A computer-implemented method for identifying primary-wave, P-wave, and secondary-wave, S-wave, characteristics of an underground formation by separating P-wave and S-wave modes of seismic data generated by applying a seismic source to a subterranean region of a geological area, the method comprising: obtaining a wavefield comprising longitudinal and transverse particle velocity components observed by geophones deployed in the subterranean region; calculating stress components for each of the P-wave and the S-wave modes of seismic data associated with the subterranean region using a wavefield extrapolation engine; computing propagation vectors for the wavefield based on the longitudinal and transverse particle velocity components and the stress components for each of the P-wave and the S-wave modes of seismic data using the wavefield extrapolation engine, wherein computing propagation vectors for the wavefield comprises computing Poynting vectors of the wavefield based on a first-order elastic wavefield equation that uses the longitudinal or transverse particle velocity components as a first input variable and the P-wave or S-wave mode stress components as a second input variable; estimating an angle, θ, between the computed propagation vectors for the wavefield and wave motion vectors observed in the wavefield, wherein the wave motion vectors observed in the wavefield comprise components corresponding to the longitudinal and transverse particle velocity components observed by the geophones, wherein the angle between the computed propagation vectors and the wave motion vectors observed in the wavefield is defined by θ x t = cos − 1 M ⋅ V M V, wherein M is a Poynting vector and v is a wave motion vector comprising the longitudinal and transverse particle velocity components of the wavefield; extracting P-wave components of the wavefield based at least in part on the angle between the propagation vectors and the wave motion vectors using a wavefield separation engine; and extracting S-wave components of the wavefield based at least in part on the angle between the propagation vectors and the wave motion vectors using the wavefield separation engine. obtaining a wavefield comprising longitudinal and transverse particle velocity components observed by geophones deployed in the subterranean region; calculating stress components for each of the P-wave and the S-wave modes of seismic data associated with the subterranean region using a wavefield extrapolation engine; computing propagation vectors for the wavefield based on the longitudinal and transverse particle velocity components and the stress components for each of the P-wave and the S-wave modes of seismic data using the wavefield extrapolation engine, wherein computing propagation vectors for the wavefield comprises computing Poynting vectors of the wavefield based on a first-order elastic wavefield equation that uses the longitudinal or transverse particle velocity components as a first input variable and the P-wave or S-wave mode stress components as a second input variable; estimating an angle, θ, between the computed propagation vectors for the wavefield and wave motion vectors observed in the wavefield, wherein the wave motion vectors observed in the wavefield comprise components corresponding to the longitudinal and transverse particle velocity components observed by the geophones, wherein the angle between the computed propagation vectors and the wave motion vectors observed in the wavefield is defined by θ x t = cos − 1 M ⋅ V M V, wherein M is a Poynting vector and v is a wave motion vector comprising the longitudinal and transverse particle velocity components of the wavefield; extracting P-wave components of the wavefield based at least in part on the angle between the propagation vectors and the wave motion vectors using a wavefield separation engine; and extracting S-wave components of the wavefield based at least in part on the angle between the propagation vectors and the wave motion vectors using the wavefield separation engine.