Student Webinar by Patrick Connolly

Noise, bias and geology – How to quantify uncertainties for probabilistic seismic inversion. 

Probabilistic inversion applications require uncertainties to be quantified. Within a Bayesian framework, uncertainties are not just to put errors bars on the results, they change the most-likely estimates, so taking care how uncertainties are specified is important. We need to both identify the potential causes of error but also model errors appropriately. We must recognise though, that uncertainty quantification is essentially subjective, so the results of probabilistic inversions are always interpretations.

No inversion applications account for all uncertainties; there are always ‘metaparameters’ whose uncertainty is ignored, so the first step is to prioritise potential causes of uncertainty to ensure we don’t miss an important source of error.

Uncertainties may often be spatially highly variable. One way to capture this is to specify errors in terms of reservoir rather than elastic properties. For example, low frequency models are a common cause of significant error.

Uncertainties may be quantified directly in terms of impedance variance, but a better approach is to tie the uncertainty to the geological model expressed in terms of prior distributions of facies proportions. This will better describe the spatial variability of the uncertainty.

Most uncertainty quantification assumes random Gaussian errors, but this may not always be appropriate. For example, we typically assign a signal-to-noise ratio to seismic data, but this model misses the most important causes of amplitude measurement errors which tend to result in local bias rather than random noise. The size of this error will depend on the local AVO gradient so again a model that accounts for AVO measurement errors will allow for the spatial variability.

In this talk I will discuss the importance of uncertainty quantification for seismic inversion, describe various sources of uncertainty and show how the corresponding errors can be modelled.