Nonlinear inversion of electrical resistivity sounding data for multi-layered 1-D earth model using global particle swarm optimization (GPSO)

Kehinde D Oyeyemi; Ahzegbobor P Aizebeokhai; Chukwuemeka S Ukabam; Olusola T Kayode; Abayomi A Olaojo; Mohamed Metwaly

doi:10.1016/j.heliyon.2023.e16528

Nonlinear inversion of electrical resistivity sounding data for multi-layered 1-D earth model using global particle swarm optimization (GPSO)

Heliyon. 2023 May 23;9(6):e16528. doi: 10.1016/j.heliyon.2023.e16528. eCollection 2023 Jun.

Authors

Kehinde D Oyeyemi^{1

2}, Ahzegbobor P Aizebeokhai¹, Chukwuemeka S Ukabam¹, Olusola T Kayode¹, Abayomi A Olaojo³, Mohamed Metwaly⁴

Affiliations

¹ Applied Geophysics Programme, Department of Physics, Covenant University, Nigeria.
² Canadian Center for Raw Material Display Inc., Saskatchewan, Canada.
³ Department of Earth Sciences, Ajayi Crowther University, Oyo, Nigeria.
⁴ Department of Archaeology, College of Tourism and Archaeology, King Saud University, Riyadh, Saudi Arabia.

Abstract

Interpreting geophysical data requires solving nonlinear optimization problem(s) in inversion. Analytical methods such as least-square have some intrinsic limitations, which include slow convergence and dimensionality, making heuristic-based swarm intelligence a better alternative. Large-scale nonlinear optimization problems in inversion can be solved effectively using a technique within the swarm intelligence family called Particle Swarm Optimization (PSO). This study evaluates the inversion of geoelectrical resistivity data with global particle swarm optimization (GPSO). We attempted to invert field vertical electrical sounding data for a multi-layered 1-D earth model using the developed particle swarm optimization algorithm. The result of the PSO-interpreted VES data was compared with that of the least square inversion result from Winresist 1.0. According to the PSO-interpreted VES results, satisfactory solutions may be attained with a swarm of 200 or fewer particles, and convergence can be reached in fewer than 100 iterations. The GPSO inversion approach has a maximum capacity of 100 iterations, more than the least square inversion algorithm of the Winresist, which has a maximum capacity of 30 iterations. The misfit error of GPSO inversion is $6.14 \times 10^{- 7}$ , much lower than that of the least square inversion of 4.0. The GPSO inversion model has lower and upper limit values of the geoelectric layer parameters model to fit the true model better. The limitations of the developed PSO inversion scheme include a slower execution time of the inversion procedures than the least-square inversion. There is a need for a priori knowledge of the number of layers from borehole reports in the study area. The PSO inversion scheme, however, estimates inverted models closer to the true solutions with greater accuracy than the least-square inversion scheme.

Keywords: Electrical resistivity; Geophysical modelling; Inversion; PSO; Vertical electrical sounding.