Parameterization of density estimation in full waveform well-to-well tomography

Seismic full-waveform inversion (FWI) is a method for estimating mainly velocity structure in the subsurface. As wave propagation is influenced by elastic parameter Vp, Vs and density, it is necessary to include these parameters in the modeling and in the inversion (Virieux and Operto 2009). On the other hand, multi-parameter full waveform inversion is a challenging problem because parameters are coupled with each other, and the coupling effects prevent from the appropriate estimation of the elastic parameters. Especially, the estimation of density is of a very difficult exercise because plural elastic parameters including density increases the dimension of the solution space so that any minimization could be trapped in local minima. Therefore, density is usually estimated using an empirical formula such as Gardner's relationship (Gardner et al., 1974) or is fixed to a constant value. Almost all elastic FWI studies have neglected the influence of inverting density parameter because of its difficulty. Since the density parameter is directly included in elastic wave equation, it is necessary to see if it is possible to estimate density value exactly or not. Moreover, Gardner's relationship is an empirical equation and could not always show the exact relation between Vp and density, for example in media such as salt dome. Pre-salt exploration conducted in recent decades could accordingly be influences.The objective of this study is to investigate the feasibility of the estimation of density structure when inverting with the other elastic parameters and to see if density is separable from the other parameters. We perform 2D numerical simulations in order to see the most important factor in the inversion of density structure as well as Vp and Vs. We first apply a P-S separation scheme to obtain P and S wavefields to apply our waveform inversion scheme to estimate Vp and density distributions simultaneously. Then we similarly estimate, Vs and density distributions. We show the effect of the inversion strategies with different parameterization on the estimation of density structures.