FDTD3C—A FORTRAN program to model multi-component seismic waves for vertically heterogeneous attenuative media

Full-waveform seismic response of horizontally layered media can be calculated by semi-analytical methods. However, for gradient velocity and randomly heterogeneous structures the semi-analytical methods face difficulties. In such cases, numerical methods such as the finite-difference (FD) method have to be used. We develop an efficient numerical scheme to calculate plane-wave response of vertically heterogeneous attenuative media by applying Radon transform to the three-dimensional wave equation. The scheme employs fourth-order FD operator in space and second-order FD operator in time to solve the wave equation. In order to facilitate applicability of the scheme we introduce the FORTRAN code FDTD3C which implements the algorithm and provides multi-component response of the media to oblique incident P-, SV-, and SH-waves incoming from arbitrary azimuth. The calculated components are three particle velocity components in three Cartesian directions, and divergence and rotation of the wavefield. The code is extremely efficient and is capable of incorporating highly fluctuating subsurface velocity and attenuation models. This program is intended for all FD users who are concerned with full-waveform seismic modelling and inversion. Wide range of applicability of the code is demonstrated with a set of numerical examples.