Finite-difference solution of the eikonal equation along expanding wavefronts

Abstract We show that a scheme to solve the 2-D eikonal equation by a finite-difference method can violate causality for moderate to large velocity contrasts (V 2 /V 1 2). As an alternative, we present a finite-difference scheme in which the solution region progresses outward from an 'expanding wavefront' rather than an 'expanding square,' and therefore honors causality. Our method appears to be stable and reasonably accurate for a variety of velocity models with moderate to large velocity contrasts. The penalty is a large increase in computational cost and programming effort.