-Gauss-Radau (LGR), Gauss-Lobatto (GLo) and Gauss-Legendre (GLe) quadrature techniques, which converge accurately to estimate the potential across two measuring points (−1,1).…”

Derivation of Five-Stage Implicit Runge-Kutta Method of Order 10 via Gauss-Legendre Quadrature for Ordinary Differential Equations

“…The resulting method is of order 10, ensuring outstanding accuracy, and its implicit nature ensures its robustness and stability. This implicit Runge-Kutta algorithm has the following form Deriving the method requires sophisticated numerical analysis techniques, such as continuous collocation and interpolation, as well as the properties of Gauss-Legendre quadrature formulas and implicit Runge-Kutta methods (Laurie, 2001;Press et al, 2007;Kulikov, 2009, Sahu & Saha Ray, 2016, Mohamed et al, 2020. Gauss-Legendre methods are founded on the quadrature formula with the highest possible order, 𝑝 = 2𝑆.…”