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This work presents advancements in multiparameter elastic full-waveform inversion (FWI) with composite alternating misfit functions. Elastic FWI is a valuable tool for seismic imaging, capable of deriving Earth attributes directly from recorded waveforms, particularly in geologically complex settings. We propose a composite misfit function that combines a time-shift term and a shifted least-squares norm. The time-shift term ensures kinematic alignment of waveforms, while the shifted least-squares norm adjusts elastic parameters to match the amplitude variation with offset (AVO) response. A dynamic weighting scheme alternates between these terms during FWI iterations, eliminating the need for static hyperparameters. Field applications illustrate the method’s effectiveness. For the 2014 Chevron FWI benchmark test, the composite elastic FWI approach reduced imaging artifacts and enhanced subsurface detail compared to conventional least-squares misfit functions. A shallow-water field example from the North Sea demonstrated its capacity to reconstruct P-wave velocity and elastic properties while handling multiples and ghosts without significant preprocessing. Although the method requires substantial computational resources, its application to minimally processed field data shows promise for imaging and elastic property extraction in complex environments. Continued research and development are needed to refine the approach and address its computational demands.