Abstract: In this chapter, I discuss an alternative perspective on interpreting the results of joint and constrained inversions of geophysical data. Typically such inversions are performed based on inductive reasoning (i.e. we fit a limited set of observations and conclude that the resulting model is representative of the Earth). While this has seen many successes, it is less useful when, for example, the specified relationship between different physical parameters is violated in parts of the inversion domain. I argue that in these cases a hypothesis testing perspective can help to learn more about the properties of the Earth. I present joint and constrained inversion examples that show how we can use violations of the assumptions specified in the inversion to study the subsurface. In particular I focus on the combination of gravity and magnetic data with seismic constraints in the western United States. There I see that high velocity structures in the crust are associated with relatively low density anomalies, a possible indication of the presence of melt in a strong rock matrix. The concepts, however, can be applied to other types of data and other regions and offer an extra dimension of analysis to interpret the results of geophysical inversion algorithms.

We introduce the concepts of waveform correlations, and the way in which they can be exploited to extract information from seismograms.We show how correlation procedures can be used to determine time and phase delays. We then consider the closely related topic of transfer functions between aspects of the wavefield, and this leads into a discussion of the ways by which seismograms can be compared – a topic of importance in the comparison of observations and simulations. We also consider the nature of receiver functions and the correlation of teleseismic signals at a receiver to yield information on local structure.