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- \( \ref{KWSINC} \): a package for
**arbitrary source and receiver positioning in finite-difference grids and seismic data resampling with Kaiser-windowed sinc functions .** - \( \ref{FDFDMATRIX3D} \) : a package for
**3D finite-difference frequency-domain seismic wave modeling**in the VTI visco-acoustic approximation.

In our codes, we first tabulate the values of the KWS function in the domain alpha in ]-0.5;+0.5], where alpha is the algebraic distance of the closest grid point from the source/receiver in a local coordinate system whose origin is the position of the source/receiver. This tabulation allows us to avoid recomputing the KWS coefficients for each source/receiver position each time we need to perform a wave simulation (for example, at each iteration of Full Waveform Inversion (FWI)). We also review how to process the free surface by mirroring the coefficients that are above the free surface with a sign -1. The algorithm is validated for different scenarios in a homogeneous half space against analytical solution. Our implementation rigorously follows the indexing convention defined by Hicks (2002). We also provide a code that subsample/oversample seismograms with KWS function and validate it with a numerical example. This can be useful when we want to store the values of the wavefields at the boundaries of the computational domain at the Nyquist limit before their recomputation backward in time during gradient computation during FWI application.

- G. J. Hicks, Arbitrary source and receiver positioning in finite-difference schemes using Kaiser windowed sinc functions, Geophysics, 67, 156--166, 2002.
- S. Operto, Seismic data resampling and source/receiver positioning in finite-difference simulatio with Kaiser-windowed sinc function (Hicks' method), WIND project, Technical report n 11, 2022 (provided as the documentation of the KWSinc package).

- H. Aghamiry, A. Gholami, L. Combe and S. Operto, Accurate 3D frequency-domain seismic wave modeling with the wavelength-adaptive 27-point finite-difference stencil: a tool for full waveform inversion,
*Geophysics*, https://doi.org/10.1190/geo2021-0606.1. - S. Operto, R. Brossier, L. Combe, L. Métivier, A. Ribodetti, and J. Virieux. Computationally-efficient visco-acoustic finite-difference frequency-domain seismic modeling in vertical transversely isotropic media with sparse direct solvers.
*Geophysics*, 79(5), 2014, https://doi.org/10.1190/geo2013-0478.1. - R. Brossier, V. Etienne, S. Operto, and J. Virieux.
**Frequency-domain numerical modelling of visco-acoustic waves based on finite-difference and finite-element discontinuous galerkin methods**. In D. W. Dissanayake, editor, Acoustic Waves, pages 125--158, SCIYO, 2010. - S. Operto, J. Virieux, P. Amestoy, J-Y. L'Excellent, L. Giraud, and H. Ben Hadj Ali, 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study,
*Geophysics*, 72(5):SM195--SM211, 2007, https://doi.org/10.1190/1.2759835.

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