## 9 Discussion  
Very often rock physics modeling and formation evaluation are treated as independent tasks. This is attributed to several causes: lack of communication between petrophysicists and seismic analysts (organizational silos), insistence on using simple linear or quasilinear models in well-log interpretation, and lack of core and fluid samples to provide calibrated rock matrix and fluid properties, salinity, critical porosity, Archie's parameters, etc.  
The joint inversion algorithm customized here utilizes an iterative global optimization machine (Appendix A). A particular type of simulated annealing is designed enabling simultaneous recovery of global and local model parameters and their associated uncertainties (Appendix B). The iteration number in VFSA has the same effect as regularization in other well-known inversion algorithms including Thikhonov regularization and singular value decomposition [24,25]. To emphasize the main disadvantages of the proposed workflow, we should confirm that the VFSA optimization is relatively slow and computing cost is high. To overcome this issue, one should employ multiphysics models to rapidly simulate well-log responses.  
We observe that simulated well-log responses match very well with true well logs (Figure 9). We also find that resistivity is the best resolved well-log response. Sonic slowness logs (DTCO and DTSM) are reasonably recovered but not as good as resistivity. Density is well recovered in the oil column and transition zone, but inverted density has a negative shift from true density in the water leg. The same shifts, but positive and milder, are also observed in DTCO and DTSM logs leading to underestimating water saturation in the water leg (Figure 12). Total porosity is the best resolved parameter. Intergranular porosity and microporosity are the next resolved parameters. Water saturation is reasonably recovered, but not as well as other properties, especially in the water leg as explained above. Salinity is the best resolved global parameter. Other global parameters are recovered but not as well as salinity, especially matrix properties (Figure 11).  
It is worth noting that the accuracy and resolution of the inverted petrophysical properties depend on the tools' depth of investigation, tools' vertical resolution, reservoir thickness, and the invasion profile in the formation. To account for these concerns, one needs to include detailed modeling of the resistivity, density, and sonic tools, and a realis  
Figure 13: Histograms of true well-log responses and their inverted values.  
tic invasion profile. In this work, we ignore the invasion profile by assuming negligible or complete invaded zone. We anticipate that our inversion workflow works best for relatively thick sandstone formations. While the stochastic component of the proposed inversion workflow is supposed to recover high-resolution petrophysical properties, it is recommended to consider detailed modeling of well-logging tools to accurately simulate shoulder-bed effects for laminated and thin bed sandstones. We further assume the formation of interest is a sandstone with mineralogy remaining constant in reservoir interval. That means a single matrix density properly represents the entire interval. If it is not the case, one may want to divide reservoir interval into several isolithologic units and apply the inversion workflow independently for each unit. The other alternative is to use gamma ray (GR), photoelectric (PEF), and neutron porosity well logs to help differentiate lithologic units. In the ideal case, our workflow can be extended to invert for volumetric fraction of minerals together with pore type, porosity, and fluid saturations.