Statistical and physical constraints in geophysical modeling.

@inproceedings{MosegaardGM2014,
 abstract = { There is some truth in a comment by Ernest Rutherford, the British chemist who laid the groundwork for the development of nuclear physics: "If your experiment needs statistics, you ought to have done a better experiment"! However, there is no doubt that in geophysics our data are often so sparse, so insufficient, so inaccurate, and so inconsistent that some statistical constraints - e.g., Least Squares - are needed to obtain a reasonable model of the Earth. Least Squares dominates geophysical modeling today, and it is an accepted technique in, for example, linear regression, signal processing, and curve fitting. It is build on assumptions of Gaussian statistics, and it is widely used to provide missing information in the many cases where data are insufficient to compute a unique solution. We shall see how the use of Least Squares influences current Earth models, often with poor results.
After this, we shall look at some recent work where Gaussian assumptions are replaced by more complex statistics, based on empirical data. This is done through an application of Bayes Rule where data are combined with "prior information" derived from observations of real Earth structure. Finally, we will explore the perspectives for supplementing statistical assumptions with constraints based purely on physics. In general, when Earth models are computed, a number of physical properties of the Earth are not involved in the modeling, and each of these properties may potentially provide constraints to help resolving the ambiguity in geophysical data. },
 author = { Mosegaard, Klaus AND Cordua, Knud Skou },
 booktitle = { Proc. 34th Gocad Meeting, Nancy },
 title = { Statistical and physical constraints in geophysical modeling. },
 year = { 2014 }
}