Single-file codes in MATLAB for acoustic and elastic wave propagation in time domain using finite-differencen approximation(FDTD). We solve second-order wave equation in displacement formulation with generic collocated scheme, second order both in space and time, O(2,2). We also apply boundary conditions with exponential decay (Cerjan, 1985). Simple, made for beginners.
Only P waves propagate in acoustic medium. Compressional wave velocity Vp is used to parametrize the medium. Scalar constant-density wave equation is solved for pressure.
P and S waves propagate in elastic medium. Compressional Vp and shear Vs wave velocities and density are used as parameters. Derivatives of elastic parameters are neglected.
Vertical transverse-isotropy is typically observed in layered media. In this case waves propagate with different velocities in horizontal and vertical directions. Medium is parametrized by density and four elastic parameters in 2D and by five elastic parameters in 3D.