Characteristic reflection wave-equation traveltime inversion using full gradient

With the advancement of oil and gas exploration into deepwater and deep formations, constructing accurate velocity models from reflection wave data has become essential for seismic imaging. The wave-equation-based reflection traveltime inversion (RTI) method typically decomposes the subsurface model into a smooth background velocity and high-wavenumber reflectors. In the Born modeling framework, both components jointly govern the generation of primary reflections. Conventional reflection-based inversion strategies often employ an alternating updating scheme to iteratively refine the background velocity and reflectivity. However, since reflectors are typically derived from migrated images that are themselves dependent on the current velocity model, this alternation can lead to inconsistencies between the updated reflectors and background velocity. In this paper, we propose a full-gradient RTI method based on the characteristic reflection wavefield (CRW). By using structural constraints from the characteristic reflectors and the imaging invariance of small-offset data, we derive the full gradient of the objective function with respect to the background velocity. The CRW enables robust measurement of traveltime shift and facilitates the construction of accurate adjoint source. The new gradient formulation comprises two key terms: A conventional reflection-based gradient term and a novel velocity-reflectivity coupling term. Numerical experiments demonstrate that the proposed full-gradient method effectively mitigates the coupling artifacts between the background velocity and reflectors during gradient computation, leading to improved gradient directions and significantly enhanced inversion convergence.