Inverse modelling for parameter estimation and experiment design

Inverse modelling forced itself on the attention of scientists in the 1960s with the advent of satellites and other revelatory technologies, despite their putative ill-posedness, when it became clear that estimation of parameters of a system not in themselves directly observed but extractable from their signatures in measured data, constituted an ineluctable problem of modern society. This paper begins by formulating the basic statement of inverse problems which have a generic form and leads through philosophical and analytical approaches to their possible solutions that are inherently non-unique. Finally, an example is provided for inverse modelling of the shear wave velocity structure of the crust beneath the ancient granites around Hyderabad from an analysis of reverberations caused by it that appear in the early part of broadband seismograms.