ABSTRACT Accurate estimation of seismic velocity and density models is essential for subsurface imaging and characterisation. We propose a global optimisation framework to estimate non‐linked P‐wave velocity ( V p ) and density ( ρ ) for post‐stack seismic data, and V p , ρ and S‐wave velocity ( V s ) for pre‐stack data, by minimising the misfit between non‐corrected normal moveout (non‐NMO) observed and synthetic seismic gathers. We demonstrate that a non‐linear, underdetermined and complex problem can be addressed by introducing an additional constraint on one of the parameters, using non‐linear forward modelling combined with global optimisation algorithms. The synthetic seismic gathers are iteratively generated by randomly and simultaneously updating initial models. Updates are accepted on the basis of the simulated annealing method, a global optimisation technique that helps to prevent entrapment in local minima. Optimisation is performed by minimising an L2‐norm misfit function. For the pre‐stack case, the observed seismic data are a real gather. For the post‐stack case, the observed gather is formed from the full stacked seismic trace, taken as a near trace, and the reflectors are spread along moveout curves that are computed from the smoothed log of V p . A two‐parameter search ( V p , ρ ) is launched in the post‐stack case, whereas a three‐parameter search ( V p , ρ and V s ) is used when pre‐stack data are available, with both starting from smoothed initial models. To reduce the number of iterations by at least one order of magnitude and to increase computational efficiency, initial estimates of the V p and ρ models can first be obtained from the post‐stack process using well logs. Then, the full three‐parameter search is performed, starting with initially estimated models for V p , ρ and smoothed V s . The proposed methodologies offer an approach for estimating elastic properties and for overcoming the limitations of conventional seismic inversion. The approach eliminates reliance on regression techniques, which often oversimplify the complex, nonlinear relationships between seismic data and subsurface properties; avoids linearisation of the inversion process, which can introduce errors again due to the inherently nonlinear nature of geological properties; and bypasses the need for normal moveout (NMO) correction, which can cause amplitude stretching and distort critical amplitude information, because the algorithm utilises the moveout. By working with fully migrated 1D gathers, we assume a constant velocity across all offsets, which allows us to bypass full wave‐equation modelling while maintaining acceptable accuracy. Additionally, the framework supports the implementation of alternative global optimisation strategies.
Kalashnikova et al. (Thu,) studied this question.