Ask geoscientists, drillers, etc., and they will tell you, unsurprisingly, that the subsurface is modelled and drilled in Depth. However, whether the seismic is (two-way) Time or Depth indexed, seismic inversion products (impedances) are ubiquitously derived in Time, as convolution of an earth model with an appropriate wavelet (an essential step in any inversion) must be done in that domain where the wavelet can usually be assumed stationary. Put a different way, convolution is not easily or naturally represented in Depth, as the effective wavelet shortens or lengthens with varying subsurface velocity, one of the very quantities the seismic inversion attempts to determine. So in the case of Depth indexed seismic, first a Depth to Time conversion must take place. After the inversion is performed in Time, the Time indexed results are usually Time to Depth converted, for use in e.g. geomodeling workflows. Note that the various domain conversions are often concealed from the user. Whilst this approach is awkward (two domain conversions for Depth indexed seismic, a natural product of PSDM or FWI processing), it is so far acceptable for straightforward, impedance only seismic inversions. In this paper, we propose an alternative approach to seismic inversion that delivers the desired output impedance and other products directly in the depth domain, whilst acknowledging wavelet non-stationarity in depth and performing the seismic misfit analysis ‘on the fly’ in the Time domain