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

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.