This tutorial endeavours to lay out the basic scheme using the adjoint state method for setting up the basic equations for inversion of acoustic, elastic or electromagnetic data. The basic scheme is simple and relies on three basic ingredients consisting of a forward modelling package, the definition of a misfit norm and a gradient descent method. The adjoint state method will be presented in its continuous and discrete forms. The continuous adjoint state method will be developed for the full elastic equations in the time domain, while the discrete adjoint state method will be developed in the frequency domain.
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