We here establish basic inversion framework in a Bayesian context, with introduction of measures of data fit and model suitability. We introduce Bayes’ theorem and identify the conditional probability with posterior probability distribution for model parameters through a composite misfit combining the match between observations and simulations and assumptions about the nature of acceptable models. We discuss Monte Carlo techniques and the assessment of model resolution, leading into the formulation of the non-linear inversion process in terms of optimisation of a measure of misfit.

We here describe the process of waveform inversion for earthquake data, by reference to inversion for 3-D structure in seismic wavespeed and density in the eastern Mediterranean region using numerical simulation with the spectral element technique. Such waveform inversion needs to start from a good initial model, using low frequencies in the first stage. As the inversion proceeds higher frequencies and additional data can be to incorporated to achieve model refinement. We also examine the issues of practical resolution assessment, and validation of proposed models.

Current seismology depends on well-developed networks of instruments and a range of advances in both theoretical and computational developments. We provide a survey of the development of seismic recording, including the introduction of dense sets of portable instruments, so that major earthquakes are now captured by thousands of seismometers. We then discuss the way in which understanding of seismic waveforms has developed through the computation of synthetic seismograms and their exploitation in inversion. The last part of the chapter provides a description of the structure of the four Parts of the book