1. A computer-implemented method of generating a seismic data set corresponding to a computer-generated modeling geometry for a subsurface region of interest, comprising: establishing a seismic exploration volume for the subsurface region of interest; determining the modeling geometry; propagating at least one wavefield through the seismic exploration volume utilizing the modeling geometry for initial conditions; preventing the accumulation of quasi-shear wave energy along an axis of symmetry of anisotropic regions located within the seismic exploration volume; ensuring positive stiffness coefficients in stress-strain relations in the at least one wavefield utilizing finite quasi-shear wave velocities thereby to stabilize the wavefield, and utilizing the stabilized wavefield to generate subsurface seismic images of the subsurface region of interest; wherein each of the foregoing steps is performed by a processor operating in conjunction with a data storage device or memory, the processor being configured to execute instructions to perform each of the foregoing steps, and the resulting subsurface images corresponding to the seismic data set are representative of pseudo acoustic quasi-P wave propagation configured to remain stable in variable tilt anisotropic media that is not limited by weak anisotropic conditions.