Stability analysis of velocity imaging of 2D multilayered structures through inverse reflected rays

Abstract

Inverse reflected rays are used to image velocities and interfaces in 2D multilayered media. Their direction cosines are specified from the receiver and the source, related respectively to the traveltime gradients of the common-source and common-receiver gathers. Based on the geometry of an inverse ray through the lowest layer, the velocity near the reflection point is derived from either an exact solution or a transcendental equation. For the transcendental equation, the velocity bounds and the imaging stability depend on the interface dips, and the incident angles upon the interface above the reflection point. The velocity imaging is stable or quasi-stable when the reflection point is located between the intersections of the inverse rays and the upper interface. Application of the technique to a discontinuous normal fault and a forearc basin show that most of the velocity imaging is stable. However, if the inverse reflected rays pass through steep interfaces, the fault plane or highly inhomogeneous media, the imaging is usually unstable because multivalued and incorrect velocities are generated. I conclude that the method is fast and capable of imaging seismic sections with poor quality when compared with prestack depth migration and reflection tomography.