Elastic Wavefield Modelling Using a Set of Coupled Second‐Order Wave Equations With the Vector Reflectivity of the P‐ and S‐Waves in Isotropic Media

ABSTRACT We have developed a new set of coupled second‐order elastic wave equations parameterized by velocity and vector reflectivity of P‐ and S‐waves for seismic wave propagation in isotropic media. These equations are contrasted with the conventional second‐order elastic wave equations, and we have demonstrated their mathematical equivalence through numerical experiments. The detailed analysis of the contribution of each term in the proposed equations is also presented. In addition, we have derived an extended version of the coupled second‐order wave equations that incorporates density effects. Seismic modelling with three geological models shows that density‐gradient effects influence wavefields and synthetic data only in amplitude. For the numerical solution of the proposed equations, we have employed a scheme based on the Lie product formula, in which the time‐evolution operator of the analytical solution is expressed as a product of exponential matrices, with each exponential term approximated by its Taylor series expansion.