Simultaneous AVO Inversion for Accurate Prediction of Rock Properties
Authors: Maver Kim Gunn , Rasmussen Klaus Bolding 
Published: October 2008

Abstract
The usefulness of seismic AVO attributes increased dramatically when elastic inversion of partial stacks was introduced. Utilizing the mathematical concept of elastic impedance the technology from the inversion of full stack data for acoustic impedance could be transferred to partial stacks. Each partial stack was inverted for elastic impedance and the elastic impedance results were combined to estimates of physical properties like acoustic impedance, shear impedance and Vp/Vs. This type of AVO inversion has, however, some serious drawbacks that recent developments in simultaneous inversion have overcome. This new simultaneous inversion method is based on global optimization and includes features for working with partial offset stacks and calculation of the high frequency variation of the angle of incidence as part of the inversion. The method is implemented such that the same numerical kernel is used for inversion in different physical domains and of different data types including AVO surface seismic, PS data and time-lapse data.
Applying simultaneous seismic inversion it is possible in general to estimate shear impedance, Vp/Vs or Poisson's ratio with the same resolution as the acoustic impedance even though these properties are mainly related to the far stack seismic data with lower resolution. Furthermore very reliable density estimates can be derived from the seismic data, which have proven very useful in prediction of certain lithologies and saturations.

Elastic inversion
The introduction of the elastic impedance concept in the late 1990's [Connolly, 1999] was a significant improvement in theuse of seismic AVO attributes and increased the accuracy of lithology, fluid and porosity prediction in oil exploration and reservoir characterization. In the implementation of elastic inversion, however, severe assumptions were made, such as a constant average Poisson's ratio. Elastic impedance is furthermore an angle dependent quantity so often several elastic impedances from several partial stacks are combined into estimates of angle independent quantities such as acoustic impedance, shear impedance, VP/VS and gradient impedance. The calculated angle independent quantities, however, give synthetic seismic for each partial stack that has a poorer match (greater misfit) to the seismic data compared to the synthetic seismic direct from the elastic inversions, i.e. the information from the seismic data has not been fully utilized in the calculation of the angle independent quantities, a fact almost never displayed or quantified although it is a very important issue.
Another issue is the frequency content of the partial stacks that go into the elastic inversions, where the far offset data will contain lower frequencies due to attenuation and NMO stretch. The problem arises when the elastic impedances are combined into angle independent quantities. Combining data with different frequency content gives noise on the estimates of the angle independent quantities. Therefore frequency balancing must, in many cases, be performed on the seismic data, limiting the resolution on the results.

Simultaneous inversion
In simultaneous inversion all the seismic data are simultaneously inverted for angle independent quantities [Ma, 2002]. See Figure 1 for a drawing of the data flow in elastic and simultaneous inversion.