PETGEM: A parallel code for 3D CSEM forward modeling using edge finite elements

Abstract

We present the capabilities and results of the Parallel Edge-based Tool for Geophysical Electromagnetic modeling (PETGEM), as well as the physical and numerical foundations upon which it has been developed.PETGEM is an open-source and distributed parallel Python code for fast and highly accurate modeling of 3D marine controlled-source electromagnetic (3D CSEM) problems. We employ the Nédélec Edge Finite Element Method (EFEM) which offers a good trade-off between accuracy and number of degrees of freedom, while naturally supporting unstructured tetrahedral meshes. We have particularised this new modeling tool to the 3D CSEM problem for infinitesimal point dipoles asumming arbitrarily isotropic media for lowfrequencies approximations. In order to avoid source-singularities, PETGEM solves the frequency-domain Maxwell's equations of the secondary electric field, and the primary electric field is calculated analytically for homogeneous background media. We assess the PETGEM accuracy using classical tests with known analytical solutions as well as recent published data of real life geological scenarios. This assessment proves that this new modeling tool reproduces expected accurate solutions in the former tests, and its flexibility on realistic 3D electromagnetic problems. Furthermore, an automatic mesh adaptation strategy for a given frequency and specific source position is presented. We also include a scalability study based on fundamental metrics for high-performance computing (HPC) architectures. contributed to the parallel implementation and its documentation.2 Josep de la Puente contributed to the math background and to the meshes generation. 3 José María Cela carried out simulations and its scalability analysis.

Land CSEM Simulations and Experimental Test Using Metallic Casing in a Geothermal Exploration Context: Vallès Basin (NE Spain) Case Study

“…The electric dipole transmitter and the receivers measuring EM responses are assumed to be on the Earth's surface and on the x-y plane at z = 0. As in our previous studies [8], [9], we consider the frequency-domain Maxwell's equations in a diffusive form, hence neglecting dis-placement currents. By assuming a time-harmonic dependence e −iωt , these equations can be expressed as…”

“…PETGEM has been introduced by [8], where the authors described the numerical formulation and computational details. More concretely, the authors explained the low-order Nédélec Finite Element Method (EFEM) as the numerical scheme for the solution of 3-D marine CSEM and its parallel implementation using Python and third-party libraries.…”

“…In the GEO-URBAN scope, we carried out several 3-D land CSEM experiments in the Vallès basin to study a surfaceto-surface CSEM profile and different source-receiver configurations using steel-cased wells to improve the sensitivity and quality of EM measurements. To compute synthetic EM responses, we have used the PETGEM code [8], which has proven to be a flexible, accurate, and efficient large-scale modeling tool on cutting-edge high-performance computing (HPC) architectures. Section II describes the PETGEM mathematical background and details about its computational implementation.…”

Parallel 3-D marine controlled-source electromagnetic modelling using high-order tetrahedral Nédélec elements

“…Secondly, large contrasts in conductivity produce jumps of the vertical electric field, causing difficulties for any discretisation method. This numerical instability is reflected in a large condition number of the linear system and often results in poor convergence for iterative Krylov solvers(Schwarzbach 2009;Key et al 2011).The Nédélec FE implementation of 2 nd and 3 rd order introduced in this paper generates a matrix A whose coefficients have a better conditioning number than those obtained by our preceding solutions based on Nédélec FE of 1 st order for the same problem(Castillo-Reyes et al 2017;Castillo-Reyes et al 2018).…”

“…of our previously published scheme in Castillo-Reyes et al (2018), where a first order method has been implemented and studied. Therefore, we investigate the advantages of our new highorder algorithm regarding convergence rate, accuracy, and computational cost.…”