Dinver:Parameterization
There is no unique way of defining a correct parameterization and there is currently no commonly accepted strategy to conduct an inversion. This document presents an example based on the same dispersion curve as in Dispersion curve inversion, revisited with various parameterizations.
Contents
A 3-layer model
From the 2-layer model described in Dispersion curve inversion:
- Add two layers for Vs profile by clicking once times on Add button in Shear velocity profile.
- Re-link Vp interface to Vs interface by selecting Vs1 in Linked to combo box.
Add a new run and start it. Misfit now drops far below 0.01, with a much better fit of the dispersion even at high frequency. The true profile is correctly retrieved. Vp is also well estimated because the dispersion curve contains absolutely no noise. For real cases, fitting the dispersion curve with a misfit below 5-10% is not frequent.
Do we recover Vs profile down to 100 m (and probably below, because parameterization was forced to 100 m) with a dispersion curve from 2 to 20 Hz (maximum wave length=318 m)? The uncertainty in the bottom part of the model is investigated in Uncertainty at depth.
A better profile for Vp at shallow depths could be obtained by adding a supplementary layer on Vp profile like on Vs profile. On one hand, a variation in Vp is not to exclude especially in superficial layers at the level of the water table in soft sediments. However we have no clues from the dispersion itself that such a layer can exist. On the other hand, the uncertainty of Vp close to the surface is likely to have some contributions in the uncertainty of Vs at depth. Hence playing with Vp parameterization might be of interest.
Vs only with constant Poisson's ratio
From a 3-layer parameterization, keep only one layer for Vp and Nu profiles.
- Fix the value for Poisson's ratio to the expected value.
- Fix also the value for Vp to any value. Profiles must all have at least one layer and we do not want to add a variable parameter for Vp. Vp profile will be over written once Vs profile is known.
Add a new run and start it. Misfit now drops far below 0.01, with a much better fit of the dispersion even at high frequency. The true profile is correctly retrieved. Vp is also well estimated because the
