## Dealing with uncertainty

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Symo_5
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Joined: Mon Jul 13, 2015 1:56 am

### Dealing with uncertainty

Greetings,

I am interested in the approaches to dealing with uncertainty in the velocity profiles generated by inverting in dinver. One approach used by my colleges is to visualise all the model runs with a misfit within 10% of the minimum misfit model while regarding the model with the lowest misfit as the best model.

However given the non-uniqueness of models fitting measured dispersion/ autocorrelation/ ellipticity curves is choosing a best model as a single answer with an arbitrary number like 10% used essentially as error bars the best approach? Although I understand that there is no general theory for characterising uncertainty in non-linear systems are there any technique for describing the output of model probabilistically?

Thanks kindly

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### Re: Dealing with uncertainty

Hi,

The "best" approach would be importance sampling proposed among others by Sambridge, 1999b (GJI). However, our many tries to apply such approach drove to unsatisfactory results. The probability density function is approximated on the NA grid cells and computed from the misfit. The full covariance matrix of the data must be known as well as the "true" degrees of freedom in the model parameterization. In most practical cases, for both points, we can just propose a best guess of these values. From our experience, the values drastically influence the final statistical results. So from a theoretical speaking better approach, we do not get less subjective results.

Just a note, any statistical analysis made on the model ensemble generated by the basic NA inversion is false or biased. According to user tuning parameters (e.g. number of iterations), the density of models around the best one may be different. If you run the inversion for high number of iterations, you will decrease the dispersion around the mean.

One of the option I prefer is to run the inversion with the "minimum misfit" option (in target panel). For instance, select a minimum of 1, NA will generate models with a uniform distribution (alas in the parameter space would have been better in the data space) inside one standard deviation (all models with a misfit equal to 1). The envelope of the model ensemble gives you a possible range for Vs profiles given an uncertainty in the data space.