Three effective inverse Laplace transform algorithms for computing time domain electromagnetic responses
ABSTRACTThe inverse Laplace transform is one of the methods used to obtain time domain electromagnetic (EM) responses in geophysics. The Gaver Stehfest algorithm has so far been the most popular technique to compute the Laplace transform in the context of transient electromagnetics. However, the accuracy of the Gaver Stehfest algorithm, even when using double precision arithmetic, is relatively low at late times due to round off errors. To overcome this issue, we have applied variable precision arithmetic in the MATLAB computing environment to an implementation of the Gaver Stehfest algorithm. This approach has proved to be effective in terms of improving accuracy, but it is computationally expensive. In addition, the Gaver Stehfest algorithm is significantly problem dependent. Therefore, we have turned our attention to two other algorithms for computing inverse Laplace transforms, namely, the Euler and Talbot algorithms. Using as examples the responses for central loop, fixed loop, and horizontal electri.