Massive database generation for 2.5D borehole electromagnetic measurements using refined isogeometric analysis

Abstract

Borehole resistivity measurements are routinely inverted in real-time during geosteering operations. The inversion process can be efficiently performed with the help of advanced artificial intelligence algorithms such as deep learning.These methods require a massive dataset that relates multiple Earth models with the corresponding borehole resistivity measurements. In here, we propose to use an advanced numerical method -refined isogeometric analysis (rIGA)to perform rapid and accurate 2.5D simulations and generate databases when considering arbitrary 2D Earth models.Numerical results show that we can generate a meaningful synthetic database composed of 100,000 Earth models with the corresponding measurements in 56 hours using a workstation equipped with two CPUs.

Refined isogeometric analysis of quadratic eigenvalue problems

“…We discretize our model problems using PetIGA-MF [54], which is a multifield extension of PetIGA [55] -a high-performance isogeometric analysis framework based on PETSc [56]. PetIGA-MF, utilized in many scientific and engineering applications (see, e.g., [3,7,[57][58][59][60][61][62]), uses different spaces for each field of interest and employs data management libraries to condense the data of multiple fields in a single object, thus simplifying the discretization construction.…”

“…We investigate the electromagnetic wave propagation eigenproblem. In particular, we consider a three-layer heterogeneous Earth model as a common case study in geosteering applications (see, e.g., [7,69]). This 2D Earth model is essential in studying the full 3D wave propagation eigenproblem in transversely isotropic media [70].…”

“…Refined isogeometric analysis (rIGA), introduced by Garcia et al [1], proved to be a successful extension of isogeometric analysis (IGA) [2] when using multifrontal direct solvers to approximate solutions to partial differential equations (c.f., [3][4][5][6][7]). rIGA preserves the desirable properties of maximum-continuity IGA discretizations while partitioning the computational domain into macroelements interconnected by low-continuity basis functions.…”

Performance of Refined Isogeometric Analysis in Solving Quadratic Eigenvalue Problems

“…We discretize our model problems using PetIGA-MF [53], which is a multifield extension of PetIGA [54] -a high-performance isogeometric analysis framework based on PETSc [55]. PetIGA-MF, utilized in many scientific and engineering applications (see, e.g., [3,7,[56][57][58][59][60][61]), uses different spaces for each field of interest and employs data management libraries to condense the data of multiple fields in a single object, thus simplifying the discretization construction.…”

“…We investigate the electromagnetic wave propagation eigenproblem. In particular, we consider a three-layer heterogeneous Earth model as a common case study in geosteering applications (see, e.g., [7,68]). This 2D Earth model is essential in studying the full 3D wave propagation eigenproblem in transversely isotropic media [69].…”