Does Accuracy Matter? the Role of Approximations in Geophysical Inverse Theory

Abstract:

In recent years, the computational techniques and resources available to geophysicists have advanced enormously: for many geophysical problems, physically-complete simulations are now feasible. Nevertheless, the computational costs remain daunting, encouraging the development of various hybrid inversion schemes that combine fully-accurate modelling techniques with those based upon various approximations. These are argued to give more accurate results than those based solely on approximate techniques, but at much lower cost than would be required if full simulations were conducted throughout.
While these arguments are superficially attractive, we do not believe that they have yet been fully justified within the framework of inverse theory. It is therefore important to investigate how modelling approximations propagate into the solutions to inverse problems. Understanding this will enable us to develop algorithms that optimally balance accuracy with efficiency, and will aid the interpretation of models produced by hybrid techniques.
We present results from mathematical and experimental analysis of geophysical inverse problems, focussing particularly on the framework of the least squares algorithm. We suggest that the efficacy of hybrid approaches depends significantly upon the particular approximations used, and on the character of their manifestation in the data. The interaction between approximations and regularisation is also important for both convergence and accuracy.