Stats4Grads: Emulation applied to geophysical joint inversion
16 June 2010 14:15 in CM221
Combining information from several techniques rather than simply using one technique to probe the Earth affords the Earth scientist considerably greater insight into the structure he/she is investigating. This is because (albeit uncertain) relationships exist between different physical parameters associated with the Earth, for example density, seismic velocity and resistivity. Geophysicists in particular are therefore keen utilise methods to jointly constrain regions of the Earth based on measured datasets from various techniques. To date, the prefered strategy for carrying this out has been to use deterministic inversion methods. However, using these methods, it is non-trivial to fully include all uncertainity information, especially regarding the uncertainty associated with the inter-parameter physical relationship. MCMC methods have also been developed which in principle can deal properly with these uncertainities. However, modern datasets, are very large, and the models can contain more than 100,000 parameters. The forward simulation of large 3D models in geophysics therefore requires considerable time and computational expense; a single seismic forward modelling step can take of order a couple hours. Only a limited number of forward simulations can therefore be practicably carried out. For the purposes of properly handling the uncertainities associated with a large dataset, for example by an MCMC scheme, or even for the purposes of a standard deterministic inversion method, running the necessary forward simulation cycles is therefore not feasible. We apply emulation to a joint 1D problem and demonstrate that it is a very powerful Bayesian tool for quickly excluding large regions of implausible model space. At the same time it provides a very natural means to fully include all prior information regarding the uncertainties associated with the datasets, models, as well as the physical parameter relationships. We posit that emulation, so far not widely used among geophysicists, is an important methodological development, which has the potential to be applied widely among the Earth sciences.
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