Velocity estimation by beam stack

Abstract

Imaging seismic data requires detailed knowledge of the propagation velocity of compressional waves in the subsurface. In conventional seismic processing, the interval velocity model is usually derived from stacking velocities. Stacking velocities are determined by measuring the coherency of the reflections along hyperbolic moveout trajectories in offset. This conventional method becomes inaccurate in geologically complex areas because the conversion of stacking velocities to interval velocities assumes a horizontally stratified medium and mild lateral variations in velocity. The tomographic velocity estimation proposed in this paper can be applied when there are dipping reflectors and strong lateral variations. The method is based on the measurements of moveouts by beam stacks. A beam stack measures local coherency of reflections along hyperbolic trajectories. Because it is a local operator, the beam stack can provide information on nonhyperbolic moveouts in the data. This information is more reliable than traveltimes of reflections picked directly from the data because many seismic traces are used for computing beam stacks. To estimate interval velocity, I iteratively search for the velocity model that best predicts the events in beam‐stacked data. My estimation method does not require a preliminary picking of the data because it directly maximizes the beam‐stack’s energy at the traveltimes and surface locations predicted by ray tracing. The advantage of this formulation is that detection of the events in the beam‐stacked data can be guided by the imposition of smoothness constraints on the velocity model. The optimization problem of maximizing beam‐stack energy is solved by a gradient algorithm. To compute the derivatives of the objective function with respect to the velocity model, I derive a linear operator that relates perturbations in velocity to the observed changes in the beam‐stack kinematics. The method has been successfully applied to a marine survey for estimating a low‐velocity anomaly. The estimated velocity function correctly predicts the nonhyperbolic moveouts in the data caused by the velocity anomaly.