High Frequency Asymptotics and Velocity Estimation

Diierential semblance is unique amongst velocity inversion objectives in having well-deened and smooth high frequency asymptotics. A version appropriate for analysis of CMP gathers and layered models is particularly easy to analyse and economical for numerical experimentation. For model-consistent data, the DS objective measures the error in RMS velocity, weighted by the energy in the data-without requiring event-picking of any sort. Numerical experiments with synthetic data illustrate the theoretical properties. Tests with eld CMPs suggest that diierential semblance optimization is suuciently robust to function as an automatic alternative or enhancement to interactive velocity analysis in some circumstances.