A modified parabolic equation for adaptive monotone difference schemes based on equal-arclength mesh, applied to the linear convection equation, is derived and its convergence analysis shows that solutions of the modified equation approach a discontinuous (piecewise smooth) solution of the linear convection equation at order one rate in the L1-norm. It is well known that solutions of the monoto...

Beside the complexities and not readily practical applications resulting from full Zoeppritz equation, seismic amplitude reflection does give enough information beyond critical angle. Consequently, there are breakdown of equation approximations at angle incidence (Shuey’s approximation). More so, validity is only for slight contrast in elastic parameters across formations small assumed. In an a...