Large numbers of earthquakes occur in subduction zones that are marked by dipping, narrow high seismic velocity slabs. The existence of these fast velocity slabs can cause serious earthquake mislocation problems that can bias estimates of seismic travel time residuals. This can affect the recovery of subducting slabs in tomography as well as introduce significant artifacts into lower mantle structure in tomography models. In order to better account for known subducting slabs, we performed a new P and S wave joint tomography inversion incorporating a three‐dimensional thermal model of subducting slabs in the starting model. In addition, velocity and source locations were inverted for simultaneously. Our new P and S models feature higher‐amplitude subducting slabs compared with previous global tomography results. The S to P heterogeneity ratio based on the new tomography model indicates that thermal elastic effects alone cannot explain all the heterogeneities in the lower mantle. Much of the observed abnormal S to P heterogeneity ratio can be explained by anelastic effects, the spin transition, and phase transitions of bridgmanite to post‐perovskite in the lower mantle. Plain Language Summary: Seismic tomography uses seismic travel time data to image deep earth velocity structure. However, it has been shown that the existence of subducting slabs can significantly bias the imaging result. In order to reduce this effect, we produced a new P and S wave tomography model that included theoretical three‐dimensional subducting slab structures in the starting model. The new model has higher‐amplitude subducting slabs compared with other models. Based on the new model, we conclude that it is difficult to explain the P and S velocity anomalies found in the deep mantle by temperature variations alone without invoking complex mineral phase transitions, large anelastic effects, or chemical variations. Key Points: We developed new P and S tomography models incorporating 3‐D subducting slabsMislocation effects caused by subducting slabs were reduced by inverting for velocity and source location simultaneouslyThe spin transition and the post‐perovskite phase transition may explain lower mantle heterogeneities [ABSTRACT FROM AUTHOR]