Vol.:(0123456789) 1 3 Modeling Earth Systems and Environment (2021) 7:117–123 https://doi.org/10.1007/s40808-020-00898-4 ORIGINAL ARTICLE Direct current electrical resistivity forward modeling using comsol multiphysics Oluseun A. Sanuade 1  · Joel O. Amosun 2  · Tokunbo S. Fagbemigun 2  · Ajibola R. Oyebamiji 3  · Kehinde D. Oyeyemi 4 Received: 9 May 2020 / Accepted: 16 July 2020 / Published online: 22 July 2020 © Springer Nature Switzerland AG 2020 Abstract Forward modeling of direct current (DC) resistivity is very important for the inversion of the resistivity data to obtain the true resistivity of the subsurface. In this study, we demonstrated fnite-element forward modeling of DC resistivity method with point electric source using COMSOL Multiphysics. We employed the AC/DC module in COMSOL which often provides comparatively easy implementation of models and permits exterior boundaries to be placed at infnity, a boundary condition often experienced in most geophysical problems. The validity and efectiveness of the results of numerical simulation using COMSOL Multiphysics were evaluated by comparing the output of the numerical simulations with the calculated analytic solutions. The result reveals that the numerical simulation is in agreement with the analytic solution. This study shows that COMSOL Multiphysics can be used to simulate the distribution of electrical potentials of point source in 3D space in real life and the information from this study can be used for further studies, such as DC resistivity inversions. Keywords Forward modeling · COMSOL · resistivity · Simulation List of symbols ρ a Apparent resistivity ∆V Diference in electrical potential σ Electrical conductivity n Normal to the surface σ 2 Anomaly conductivity V Electrical potential E Error analysis G Geometrical factor I Current injected I o Current intensity σ 1 Electric background conductivity V ana Analytical potential r Radius x, y and z Points Introduction The geophysical surveys involving the use of DC resistivity methods are used to evaluate the electrical resistivity distri- bution in the subsurface usually by taking measurements on the ground surface. The measurements of the electrical resis- tivity could in turn be used to determine the true resistivity of the subsurface. The DC resistivity techniques have been used over the years in groundwater exploration (Gautam and Biswas 2016; Oyeyemi et al. 2018a, b), engineering investi- gations (Oladunjoye et al. 2017; Oyeyemi et al. 2017, 2020), mineral exploration (Zhang et al. 2015; Sanuade et al. 2018), and environmental studies (Rosales et al. 2012; Akinola et al. 2018; Olaojo et al. 2018; Olaseeni et al. 2018). How- ever, to obtain the electrical resistivity image that would be a representation of the subsurface, the electric potential data that are measured on the feld must be inverted, and forward modeling is an important step for any inversion algorithms to be used (Gao et al. 2020). Forward modeling is very important in electrical pros- pecting method to understand the subsurface distribution of structures and anomalies (Wang et al. 2011; Butler and Sinha 2012; Song et al. 2017; Udosen and George 2018; Gao et al. 2020). Forward modeling is necessary in geophysics, as it allows model parameters to be adjustable so as to ft observations. This process is part of routine that is usually * Tokunbo S. Fagbemigun tsfagbemigun@gmail.com 1 Boone Pickens School of Geology, Oklahoma State University, Stillwater, OK, USA 2 Department of Geophysics, Federal University Oye Ekiti, Oye-Ekiti, Nigeria 3 Department of Geology, Federal University Oye Ekiti, Oye-Ekiti, Nigeria 4 Department of Physics, Covenant University, Ota, Nigeria