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A reconstruction process featuring full parameterization of the three dimensional, time-harmonic equations of linear elasticity is developed and reconstructed property images are presented from simulation-based investigation. While interesting in its own right through the potential for increased adaptability of these reconstructive elastic imaging techniques, this study also presents a set of analysis tools used to study the poor convergence behavior found in the case of tissue like conditions (i.e. nearly incompressible materials). The choice of elastic properties for imaging in elastography research remains an open question at this point; the use of the stability and sensitivity-based analytical methods described here will help to predict and understand the value and reliability of different parameterizations of elasticity imaging. Additionally, though results indicate significant work needs to be done to achieve effective multiparameter reconstructive imaging, the methods detailed here offer the promise of increased flexibility and sophistication in elastographic imaging techniques.