Analytical and numerical analysis of tomographic resolution with band‐limited signals

Abstract

We investigate the resolution of band‐limited seismic signals using analytical arguments, based on the Rytov approximation of the single scattering problem and numerical modeling of the full wave equation. The experimental framework is seismic transmission tomography. Contrary to intuition, Rytov's theory predicts that time delays carry only limited information about the velocity of the medium along the shortest path (mathematical ray);, the information loss being more severe in 3D than in 2D geometries. We show that signal amplitude provides the information missing in time delay, and we argue that a complete imaging should invert both delays and amplitudes. We also address the question of picking time delays and show that this should be done on the signal peak when using the Rytov approximation for data inversion. Finally, we test the case of extended velocity perturbations and we show that the Rytov approximation handles fairly well a thin, high‐velocity layer including both source and receiver, while its validity is more critical with low‐velocity layers.