IMMI and geological complexity IMMI: the role of well calibration in the context of high geological complexity Sergio Romahn and Kris Innanen ABSTRACT Iterative modelling, migration and inversion (IMMI) aims to incorporate standard pro- cessing techniques into the process of full waveform inversion (FWI). IMMI proposes the use of any depth migration method to obtain the gradient, while FWI uses a two-way wave migration, commonly reverse time migration (RTM). IMMI uses well calibration to scale the gradient, instead of applying a line search to find the scalar or an approximation of the inverse Hessian matrix. We used a phase shift plus interpolation (PSPI) migration with a deconvolution imaging condition that works as a gain correction. We show the suitability of estimating the subsurface velocity model by applying IMMI’s approach using synthetic examples with increasingly geological complexity. We found consistently low errors in the well calibration location, even in the most complex settings. This suggests that the gradient obtained by applying PSPI migration points to the correct direction to minimize the objec- tive function, and that well calibration provides an optimal scale. This is promising in the context of reservoir characterization, where we may have many control wells. We found that IMMI satisfactorily performs in the presence of moderate lateral velocity changes. The results, for the scenario of strong lateral velocity changes, indicate that well calibration is a worthy option providing that the well is representative of the geology in the zone of interest. INTRODUCTION Lailly (1983) and Tarantola (1984) provided the mathematical basis for full waveform seismic inversion. They showed that FWI and migration are strongly linked, in what Mar- grave et al. (2010) call the fundamental theorem of FWI, which is summarized in Equation 1. δv(x, z )= λ∇ v φ k (x,z,w)= λ   s,r ω 2 ˆ Ψ s (x,z,ω)δ ˆ Ψ * r(s),k (x,z,ω)dω (1) Where δv(x, z ) is the velocity update, λ is a scalar constant, ∇ v is the gradient with respect to the velocity model v, φ k (x,z,w) is the objective function, w is angular fre- quency, ˆ Ψ s (x,z,ω) is a model of the source wavefield for source s propagated to all (x, z ), δ ˆ Ψ * r(s),k (x,z,ω)dω is the k th data residual for source s back propagated to all (x, z ), ∗ means complex conjugation. The residual δ ˆ Ψ * r(s),k (x,z,ω) is the difference between the observed data Ψ r and the modeled data Ψ r,k . The objective function measures the difference between the recorded data Φ and the modelled data Φ k at the k th iteration (Equation 2). CREWES Research Report — Volume 28 (2016) 1