Seismic Inversion tools designed to estimate impedance have been available to Geophysicists for over twenty years. Most of the available methods are based on minimising the difference between the seismic trace and the forward convolution of the solution with the estimated wavelet. Whether generalised linear inversion, sparse spike or simulated annealing, all the algorithms work on this basic principle of minimisation. Methods based on minimisation are commonly referred to as “deterministic”.
Seismic data is bandlimited. In particular, it does not contain low frequencies and therefore absolute impedances cannot be recovered directly from the seismic trace. All inversion schemes with an absolute impedance output require a low frequency model or constraint. The low frequency scalar is usually obtained from interpolation of well data, stacking velocities or a combination of these. After inversion the low frequency model is embedded in the deterministic inversion. Artefacts in the low frequency model manifest themselves as equivalent artefacts in the deterministic inversion. An example from Francis and Syed (2001) is shown in Figure 1.