Symplectic structure of wave-equation imaging: a path-integral approach based on the double-square-root equation

We carry out high-frequency analyses of Claerboutʹs double-square-root equation and its (numerical) solution procedures in heterogeneous media. We show that the double-square-root equation generates the adjoint of the single-scattering modelling operator upon substituting the leading term of the generalized Bremmer series for the background Green function. This adjoint operator yields the process of ‘wave-equation’ imaging. We finally decompose the wave-equation imaging process into common image point gathers in accordance with the characteristic strips in the wavefront set of the data.