A density log can be generated from a DT log using a relationship known as the "Chevron plot" or "Chevron method".
This relationship is based on the fact that the density of a rock is inversely proportional to the compressional and shear wave velocities of the rock.
You can follow these steps:
Measure the compressional and shear wave velocities from the DT log.
Calculate Vp/Vs.
Plot the Vp/Vs ratio against the compressional wave velocity on a graph, it is called "Chevron plot".
Use a set of reference points, known as "Chevron points," to establish a relationship between the Vp/Vs ratio and the density of the rock. These reference points can be obtained from laboratory measurements or from other sources such as well logs or core data.
Use this relationship to calculate the density of the rock for each point on the DT log.