Fresnel rays and resolution of tomographic imaging

Ray-theoretic travel-time tomography assumes an infinite signal bandwidth. When this condition is not met, energy propagates from source to receiver along Fresnel rays of finite cross-section, instead of infinitely thin mathematical rays. We use approximate analytical solutions of the weak scattering problem and numerical modelling of the full wave equation to discuss the resolution of bandlimited records. The setting of the numerical simulations is illustrative of a cross-well seismic experiment. We show that bandlimited travel-time data suffer an unexpected loss of resolution just along the mathematical ray. Nevertheless, this loss can be fully recovered including signal amplitude in an inversion procedure. We also discuss the problem of time picking, and show that, to be consistent with the weak scattering assumption, arrival time must be estimated at the signal peak.