Progress in Seismic Diffraction Theory – From Edge and Tip Waves to Multiple Reflections-transmissions with Diffractions

Seismic waves traveling in the subsurface can be described by two physically different processes: propagation inside layers with smoothly varying properties and reflection and transmission at internal reflectors, which are formed by parameter discontinuities. Evaluation of the multiple reflections-transmissions for complex subsurface geometries is not straightforward. The presence of diffracting edges and vertices limits the applicability of geometrical seismics. Reflections-transmissions in the Fresnel zones near the shadow boundaries of the ray tubes can be described as the sum of geometrical seismic waves and diffracted waves in the boundary-layer approximation. To describe the reflection-transmission in the caustic zones caused by interface curvatures, we introduced the tip-wave superposition method. This method explicitly represents the scattered wavefield as the superposition of events multiply reflected and transmitted in accordance with the wavecodes, which allows modeling of selected events independently. Each event is formed by the sequential action of the propagator matrices inside heterogeneous layers with effective reflection and transmission coefficients at curved interfaces. Each element of the matrix contains the tip waves diverging from a small interface element. Effective coefficients generalize plane-wave coefficients used in the conventional seismic modeling for curved reflectors, non-planar wavefronts and finite frequencies.