Fast Fourier transform of electromagnetic data for computationally expensive kernels

Abstract

SUMMARY 3-D controlled-source electromagnetic data are often computed directly in the domain of interest, either in the frequency domain or in the time domain. Computing it in one domain and transforming it via a Fourier transform to the other domain is a viable alternative. It requires the evaluation of many responses in the computational domain if standard Fourier transforms are used. This can make it prohibitively expensive if the kernel is time-consuming as is the case in 3-D electromagnetic modelling. The speed of modelling obtained through such a transform is defined by three key points: solver, method and implementation of the Fourier transform, and gridding. The faster the solver, the faster modelling will be. It is important that the solver is robust over a wide range of values (frequencies or times). The method should require as few kernel evaluations as possible while remaining robust. As the frequency and time ranges span many orders of magnitude, the required values are ideally equally spaced on a logarithmic scale. The proposed fast method uses either the digital linear filter method or the logarithmic fast Fourier transform together with a careful selection of evaluation points and interpolation. In frequency-to-time domain tests this methodology requires typically 15–20 frequencies to cover a wide range of offsets. The gridding should be frequency- or time-dependent, which is accomplished by making it a function of skin depth. Optimizing for the least number of required cells should be combined with optimizing for computational speed. Looking carefully at these points resulted in much smaller computation times with speedup factors of ten or more over previous methods. A computation in one domain followed by transformation can therefore be an alternative to computation in the other domain domain if the required evaluation points and the corresponding grids are carefully chosen.

Dynamics of Electric Polarization and Relaxation of Ions at Humid Calcite Surfaces

“…The dynamic responses of the potential and ion distribution are solved in the frequency domain (i.e., we calculate the response of the system to a sinusoidally oscillating field applied to the probe at different frequencies). To connect with the experiment, the frequency domain results are transformed to the time domain by using the Fourier transform methods provided in the open-source tool empymod − to determine the response to a step-function in voltage. After solving for the fields and charge distributions, the force on the probe was calculated by applying eq 7 from Sadeghi et al, which determines the force on the probe by integrating over the probe’s surface elements.…”

Modeling the connection between oil painting creation and university students’ inspiration in the context of “Internet+”

“…The continuous signal time domain is sampled to obtain a discrete practice signal, and the Fourier transform of the discrete time signal is called the discrete-time Fourier transform, which corresponds to a discrete non-periodic signal in the time domain, and the spectrum obtained is a continuous periodic signal [21]. The formula is as follows:…”