I am trying to obtain the temperature (T) perturbation from shear wave velocity (Vs) perturbation. The intermediate variable is the density (rou) perturbation. As mentioned in the manual, delta_ln(rou) == epsilon * delta_ln(Vs) and delta_T == -1/alpha * delta_ln(rou). So, delta_T == -epsilon/alpha * delta_ln(Vs).
The default values of epsilon and alpha are 0.25 and 3e-5/K. If so, how can we define the delta_ln(Vs)? Does it means perturbation of the logarithmic(Vs)? Let’s suppose that the background Vs is 4.5 km/s and the regional Vs is ~0.3 km/s larger. Then, delta_ln(Vs) is log(0.3)/log(4.5), which is -0.8. So, the delta_T is 6666.7 K ( (0.25/3e-5)*0.8 K). Incredible!
What’s wrong with such a scaling law?