Multi-dimensional Fourier transform on an irregular grid is a useful tool for various seismic forward problems caused by complex media and wavefield distributions. Using a shape-function-based strategy, we develop four different algorithms for 1D and 2D non-uniform Fourier transforms, including two high-accuracy Fourier transforms (LSF-FT and QSF-FT) and two non-uniform fast Fourier transforms (LSF-NUFFT and QSF-NUFFT), respectively based on linear and quadratic shape functions. The main advantage of incorporating shape functions into the Fourier transform is that triangular elements can be used to mesh any complex wavefield distribution in the 2D case. These algorithms, therefore, can be used in conjunction with any irregular sampling strategies. The accuracy and efficiency of the four non-uniform Fourier transforms are investigated and compared by applying them in the frequency-domain seismic wave modeling. All algorithms are compared with exact solutions. Numerical tests show that the quadratic shape-function-based algorithms are more accurate than those based on linear shape function. Moreover, LSF-FT/QSF-FT exhibits higher accuracy but much slower calculation speed, while LSF-NUFFT/QSF-NUFFT is highly efficient but has lower accuracy at near-source points. In contrast, a combination of these algorithms by using QSF-FT at near-source points and LSF-NUFFT/QSF-NUFFT at others, achieves satisfactory efficiency and high accuracy at all points. Although our tests are restricted to seismic models, these improved non-uniform fast Fourier transform algorithms may also have potential applications in other geophysical problems, such as forward modeling in complex gravity and magnetic models.
Dynamically Modulating Plasmonic Field by Tuning the Spatial Frequency of Excitation Light
