An open-source full 3D electromagnetic modeler for 1D VTI media in Python']Python: empymod

The Python-code empymod computes the 3D electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal. The bottleneck in frequency-and time-domain calculations of electromagnetic responses derived in the wavenumber-frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain, the so-called Hankel and Fourier transforms. Three different Hankel transform methods (quadrature, quadrature-with-extrapolation [QWE], and filters) and four different Fourier transform methods (fast Fourier transform [FFT], FFTLog, QWE, and filters) are included in empymod, which allows us to compare these different methods in terms of speed and precision. The best transform in terms of speed and precision depends on the modeled frequencies. Published digital filters for the Hankel transform are very fast and precise for frequencies in the range of controlled-source electromagnetic data, but they fail in the frequency range of ground-penetrating radar. Conventional quadrature, on the other hand, is in comparison very slow but can model any frequency. Examples comparing empymod with analytical solutions and with existing electromagnetic modelers illustrate the capabilities of empymod.