Abstract Owing to the lack of long-offset signals and effective low-frequency components, it is extremely difficult for classical full-waveform inversion (FWI) obtain long-wavelength components medium deep elastic parameter models. Considering ray theory, reflection traveltime tomography restricted by resolution, waveform (RWI) method wave equation, its practicability, has received greater atte...

This paper presents explicit formulae for multivariate Maclaurin-Lagrange M : Kn1×n2×...×nd → Kn1×n2×...×nd and Maclaurin-Newton P : Kn1×n2×...×nd → Kn1×n2×...×nd transformations with respect to points whose coordinates form geometric sequences. Moreover, efficient algorithms for these transformations are given. Both of them perform computations with a running time of O (∏d j=1 nj · log ∏d j=1 ...