3-D Full-Time TEM Modeling Using Shift-and-Invert Krylov Subspace Method

The 3-D time-domain electromagnetic (TEM) modeling is computationally expensive. Shift-and-invert (SAI) Krylov subspace technique has proved efficient for the modeling of OFF-time TEM data. However, the ON-time data, which also involves useful Earth conductivity information, have not been well treated. In this article, we extend the SAI Krylov subspace method to deal with the ON-time data and obtain a complete algorithm for modeling of the full-time data. To deal with the ON-time problem, while retaining the whole framework of an SAI-style method, we have developed a new time integration method, based on the exponential trapezoidal rule, to help discrete the integral terms into matrix exponential function. Next, the solution of this matrix exponential function is obtained by constructing a new type of SAI Krylov subspaces. Numerical results for typical transmitting waveforms, such as half-sine, versatile-time-domain-electromagnetic (VTEM), and MULTIPULSE, demonstrate that the novel algorithm is accuracy for full-time TEM modeling.