Ikon Science promote inversion as a tool and not an end in itself. It can be used to good effect in reservoir characterisation from exploration to reservoir monitoring. A selection of inversion algorithms exist, in house we refer to this as the inversion menu. Further information on inversion algorithms can be read in the Kemper paper on the subject. This paper also explains the importance of constructing a quality Low Frequency Background Model, should an absolute impedence result be required.
This technique introduced by Lancaster and Whitcombe in 2000 makes and applies a matching filter to map the seismic spectrum onto a more broadband 'earth spectrum' as defined from well impedance profiles. This explains the spectral blueing characteristics of this process. No wavelet is required, and the inversion is band-limited, so a spectral merge with a low frequency background model may be carried out, as required.

Lancaster, S. and Whitcombe, D. [2000] Fast-track ‘coloured’ inv.
70th SEG annual meeting, expanded abstracts 1572-1575
This essentially is spectral decomposition in the impedance domain. After a spectral decomposition into bandlets, each one is inverted to 'implets', which are then recombined to provide the spectral impedance result. No wavelet is required, and the inversion is band-limited, so a spectral merge with a low frequency background model may be carried out, as required.

Figure from RokDoc
Interactive and integrated in a geological model, the stochastic inversion creates high resolution models of impedance, incorporating reservoir heterogeneities and geological trends by using geostatistical techniques honouring both well and seismic data. Consider using stochastic inversion when you want fine detail and a measure of uncertainty in that detail. Our stochastic inversion implementation is extremely interactive; many parameters can be tested and inversions can be adjusted to provide the best possible results.
Using cloud transform, a rock physics model that describes the statistical relationship between two or three impedances from log data, the stochastic inversion algorithm can be employed to provide pairswise/triplet-wise impedance realizations, so essentially an AVO stochastic inversion.
The multiple realization can be analyzed in many ways to provide the user with statistical descriptions of the reservoir, such as a PDF of volumes of hydrocarbon bearing reservoir to be expected at a to-be-drilled well location, or a P10,P50,P90 description of the NtG of a field.
Haas, A. and Dubrule, O. [1994]
Geostatical inversion - a sequential method of stochastic reservoir modeling constrained by seismic data.
First Break , 12 (11), 561-569.
Delivery is an open source Bayesian Inversion program. It is considered state-of-the-art in the industry, and is virtually impossible to use as is. That's why in RokDoc we have developed a highly interactive wrapper to this tool, that exposes all its power to the user. The user has to specify all information that goes into calculating amplitudes in the form of a normal distribution, so per trace: top, base, NtG, Por, Satn, Vp, Vs, Rho etc. This information together with the seismic to be inverted is used to create a likelyhood function, from which the posterior distribution is calculated (using MCMC techniques). The posterior distribution can be analysed in any way conceivable. Delivery is the only inversion tool in the market place that can invert for the position of top and base of a layer, i.e. for its thickness. Very relevant to determine in-place volumes in a flat structure: the depth of the OWC is then crucial.
Gunning, J. & Glinsky, M.E. [2004]
Delivery: an open–source model–based Bayesian seismic inversion program. Computers & Geosciences,
30, 619−636.
We have state of the art inversion technologies for 4D inversion, be it Neural Net or Rock Physics Model Template driven. More info in our reservoir monitoring page.