Implicit finite-difference time-domain schemes for TDEM modeling in three dimensions

Abstract

Geophysical exploration methods that use controlled electromagnetic sources in time-domain are becoming ubiquitous because of their ease of deployment and data coverage capabilities. While these prospection methodologies have evolved significantly, most computational numerical modeling techniques have been developed in the frequency domain. Given this evolution, it is pertinent to ask whether some known advantages of implicit finite-difference modeling techniques, that are common among other disciplines, apply to the TDEM problem in geophysics. In order to explore the potential advantages of 3D time-domain modeling for TDEM we analyze the differences between two implicit finite-difference formulations: a single order Backward Euler scheme and a 2nd order Crank-Nicolson scheme. To validate our algorithms we tested them with existing analytical solutions for simple geometries for various electromagnetic sources. The results show an acceptable match of both numerical schemes to the analytical solutions and higher accuracy of the 2nd order discrete operator without significant difference in computing time.

Research and application of surface heat treatment for CO2 continuous laser ablation of polymeric methyl methacrylate materials

“…The initial condition was set to approximately 300 K at room temperature, the heat energy transmission at the surface of PMMA plate was the absorption of laser energy by the material surface, and there was no further heat energy transmission at the maximum ablation depth of the sheet. [21][22][23] The nite-difference time-domain method was used to study the heat transfer physical model and boundary conditions, 24,25 and establishing a grid Fourier number, the heat transfer physical model of CO 2 continuous laser ablation of PMMA material was established as follows: 26,27 (see Appendix A)…”

“…T(l,t) = T 0 , t = 0 The nite-difference time-domain method is a numerical method for solving differential equations, which can be used to solve ordinary differential equation and partial differential eqn (24) and (25). Therefore, the nite difference equations for the heat transfer physical model (20) and boundary conditions ( 17)- (19) were established as follows:…”

“…Aer organizing eqn (24), we could obtain: Aer establishing the grid Fourier number F0 1 ¼ kDt rcðDlÞ 2 , eqn (28) could be transformed into the following form: 25,26 Experiment for ultrasonic cleaning. In order to reduce the inuence of impurities such as droplets and dust on the observation results, the experimental acrylic sheets were placed in the ultrasonic cleaner and cleaned with puried water before laser ablation of PMMA materials and surface topography detection.…”

Fine Detection and Analysis of Hidden Karst in Wellsite with Quasi-Three-Dimensional TDEM Based on Lateral Constraint

“…This method is an artificial source secondary field method, which has advantages such as high data signal-tonoise ratio, no interference from the primary field, less affected by topographic relief in high-resistivity surrounding rock areas, strong ability to penetrate high-resistivity overburden, and large detection depth. In recent years, it has been favored by karst researchers and applied to karst detection [20][21][22]. Since TDEM observes the electromotive force data in the time domain, it is necessary to obtain the resistivity in the depth domain through inversion and then interpret related geological problems.…”