WAVE EQUATIONS

The general modeling implementation is based on a wave equation of the form  

$$a(x) \nabla b(x) \nabla^{T} u(x,t) - {{\partial}\over{\partial{t^2}}}u(x,t) = f(t)$$ (1)

u is an arbitrary wave field (scalar or vector); f is the force applied at a source location. $\nabla$ is a gradient and $\nabla^T$the divergence operator applied to the wavefield components. a and b are medium property fields (density, velocity or stiffnesses). Equation (1) can be rewritten as a sequence of first order partial differential equations. Numerical calculations typically use those on a staggered grid for improved accuracy.