Chapter 2: A Conversation with Aldo Zollo
Can you describe your field briefly? Present a paradigmatic example of a model in your field, describing it in terms that are accessible to non-experts.
The basic model example I want to propose is the theory of seismic wave propagation which represents the Earth’s internal structure in terms of spatially variable elastic properties such as rigidity or density. Actually, it is better if seismologists use seismic velocities (e.g. the speed of primary P and S waves in Earth rock materials) and density as the parameters to describe the elastic behaviour of geological media. Depending on the observed parameter to reproduce, a model can show the generally nonlinear, mathematical relationship between data and model parameters. The travel times of seismic waves propagating from a deep earthquake source to the receivers deployed at the Earth’s surface are typically the physical quantities which seismologists measure and use to reconstruct elastic images of the Earth’s interior in terms of spatially varying seismic velocities. In this case, the model is the theory allowing us to compute the travel time of the seismic waves. This requires the estimation of the wave trajectory and knowledge about the local variation of the seismic velocity along the travel path. In a simple uniform velocity medium, wave trajectories are straight lines, so the model is a simple linear equation (T=rv, T is the travel time, r is the travelled distance and v is the seismic wave velocity). In a more complex geological medium, the seismic velocity can vary according to the different rock materials encompassed by seismic waves. In this case, the models become an integral equation (T=∫pathdsv(x,y,z), where ds is a small portion of the ray trajectory , v(x, y, z) is the velocity field) where the integral extends to the wave trajectory and the total travel time is obtained from the integral of partial travel times along a small portion of the wave path.
