The efficient hybrid kinematic-dynamic technique for finite-difference (FD) computation and storing the seismic wavefields is presented. At every time step of the FD scheme computations are done only in the moving window, around the first-arrival wave front that is consistent with the dominant wavelength. The specific feature of the proposed method is that all computational arrays: velocity, density, particle velocities e.t.c are stored in the original first-arrival traveltimes increasing order. The presented fashion allows us to obtain significant reduction in memory requirements and CPU time for first-arrival waveform computations. The considered approach allows one to store the wavefield in the window at every time step. That is very useful for constructing gradients for wave-equation based seismic data inversion methods, such as full waveform inversion, reverse time migration, wave equation tomography and other. The proposed forward modelling modelling method is illustrated by numerical examples
