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. geomodelling 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 seismic inversions.
In this paper we introduce a new, practical approach to directly obtaining Depth indexed seismic inversion products, both impedances and facies, independent of whether the seismic is Time or Depth indexed. The new method is a modification of the facies-based inversion system of Gunning and Sams (2018). The model is represented in Depth, so no lossy Time to Depth conversion model remapping is required. The Depth model representation has the considerable benefit of allowing regular or irregular gridding, e.g. corner point grids, with stratigraphic alignment in Depth, which marries well with the discrete facies model.
